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1
Giraldo-Londoño, Oliver, and Glaucio H. Paulino. "A unified approach for topology optimization with local stress constraints considering various failure criteria: von Mises, Drucker–Prager, Tresca, Mohr–Coulomb, Bresler– Pister and Willam–Warnke." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 476, no. 2238 (2020): 20190861. http://dx.doi.org/10.1098/rspa.2019.0861.
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An interesting, yet challenging problem in topology optimization consists of finding the lightest structure that is able to withstand a given set of applied loads without experiencing local material failure. Most studies consider material failure via the von Mises criterion, which is designed for ductile materials. To extend the range of applications to structures made of a variety of different materials, we introduce a unified yield function that is able to represent several classical failure criteria including von Mises, Drucker–Prager, Tresca, Mohr–Coulomb, Bresler–Pister and Willam–Warnke, and use it to solve topology optimization problems with local stress constraints. The unified yield function not only represents the classical criteria, but also provides a smooth representation of the Tresca and the Mohr–Coulomb criteria—an attribute that is desired when using gradient-based optimization algorithms. The present framework has been built so that it can be extended to failure criteria other than the ones addressed in this investigation. We present numerical examples to illustrate how the unified yield function can be used to obtain different designs, under prescribed loading or design-dependent loading (e.g. self-weight), depending on the chosen failure criterion.
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Zhang, Tan, Song-Tao Lin, Hong Zheng, and Yan-Jiang Chen. "Elastoplastic Integration Method of Mohr-Coulomb Criterion." Geotechnics 2, no. 3 (2022): 599–614. http://dx.doi.org/10.3390/geotechnics2030029.
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A new method for implicit integration of the Mohr-Coulomb non-smooth multisurface plasticity models is presented, and Koiter’s requirements are incorporated exactly within the proposed algorithm. Algorithmic and numerical complexities are identified and introduced by the nonsmooth intersections of the Mohr-Coulomb surfaces; then, a projection contraction algorithm is applied to solve the classical Kuhn–Tucker complementary equations which provide the only characterization of possible active yield surfaces as a special class of variational inequalities, and the actual active yield surface is further determined by iteration. The basic idea is to calculate derivatives of the yield and potential functions with the expressions in the principal stresses and perform the return manipulations in the general stress space. Based on the principal stress characteristic equation, partial derivatives of principal stresses are calculated. The proposed algorithm eliminates the error caused by smoothing the corner of Mohr-Coulomb surfaces, avoids the numerical singularity at the intersections in the general stress space, and does not require the stress transformation needed in the principal stress space method. Lastly, several numerical examples are given to verify the validity of the proposed method.
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Seta, E., T. Kamegawa, and Y. Nakajima. "Prediction of Snow/Tire Interaction Using Explicit FEM and FVM." Tire Science and Technology 31, no. 3 (2003): 173–88. http://dx.doi.org/10.2346/1.2135267.
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Abstract A three-dimensional prediction model has been developed in which the interaction between snow and a rolling tire with tread pattern is considered. An explicit finite element method (FEM) and a finite volume method (FVM) are used to model tire and snow respectively. Snow deformation is calculated by the Eulerian formulation to solve the complex interaction between snow and tire tread pattern. Coupling between a tire and snow is automatically computed by the coupling element. Numerical modeling of snow is essential to the tire performance prediction on snow. In this study, snow is assumed to be homogeneous and considered to be an elasto-plastic material. The Mohr-Coulomb yield model, in which the yield stress is a single function of pressure, is adopted. This function is investigated by tire traction tests under a wide range of tire contact pressures using several tires with different inflation pressures and patterns. The predicted results using the Mohr-Coulomb yield model are compared with those using the Capped Drucker-Pragger and the Cam-Clay yield models. Snow traction of a tire featuring different tread patterns is simulated by this technology. Results are shown to be in good qualitative agreement with experimental data.
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Sloan, S. W., and J. R. Booker. "Removal of singularities in tresca and mohr-coulomb yield functions." Communications in Applied Numerical Methods 2, no. 2 (1986): 173–79. http://dx.doi.org/10.1002/cnm.1630020208.
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Linnik, E. Yu. "EVALUATING CONTACT STRESSES IN AN IMPACTOR PENETRATING A HARD SOIL." Problems of strenght and plasticity 82, no. 1 (2020): 52–63. http://dx.doi.org/10.32326/1814-9146-2020-82-1-52-63.
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Finite formulas have been derived for evaluating contact stresses in a rigid impactor penetrating a soil, taking into account the friction in the framework of the local interaction model. In analyzing dynamic deformation of the soil, its volumetric compressibility, shear resistance and initial strength are accounted for. The obtained evaluations of resistance to penetration of an impactor into the soil are based on a quadratic relation between the stress normal to the impactor surface and impact velocity. The authors have pioneered in deriving finite expressions for coefficients of a trinomial approximation as a function of experimentally determined physical-mechanical parameters of the soil - a dynamic compressibility diagram (a shock adiabat) and a yield strength - pressure diagram. Impact compressibility of soils is described based on Hugoniot's adiabat - a linear relation between shock wave velocity and mass velocity of the medium particles behind the shockwave front. Plastic deformation obeys the Mohr - Coulomb yield criterion with a constraint on the limiting value of maximal tangential stresses according to Tresca's criterion - the Mohr - Coulomb - Tresca plasticity condition. An earlier obtained analytical solution of a one-dimensional problem of a spherical cavity expanding at a constant velocity from a point in a half-space occupied by a plastic soil medium is used. A formula for determining critical pressure (a minimal pressure required for the formation of a cavity, accounting for internal pressure in the framework of Mohr - Coulomb's yield criterion) is also used, which generalizes a known solution for an elastic ideally plastic medium with Tresca's criterion. The derived formulas have been verified by comparing their results with the available data from experiments on the penetration of a steel conical impactor into a frozen sandy soil. It is shown that the disagreement between the numerical and experimental results is within 10%.
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Zhan, Tao, Tengfei Jiang, Shengbiao Shan, Fu Zheng, Annan Jiang, and Xinping Guo. "Research on Constitutive Model and Algorithm of High-Temperature-Load Coupling Damage Based on the Zienkiewicz–Pande Yield Criterion." Applied Sciences 13, no. 17 (2023): 9786. http://dx.doi.org/10.3390/app13179786.
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The mechanical properties of rock can be weakened under the influence of high temperatures. To describe the mechanical behavior of rock under the action of high temperature more accurately, based on the Zienkiewicz–Pande yield criterion, the damage variable Dc which accounts for the coupling between high temperature and load is introduced. According to plastic potential theory and plastic flow law, the iterative incremental method for a high-temperature and load-coupled damage constitutive model in Flac3D is deduced in detail and compiled into the corresponding dynamic link library file (.dll file). By modifying the shape function to degenerate into the Mohr–Coulomb constitutive model, an elastic–plastic analysis of an ideal circular tunnel is performed, and a comparison is made between calculation results obtained from the built-in Mohr–Coulomb constitutive model in Flac3D, proving the correctness of the secondary development program. Finally, numerical simulations are conducted to study the effects of high-temperature damage using rock uniaxial compression tests, and the model’s validity is established by comparing it with previous experimental results.
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Chakraborty, Manash, and Jyant Kumar. "Lower Bound Axisymmetric Limit Analysis Using Drucker–Prager Yield Cone and Simulation with Mohr–Coulomb Pyramid." International Journal of Computational Methods 12, no. 05 (2015): 1550023. http://dx.doi.org/10.1142/s0219876215500231.
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This paper presents a lower bound limit analysis approach for solving an axisymmetric stability problem by using the Drucker–Prager (D–P) yield cone in conjunction with finite elements and nonlinear optimization. In principal stress space, the tip of the yield cone has been smoothened by applying the hyperbolic approximation. The nonlinear optimization has been performed by employing an interior point method based on the logarithmic barrier function. A new proposal has also been given to simulate the D–P yield cone with the Mohr–Coulomb hexagonal yield pyramid. For the sake of illustration, bearing capacity factors Nc, Nq and Nγ have been computed, as a function of ϕ, both for smooth and rough circular foundations. The results obtained from the analysis compare quite well with the solutions reported from literature.
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Zhao, Jun-hai, Yue Zhai, Lin Ji, and Xue-ying Wei. "Unified Solutions to the Limit Load of Thick-Walled Vessels." Journal of Pressure Vessel Technology 129, no. 4 (2006): 670–75. http://dx.doi.org/10.1115/1.2767356.
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Unified solutions to the elastoplastic limit load of thick-walled cylindrical and spherical vessels under internal pressure are obtained in terms of the unified strength theory (UST) and the unified slip-line field theory (USLFT). The UST and the USLFT include or approximate an existing strength criterion or slip-line field theory by adopting a parameter b, which varies from 0 to 1. The theories can be used on pressure-sensitive materials, which have the strength difference (SD) effect. The solutions, based on the Tresca criterion, the von Mises criterion, the Mohr–Coulomb criterion, and the twin shear strength criterion, are special cases of the present unified solutions. The results based on the Mohr–Coulomb criterion (b=0) give the lower bound of the plastic limit load, while those according to the twin shear strength criterion (b=1) are the upper bound. The solution of the von Mises criterion is approximated by the linear function of the UST with a specific parameter (b≈0.5). Plastic limit solutions with respect to different yield criteria are illustrated and compared. The influences of the yield criterion as well as the ratio of the tensile strength to the compressive strength on the plastic limit loads are discussed.
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Ruggiero, Andrew, Gianluca Iannitti, Stefano Masaggia, and Federico Vettore. "ADI 1050-6 Mechanical Behavior at Different Strain Rates and Temperatures." Materials Science Forum 925 (June 2018): 196–202. http://dx.doi.org/10.4028/www.scientific.net/msf.925.196.
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An experimental characterization of the austempered ductile iron ISO 17804/JS/1050-6/S was performed carrying out tensile tests under different strain rates, temperatures and stress triaxiality levels. Then, composing a yield function surface, a hardening relation, and a damage criterion, a constitutive model was developed to describe the salient features of the observed macroscopic response. In particular, the Mohr-Coulomb yield function was selected to account for the pressure effect observed on the yield surface. A new hardening relation was proposed in order to account for both strain rate and temperature effects. The Bonora’s damage model, developed in the framework of the continuum damage mechanics, was adopted to capture the failure condition under different stress triaxiality levels. The damage model was appropriately modified to account for the effect of strain rate and temperature on the failure strain.
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Liu, Yuhang, Ruiqiang Bai, and Dongqing Li. "Study on the Strength and Yield Behaviors of Modified Silty Clay." Geofluids 2022 (July 16, 2022): 1–17. http://dx.doi.org/10.1155/2022/6337345.
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To study the strength and yield behaviors of the modified soil, a series of triaxial compression tests were carried out for modified silty clay with different contents of red Pisha sandstone and carbide slag, respectively. The test results showed that the strength variation of the modified soils are obviously nonlinear with the hydrostatic pressure increasing, and the nonlinear strength can be described by a modified critical state function. Then, the friction angle and the cohesive force of the modified soils were obtained according to the nonlinear Mohr-Coulomb equation, and the relationships between the friction angle, the cohesive force, and the hydrostatic pressure were studied. Finally, the yield behavior of the modified soil was investigated based on a generally criterion, and the yield surface of the modified soils locates between the SMP criterion and the Lade-Duncan criterion. This study will help to understand the strength and yield characteristics of modified soils.
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Hu, Chao, Fei Ye, Wenxi Fu, and Zhuo Chen. "A Return Mapping Algorithm for Nonlinear Yield Criteria with the Equivalent Mohr–Coulomb Strength Parameters." Advances in Civil Engineering 2020 (November 24, 2020): 1–8. http://dx.doi.org/10.1155/2020/8823988.
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This paper proposes a modified return mapping algorithm for a series of nonlinear yield criteria. The algorithm is established in the principal stress space and ignores the effect of the intermediate principal stress. Three stress return schemes are derived in this paper: return to the yield surface, return to the curve, and return to the apex point. The conditions used for determining the correct stress return type are also constructed. After the proposed algorithm is programmed in the finite element software, we merely need the equivalent Mohr–Coulomb (M-C) strength parameters, the derivatives of their functions, and the tensile strength of these nonlinear yield criteria. In addition, the Hoek–Brown (H-B) yield criterion is taken as an example to validate the proposed method. The results show that the updated stresses and the final principal stresses obtained by the proposed method are in good agreement with those obtained by other methods. Furthermore, the proposed method is more suitable for the associated plastic-flow rule.
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Mishchuk, Yevhen. "Analysis of common geological models of materials." Gіrnichі, budіvelnі, dorozhnі ta melіorativnі mashini, no. 104 (December 19, 2024): 5–14. https://doi.org/10.32347/gbdmm.2024.104.0101.
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The paper analyzes the physical models used in the study of the stressed state of geological rocks. Common physics models include: 1) soil and foam; 2) pseudo-tensor; 3) geological; 4) Schwer-Murray; 5) continuous surface of the cap; 6) Mohr-Coulomb; 6) connected stone. A graphical representation of the description of the soil and foam model is given. At the initial stages of loading with small deformations, the model behaves linearly elastically. When the level of deformations increases, it turns into a non-linear model. The graphical presentation of the pseudo-tensor model reflects two modes of operation of the model depending on the physical properties of the material. The geological model is one of the subspecies of the geological cap model and is used in solving geo-mechanical problems, as well as in modeling such materials as concrete. The graphic representation of the geological model is described by three curves, the functions of which are given in the paper. The Schwer-Murray model is an extended version of the geological model that includes viscoplasticity to calculate velocity effects and damage mechanics. The prize is designed for the study of such materials as soils, concrete and rocks. An improved Schwer-Murray model is the continuous cap surface model (CSCM), the yield surface of which is defined by three stress invariants. The Coulomb-Mohr model is intended for the study of solid elements, thick shells and SPH particles. It is used to represent cohesive or non-cohesive rocks, soils, clastic cemented rocks, sandy soils, and other granular materials. The joint stone model is analogous to the Drucker-Prager and Coulomb-Mohr models. The oriented crack model is used to model brittle materials (ceramics) or porous materials, such as concrete, which undergo failure due to high tensile loads. Basically, it can be an isotropic elastoplastic or elastic material with an oriented crack.
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Ip, Bill, W. D. Hibler, and Greg Flato. "The Effect Of Rheology On Seasonal Sea-Ice Simulations." Annals of Glaciology 14 (1990): 340. http://dx.doi.org/10.3189/s0260305500009046.
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On the seasonal time scales relevant to numerical investigations of climate, the rheology used in large-scale sea ice models significantly affects the ice thickness build-up and ice velocity fields. Plastic rheologies with a normal flow rule have been used to-date in seasonal dynamic thermodynamic simulations. These rheologies have proved useful in simulating discontinuous slip near the coast while still supplying relatively robust velocity fields in the central Arctic Basin. However, as indicated by limited numerical sensitivity studies with different types of elliptical yield curves, the amount of shear strength significantly affects the ice build-up and can possibly cause a stoppage of the ice outflow through Fram Strait. In addition to the shear strength issue, there is also the possibility that non-normal flow rule rheologies, such as the Mohr Coulomb failure criterion used in soil mechanics, may cause somewhat different types of flow patterns, especially in the Fram Strait region. However, to date no seasonal simulations with such non-normal flow rule rheologies have been carried out.In order to investigate the role of different rheologies on the large-scale flow patterns in the Arctic Basin, a more general numerical scheme than that of Hibler (1979) is developed, which allows the simulation of the dynamic thermodynamic behavior of sea ice with a wide variety of different non linear rheologies. Using this numerical scheme, comparative simulations are carried out to seasonal equilibrium with several variations of the Mohr Coulomb rheology and compared to the more standard Elliptical yield curve results. In particular, the main control Mohr Coulomb case is a capped rheology in which the shear strength is taken to be proportional to the compressive stress. In this capped case only shear flow is allowed until a maximum allowable compressive stress is reached. This cap strength is parameterized to be a function of the ice thickness and compactness. For comparison, a simulation with a very large cap strength is also carried out, and an experiment with a similar compressive cap but much lower shear strength. Overall the results are analyzed to determine the sensitivity of the ice build-up to flow rule and shear strength magnitude. In addition special attention is given to the character of the flow and stoppage (if any) through Fram Strait.
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Ip, Bill, W. D. Hibler, and Greg Flato. "The Effect Of Rheology On Seasonal Sea-Ice Simulations." Annals of Glaciology 14 (1990): 340. http://dx.doi.org/10.1017/s0260305500009046.
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On the seasonal time scales relevant to numerical investigations of climate, the rheology used in large-scale sea ice models significantly affects the ice thickness build-up and ice velocity fields. Plastic rheologies with a normal flow rule have been used to-date in seasonal dynamic thermodynamic simulations. These rheologies have proved useful in simulating discontinuous slip near the coast while still supplying relatively robust velocity fields in the central Arctic Basin. However, as indicated by limited numerical sensitivity studies with different types of elliptical yield curves, the amount of shear strength significantly affects the ice build-up and can possibly cause a stoppage of the ice outflow through Fram Strait. In addition to the shear strength issue, there is also the possibility that non-normal flow rule rheologies, such as the Mohr Coulomb failure criterion used in soil mechanics, may cause somewhat different types of flow patterns, especially in the Fram Strait region. However, to date no seasonal simulations with such non-normal flow rule rheologies have been carried out. In order to investigate the role of different rheologies on the large-scale flow patterns in the Arctic Basin, a more general numerical scheme than that of Hibler (1979) is developed, which allows the simulation of the dynamic thermodynamic behavior of sea ice with a wide variety of different non linear rheologies. Using this numerical scheme, comparative simulations are carried out to seasonal equilibrium with several variations of the Mohr Coulomb rheology and compared to the more standard Elliptical yield curve results. In particular, the main control Mohr Coulomb case is a capped rheology in which the shear strength is taken to be proportional to the compressive stress. In this capped case only shear flow is allowed until a maximum allowable compressive stress is reached. This cap strength is parameterized to be a function of the ice thickness and compactness. For comparison, a simulation with a very large cap strength is also carried out, and an experiment with a similar compressive cap but much lower shear strength. Overall the results are analyzed to determine the sensitivity of the ice build-up to flow rule and shear strength magnitude. In addition special attention is given to the character of the flow and stoppage (if any) through Fram Strait.
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Li, Ze, and Zhi Lin Liang. "Research of Lower Bound Method for Wedge Slope Subjected to Pore Water Pressure and Earthquake Force." Applied Mechanics and Materials 444-445 (October 2013): 951–55. http://dx.doi.org/10.4028/www.scientific.net/amm.444-445.951.
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Based on the lower bound theory for the plastic limit analysis, rock slope is divided into rigid block and structural surface. And the mathematical programming model which takes the safety factor as the objective function is established for the calculation of slope stability. This model has to meet the balance equations of the blocks, the Mohr-Coulomb yield conditions and the boundary conditions of slope. In the end, a classic model of rock slope on consideration of the pore water pressure and earthquake force is analyzed, and its lower bound solution is worked out. This result is compared to the result worked out by limiting equilibrium to test the validity and correctness of the method and procedure used in this paper.
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Ai, Ting, Ru Zhang, Li Ren, and Wen Xi Fu. "Non-Linear Hoek-Brown Shear Strength Reduction Technique Considering the Effect of Dilation." Advanced Materials Research 446-449 (January 2012): 1524–30. http://dx.doi.org/10.4028/www.scientific.net/amr.446-449.1524.
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In order to implement the non-linear Hoek-Brown (HB) shear strength reduction (SSR) on commercially available softwares, this paper derives the relationship between the Drucker-prager (DP) criterion and HB criterion under the condition of plane strain. The equivalent DP parameters can be approximately estimated after serious transformations of parameters between the HB and Mohr-Coulomb (MC) yield functions. To assess the effect of dilation on the stability of slope, the non-associated flow rule, which cannot be contained in the existing limit equilibrium methods, is selected in our analysis, and the SSR-based results of a simple slope indicate that: If the angle of dilatancy ψ is taken to be zero, the factor of safety calculated by the SSR method is very close to that by the limit equilibrium method; if ψ is greater than zero, the factor of safety calculated by the SSR method is greater than that by the limit equilibrium method, and the effect of dilation on the stability of slope can be approximately described by a liner function.
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Li, Dongwei, Junhao Chen, and Yan Zhou. "A Study of Coupled Creep Damaged Constitutive Model of Artificial Frozen Soil." Advances in Materials Science and Engineering 2018 (June 25, 2018): 1–9. http://dx.doi.org/10.1155/2018/7458696.
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Artificial frozen soil is a kind of typical creep material, and the frozen clay under the unloading stress paths of high-confining pressure conforms to the improved the Zienkiewicz–Pande parabola-type yield criterion, and the Mohr–Coulomb yield function can describe the shear yield surface of artificial frozen clay under low-confining pressure. Based on the results of triaxial creep and shear tests for artificial frozen soil, the viscoplastic damage variable and evolution rule of artificial frozen clay were obtained by using the theory of viscoelastic-plastic mechanics and damage mechanics. An improved Zienkiewicz–Pande parabola-type yield criterion was used instead of a linear Newton body to obtain a coupled constitutive model of viscoelastic-plastic damage in the frozen soil under the unloading stress paths and to derive the coupling flexibility matrix for viscoelastic and viscoplastic damage. A finite element program of artificial frozen soil considering creep damage was written in the Visual Fortran 6.6A environment and embedded into the nonlinear finite element software ADINA as a user subroutine. The results of numerical simulation and laboratory testing were identical, with a maximum error of no more than 4.8%. This work shows that it is reasonable to describe the creep constitutive model of frozen soil with the viscoelastic-plastic-coupled constitutive model.
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Umeda, Tsutomu, and Koji Mimura. "Numerical Analysis of the Impact Fracture of Metallic Glass Based on Free Volume Model." Key Engineering Materials 794 (February 2019): 188–93. http://dx.doi.org/10.4028/www.scientific.net/kem.794.188.
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The yield behavior of amorphous metals including the metallic glass shows intrinsic dependence on the hydrostatic stress, so that yield criterion models such as Mohr-Coulomb and Drucker-Prager are often used. Both the models can explain the asymmetry in the yield stress under uniaxial compression and tension conditions, while the asymmetry in the angle of fracture surface is not able to be determined based on any of those models. The free volume model is able to provide that foundation. Shibutani et al. proposed a new constitutive model for amorphous metals that was derived from some free volume models and the flow rule using the Drucker-Prager yield function as a plastic potential, and investigated the yield behavior and the formation of localized shear band under some temperature conditions using the implicit static FEM code. The formation of shear bands is an unstable phenomenon that is greatly affected by the initial imperfection. In this model, on the other hand, the temperature or the strain rate also affects the yield behavior considerably. In this study, the impact fracture of metallic glass was investigated by implementing the constitutive model proposed by Shibutani et al. into the explicit dynamic FEM code DYNA3D, with laying emphasis on reproducing asymmetry in the angle of fracture surface and the examination of effects of strain rate and temperature change.
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Wedage, AMP, N. R. Morgenstern, and D. H. Chan. "A strain rate dependent constitutive model for clays at residual strength." Canadian Geotechnical Journal 35, no. 2 (1998): 364–73. http://dx.doi.org/10.1139/t97-085.
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Plasticity theory is extended to incorporate strain rate effects on the residual shear strength of clays. The clay is assumed to behave elastically before yielding and then in a perfectly plastic manner with no volume change during yielding. The Mohr-Coulomb failure criterion is used in the rate-dependent model in which the strain rate affects the mobilized effective friction angle of the material. During initial yielding and subsequent plastic deformation, the stress and strain states at a point will satisfy the rate-dependent yield function (loading function). When the effective plastic strain rate decreases to a threshold strain value, the loading surface moves, or collapses, to the static yield surface. A constant volume flow rule is used to calculate plastic deformation. The computed stress-strain relationship is formulated in two parts, namely a rate-independent part and a rate-dependent part. The rate-independent part is the same as that used in classical elastoplastic formulations, whereas the rate-dependent part is dependent on the current strain rate of the material. The use of the model is illustrated using a numerical example simulating a two-dimensional plane strain test.Key words: constitutive relationship, finite element, plasticity theory, pre-sheared clay, rate effects, residual strength.
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Lester, Alexander M., and Scott W. Sloan. "A smooth hyperbolic approximation to the Generalised Classical yield function, including a true inner rounding of the Mohr-Coulomb deviatoric section." Computers and Geotechnics 104 (December 2018): 331–57. http://dx.doi.org/10.1016/j.compgeo.2017.12.002.
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Liang, Zhi Lin, and Ze Li. "Study of Lower Bound Method for Plastic Limit Analysis of Wedge on Consideration of Anchor Bolt." Applied Mechanics and Materials 444-445 (October 2013): 966–70. http://dx.doi.org/10.4028/www.scientific.net/amm.444-445.966.
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The massive rock slope is made up of rocks and structural surface. The existence and strength of the structural surface decides the stability of the rock mass. By adopting the lower bound method for the plastic limit analysis of wedge slope, we can easily calculate the stability of the rocky slope under various circumstances. To apply this method, we first took the wedge-shaped slide block as a complex of rigid block and structural surface for the analysis of the slope stress under the function of anchor bolts, the integrated function of rocks and structural surfaces being considered. Then, on the basis of the lower bound theory for the plastic limit analysis, a mathematical programming model which takes safety factor of slope stability as the object function is established. This model has to meet the equilibrium condition of the bolt, the Mohr-Coulomb yield condition and the boundary condition of slope. In the end, a classic model of wedge is analyzed and its lower bound solution is worked out. This result is compared to the result worked out by limiting equilibrium to test the validity of the measure and procedure used in this paper.
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Bolton, M. D., and C. K. Lau. "Vertical bearing capacity factors for circular and strip footings on Mohr–Coulomb soil." Canadian Geotechnical Journal 30, no. 6 (1993): 1024–33. http://dx.doi.org/10.1139/t93-099.
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The method of characteristics is used to establish consistent factors for the vertical bearing capacity of circular and strip footings on soil which satisfies a linear [Formula: see text] Mohr–Coulomb strength criterion. This method of solution avoids the assumption of arbitrary slip surfaces, and produces zones within which equilibrium and plastic yield are simultaneously satisfied for given boundary stresses. Although similar solutions have previously been published for circular footings, their application has been hindered by errors and confusions over terminology. These are resolved, and the method of solution is explained. It is confirmed that Terzaghi's approach to the superposition of bearing terms containing Nq, Nγ, and Nc is both safe and sufficiently accurate for circular footings, as for strip footings. The values to be adopted are tabulated as functions of [Formula: see text]. Differences between the factors applicable to circular and strip footings far exceed the allowances of the empirical shape factors in common use. Some new shape factors are suggested that better represent the relationship between the limiting equilibrium of circular and strip foundations. Some current shape factors attempt to allow simultaneously for the differences in equilibrium solutions and the differences in axisymmetric (triaxial) and plane strain soil parameters. This cannot succeed, since the relationship between strength parameters depends strongly on relative density. The new bearing factors facilitate a more rational approach in which soil parameters appropriate to the geometry can first be determined and then used to find appropriate bearing capacity factors. Key words : bearing capacity, axisymmetry, method of characteristics, footings, plane strain.
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Gao, Feng, and Shanqing Li. "Elastic-plastic analysis of circular tunnel based on unified strength theory and considering multiple plastic zones." Advances in Mechanical Engineering 15, no. 1 (2023): 168781322211463. http://dx.doi.org/10.1177/16878132221146392.
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Considering that the internal friction angle of the surrounding rock is not a constant but a function of the mean normal stress, and the unified strength theory (UST) is used as the plastic condition of the tunnel surrounding rock, the plastic zone of the circular tunnel surrounding rock is divided into multiple annular regions. For different plastic zones, there are different yield conditions represented by different stress functions, the elastic-plastic analysis of circular tunnels is performed by using the piecewise linearization of nonlinear yield function, stress and displacement in the elastic-plastic zone and the radius of the plastic zone are obtained by combining the equilibrium equations. It is shown that the radius of the plastic zone increases, the radial stresses in the elastic-plastic zone and the circumferential stresses in the plastic zone become smaller and the circumferential stresses in the elastic zone becomes larger compared with that of only one plastic zone. By using single factor analysis method, the calculated values of the tunnel displacements and plastic radii by UST were compared with those obtained by the Mohr-Coulomb (M-C) criterion, Drucker-Prager (D-P) criterion, and Zienkiewicz-Pande (Z-P) criterion. The analysis shows that under the same conditions, the solution of UST is smaller than M-C criterion and D-P criterion, therefore, the selection of rock strength criterion has great influence on the calculation of rock mechanics and engineering, the proper application of UST will guarantee the safety of engineering practice and have more practical value.
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Michalowski, Radoslaw L. "Failure potential of infinite slopes in bonded soils with tensile strength cut-off." Canadian Geotechnical Journal 55, no. 4 (2018): 477–85. http://dx.doi.org/10.1139/cgj-2017-0041.
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Infinite slope analyses are used in practice to assess the safety of slopes against shallow slides, with much of the soil mass moving parallel to a plane failure surface. Stability calculations typically involve the Mohr–Coulomb yield function, but the limitation on tensile strength is discussed and applied in stability considerations for bonded soils. Once the strength envelope is truncated in the tensile regime, the envelope becomes nonlinear and the normality flow rule admits deformation with large volumetric strains. For gentle slopes and in the absence of seepage, the difference in factors of safety calculated with and without tensile strength cut-off is small. However, in the presence of seepage and with increasing inclination of slopes, the difference becomes significant. As the deformation regime moves into the nonlinear portion of the yield envelope, application of the traditional definition of the factor of safety is not straightforward. If the strength envelope is truncated with a circular arc, then the envelope reduced by the factor of safety assumes an elliptical shape. The novelty in this paper is in presenting an analysis for bonded geomaterials with tensile strength cut-off, and indicating that tension cut-off can have a significant impact on the outcome of stability analysis for steep slopes subjected to seepage.
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Ma, Yaocai, Aizhong Lu, and Hui Cai. "An analytical method for determining the non-enclosed elastoplastic interface of a circular hole." Mathematics and Mechanics of Solids 25, no. 5 (2020): 1199–213. http://dx.doi.org/10.1177/1081286520909489.
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Based on the Mohr–Coulomb yield criterion, an analytical method is presented to determine the plastic zone in an infinite plate weakened by a circular hole and subjected to non-hydrostatic stresses at infinity. It is worth noting that this paper considers the more complicated case that the plastic zone cannot completely surround the hole, namely the elastoplastic interface is non-enclosed. Initially, the non-circular elastic zone in the physical plane is mapped onto the outer region of a unit circle in the image plane by the conformal transformation in the complex variable method. Thereby, determining the elastoplastic interface is equivalent to solving the mapping function coefficients. The nonlinear equations for solving the coefficients are established by considering both the stress continuity conditions along the elastoplastic interface and the stress boundary conditions along the elastic part of the hole. Naturally, the problem can be further transformed into an optimization problem, which is ultimately achieved by the differential-evolution algorithm; what is more, an analytical solution with high accuracy is obtained. Based on the programmed computing, the influences of various parameters on the shape and size of the plastic zone are given.
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Niemiec, Dominik, Roman Bulko, and Juraj Mužík. "The Meshfree Localized Petrov-Galerkin Approach in Slope Stability Analysis." Civil and Environmental Engineering 15, no. 1 (2019): 79–84. http://dx.doi.org/10.2478/cee-2019-0011.
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Abstract The article focuses on the use of the meshfree numerical method in the field of slope stability computations. There are many meshfree implementations of numerical methods. The article shows the results obtained using the meshfree localized Petrov-Galerkin method (MLPG) – localized weak-form of the equilibrium equations with an often used elastoplastic material model based on Mohr-Coulomb (MC) yield criterion. The most important aspect of MLPG is that the discretization process uses a set of nodes instead of elements. Node position within the computational domain is not restricted by any prescribed relationship. The shape functions are constructed using just the set of nodes present in the simple shaped domain of influence. The benchmark slope stability numerical model was performed using the developed meshfree computer code and compared with conventional finite element (FEM) and limit equilibrium (LEM) codes. The results showed the ability of the implemented theoretical preliminaries to solve the geotechnical stability problems.
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Park, Dae-Wook, Emmanuel Fernando, and Joe Leidy. "Evaluation of Predicted Pavement Response with Measured Tire Contact Stresses." Transportation Research Record: Journal of the Transportation Research Board 1919, no. 1 (2005): 160–70. http://dx.doi.org/10.1177/0361198105191900117.
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A uniform circular vertical contact stress is commonly assumed in representing wheel loads in pavement analysis procedures. However, experimental measurements have shown that actual loading conditions are nonuniform and depend on tire construction, tire load, and tire inflation pressure. Predicted pavement response from three-dimensional (3D) finite element (FE) and layered elastic programs were compared to establish guidelines for modeling wheel loads in current layered elastic pavement analysis programs to provide a better approximation of pavement response parameters for design and evaluation. Tire contact pressure was measured with the stress-in-motion pad. In addition, tire contact pressure measurements from a previous study conducted at the University of California at Berkeley were obtained. Available contact pressure measurements on four tires were used to predict pavement response with a 3D FE program, which permitted input of measured tire contact pressures at various tire loads and tire inflation pressures. Horizontal strain at the bottom of the asphalt layer, compressive strain at the top of the subgrade, and principal stresses at different depths were predicted. Similar predictions were generated with layered elastic theory with two different representations of contact pressure and contact area. From predicted strains, service life for a range of pavements, tire load, and tire inflation pressures were estimated with limiting strain criteria. In addition, Mohr-Coulomb (MC) yield function values were calculated from predicted principal stresses at different depths. The MC yield function values and pavement life estimates from 3D FE and layered elastic analyses were compared with established guidelines for modeling wheel loads using existing layered elastic procedures.
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Chen, Jian, Jian-Hua Yin, and C. F. Lee. "Upper bound limit analysis of slope stability using rigid finite elements and nonlinear programming." Canadian Geotechnical Journal 40, no. 4 (2003): 742–52. http://dx.doi.org/10.1139/t03-032.
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In this paper, the development and application of a new upper bound limit method for two- and three-dimensional (2D and 3D) slope stability problems is presented. Rigid finite elements are used to construct a kinematically admissible velocity field. Kinematically admissible velocity discontinuities are permitted to occur at all inter-element boundaries. The proposed method formulates the slope stability problem as an optimization problem based on the upper bound theorem. The objective function for determination of the minimum value of the factor of safety has a number of unknowns that are subject to a set of linear and nonlinear equality constraints as well as linear inequality constraints. The objective function and constrain equations are derived from an energywork balance equation, the MohrCoulomb failure (yield) criterion, an associated flow rule, and a number of boundary conditions. The objective function with constraints leads to a standard nonlinear programming problem, which can be solved by a sequential quadratic algorithm. A computer program has been developed for finding the factor of safety of a slope, which makes the present method simple to implement. Four typical 2D and 3D slope stability problems are selected from the literature and are analysed using the present method. The results of the present limit analysis are compared with those produced by other approaches reported in the literature.Key words: limit analysis, upper bound, rigid finite element, nonlinear programming, sequential quadratic algorithm, slope stability.
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Lester, Alexander M., and Scott W. Sloan. "Response to discussion on “A smooth hyperbolic approximation to the Generalised Classical yield function, including a true inner rounding of the Mohr-Coulomb deviatoric section”." Computers and Geotechnics 106 (February 2019): 350. http://dx.doi.org/10.1016/j.compgeo.2018.07.021.
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Liu, Yuanjie, Lichuan Chen, Shicong Ren, Xiujun Li, Mengjiao Liu, and Kun Long. "Statistical Damage Constitutive Model for Mudstone Based on Triaxial Compression Tests." Processes 13, no. 3 (2025): 864. https://doi.org/10.3390/pr13030864.
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For the purpose of precisely depicting the failure and deformation of mudstone at varying burial depths under engineering activities, a statistical meso-damage constitutive model of mudstone was established on the basis of continuum damage mechanics, with the adoption of the compound power function and the Mohr–Coulomb yield criterion. Through triaxial compression tests under diverse confining pressures, the validity of this constitutive model was verified, and the macroscopic effects of mudstone damage evolution induced by internal defects and alterations in meso-structures were analyzed. The results reveal that an increase in confining pressure can remarkably enhance both the peak strength and the residual strength of mudstone. The constitutive model demonstrates relatively high accuracy in predicting the stress–strain responses, as well as the residual strength of mudstone. Moreover, parameter ε0 is capable of reflecting the macroscopic deformation strength of mudstone. Specifically, the larger the value of parameter ε0 is, the greater the peak deviatoric stress of mudstone will be, accompanied by a stronger bearing capacity. Parameter m, on the other hand, governs the brittle-to-ductile transition characteristics under failure. It also demonstrates that the macroscopic brittle failure characteristics of mudstone will become more noticeable as the value of parameter m increases.
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Cox, G. M., and J. M. Hill. "The limiting ideal theory for shear-index cohesionless granular materials." ANZIAM Journal 45, no. 3 (2004): 373–92. http://dx.doi.org/10.1017/s1446181100013432.
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AbstractTo model cohesionless granular flow using continuum theory, the usual approach is to assume the cohesionless Coulomb-Mohr yield condition. However, this yield condition assumes that the angle of internal friction is constant, when according to experimental evidence for most powders the angle of internal friction is not constant along the yield locus, but decreases for decreasing normal stress component σ from a maximum value of π/2. For this reason, we consider here the more general yield function which applies for shear-index granular materials, where the angle of internal friction varies with σ. In this case, failure due to frictional slip between particles occurs when the shear and normal components of stress τ and σ satisfy the so-called Warren Spring equation (|τ|/c)n = 1 − (σ/t), where c, t and n are positive constants which are referred to as the cohesion, tensile strength and shear-index respectively, and experimental evidence indicates for many materials that the value of the shear-index n lies between 1 and 2. For many materials, the cohesion is close to zero and therefore the notion of a cohesionless shear-index granular material arises. For such materials, a continuum theory applying for shear-index cohesionless granular materials is physically plausible as a limiting ideal theory, and any analytical solutions might provide important benchmarks for numerical schemes. Here, we examine the cohesionless shearindex theory for the problem of gravity flow of granular materials through two-dimensional wedge-shaped hoppers, and we attempt to determine analytical solutions. Although some analytical solutions are found, these do not correspond to the actual hopper problem, but may serve as benchmarks for purely numerical schemes. The special analytical solutions obtained are illustrated graphically, assuming only a symmetrical stress distribution.
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Mofidi Rouchi, Javad, and Mohammad Amin Nozari. "Effect of Twin Circular Underground Voids on Bearing Capacity of Strip Foundations." European Journal of Engineering Science and Technology 6, no. 2 (2024): 1–13. http://dx.doi.org/10.33422/ejest.v6i2.1137.
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Underground voids can significantly alter the stress and strain conditions of the surrounding soil mass, consequently affecting the stability of buildings located on the surface. Numerous numerical and experimental methods have been employed to investigate the effects of voids on nearby structures. In this research, a mixed lower bound-finite element method is utilized to study the stability of strip foundations situated above twin continuous voids. The soil behavior is modeled using the Mohr-Coulomb yield function along with an associated flow rule. Three-noded triangular stress elements are used to mesh the stress field, considering stress discontinuities at the common edges of adjacent elements. The study assumes that the two voids are identical in terms of radius, distance from the footing centerline, and depth from the ground level. The primary geometrical parameters considered in the analysis are the location and radius of the voids, as well as the strength parameters of the soil. By investigating the changes in bearing capacity concerning these factors, practical charts are proposed to aid in understanding the stability of the foundation. The results of the current study reveal the existence of an unsafe zone beneath the foundations, where the impact of the twin voids on bearing capacity reduction can be significant. Understanding these effects is crucial for design and construction of structures in areas prone to underground voids and also to decide where to bore infrastructure tunnels in order to have minimum effect on stability of the above buildings.
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RAMACHANDRA MURTHY, A., G. S. PALANI, and NAGESH R. IYER. "A SIMPLE ANALYTICAL MODEL FOR EVALUATION OF PENETRATION DEPTH AND RESISTANT STRENGTH OF CONCRETE TARGETS." International Journal of Structural Stability and Dynamics 13, no. 03 (2013): 1250061. http://dx.doi.org/10.1142/s0219455412500617.
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This paper presents a simple analytical model for evaluation of penetration depth and resistant strength of concrete target. The model is based on the assumption that the deformation and failure of the projectile are negligible. Normal impact is assumed in the model. It is also assumed that the penetration is steady state within the time step, the momentum balance equation can be integrated, resulting in an explicit expression for the pressure at the target interface. The expressions for spherically symmetric cavity expansion for a material with locked hydrostatic stress and constant shear strength have been developed. The constants for failure criterion are derived based on Mohr–Coulomb and Tresca-limit yield line theories. Final depth of penetration has been derived using the results of spherically symmetric cavity expansion analysis, relating the radial stress at the cavity surface to cavity expansion velocity and Newton’s second law of motion. Target resistant strength parameter is expressed as a function of penetration depth, projectile velocity, nose performance coefficient, target density, mass of projectile, and radius of the projectile. The expressions for velocity, acceleration and displacement at any instant of time have been deduced based on total depth of penetration and target resistant strength. To validate the methodologies, numerical studies have been conducted and observed that the penetration depth and target resistant strength obtained in the present study are in good agreement with the corresponding experimental values reported in the literature. It is also observed that the time history of penetration depth and projectile velocity are in good agreement with the corresponding literature values.
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Panteghini, Andrea, and Rocco Lagioia. "DISCUSSION: A smooth hyperbolic approximation to the generalised Classical yield function, including a true inner rounding of the Mohr-Coulomb deviatoric section by Alexander M. Lester and Scott W. Sloan." Computers and Geotechnics 106 (February 2019): 347–49. http://dx.doi.org/10.1016/j.compgeo.2018.07.022.
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Mahetaji, Mohatsim, Jwngsar Brahma, and Rakesh Kumar Vij. "Multivariable Regression 3D Failure Criteria for In-Situ Rock." Earth Sciences Research Journal 27, no. 3 (2023): 273–87. http://dx.doi.org/10.15446/esrj.v27n3.105872.
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Wellbore stability problems increase with the exploration and development of oil and gas reservoirs. A new 3D non-linear failure criterion is proposed as a trigonometric function considering the intermediate principal stress (2) on the triaxial compression test data. Mohr-Coulomb and Hoek-Brown are well-known failure criteria, but they do not consider the influence of (2) on rock strength. This new criterion produces a concave surface on the principal stress space (1,2, 3) with the influence of intermediate principal stress. In this study, sensitivity analysis for the variable is also done to understand the significant influence of parameters on the accuracy of the proposed criterion. Further validation of this non-linear criterion on three principal stresses (1,2, 3) was done compared with linear regression and second-degree polynomial regression results. It has been observed that the new non-linear 3D criterion with five material parameters reveals a good fit compared to linear regression and second-degree polynomial regression, which have four and six material parameters, respectively. The new non-linear criterion was further validated by comparison with existing criteria like the Priest, Drucker-Prager, and Mogi-Coulomb. It has been observed that the new 3D non-linear criterion shows a more accurate result than these existing criteria as certain rock types exhibit coefficient of determination (DC) values near one, precisely 0.95 for inada granite, 0.94 for orikabe monzonite, and 0.91 for KTB amphibolite. In contrast, other rock types have DC values ranging from 0.7 to 0.9. The new 3D non-linear criterion also yields lower root means square error (RMSE) values than the Mogi-Coulomb criterion for seven rock types. Specifically, the RMSE values by the new criterion are as follows: KTB amphibolite - 40.03 MPa, Dunham dolomite - 15.16 MPa, Shirahama sandstone - 9.08 MPa, Manazuru andesite - 22.14 MPa, Inada granite - 35.47 MPa, and Coconino sandstone - 19.047 MPa. This new 3D criterion gave precise predictions of the failure of the formation under in-situ stresses and was further helpful for the simulation of the wellbore in the petroleum industry. The variable in the new 3D criterion should be calculated from triaxial compression test data for each formation rock before applying this criterion to the wellbore stability problem and the sand production problem.
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Aghazadeh, N., and H. Taghavifar. "Study on the Track Wheeled Vehicle Designing for Off-Road Operations on Snowy and Wet Terrains." Cercetari Agronomice in Moldova 48, no. 4 (2015): 5–12. http://dx.doi.org/10.1515/cerce-2015-0047.
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Abstract Off-road vehicle trafficking is of interesting subjects for agricultural, mining and civil engineering purposes. The traversing over snowy and wet terrain is of greater importance regarding the sinkage and terrain properties. The motion resistance, traction, sinkage, and vehicle stability are functions of wheel-terrain interactions and particularly the contact patch characteristics. As adoption of wheeled vehicles on snowy terrain is difficult, tracked wheel vehicles are of greater interest and applicability. In this paper, the designing and analysis of tracked wheel system mounted on a light weight all-terrain vehicle (ATV) is addressed. The designing considerations are based on semi-empirical models (Bekker and Mohr-Coulomb criterion) and experimentally obtained data on the snow mechanical properties for the test region. Based on the analysis, it is observed that the greatest value of total deformation for the front and rear chasses are obtained at 0.00028485 and 0.00026229 m, respectively. The von Mises yield criterion addresses that the yielding of materials starts when the second deviatoric stress invariant gets to a critical value close to failure. Furthermore, the greatest values of von Mises stress for the front and rear tracked wheel chassis are equal to 64.60 and 62.48 MPa, respectively. The similarity is that the critical point is situated at the coincidence point between the inclined and longitudinally oriented rods (joint point). It is concluded that the developed vehicle could serve as a functional vehicle to perform on different off-road operational condition particularly wet terrains.
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Sawicki, Andrzej, Marek Kulczykowski, and Robert Jankowski. "Estimation of Stresses in a Dry Sand Layer Tested on Shaking Table." Archives of Hydro-Engineering and Environmental Mechanics 59, no. 3-4 (2012): 101–12. http://dx.doi.org/10.2478/heem-2013-0002.
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Abstract Theoretical analysis of shaking table experiments, simulating earthquake response of a dry sand layer, is presented. The aim of such experiments is to study seismic-induced compaction of soil and resulting settlements. In order to determine the soil compaction, the cyclic stresses and strains should be calculated first. These stresses are caused by the cyclic horizontal acceleration at the base of soil layer, so it is important to determine the stress field as function of the base acceleration. It is particularly important for a proper interpretation of shaking table tests, where the base acceleration is controlled but the stresses are hard to measure, and they can only be deduced. Preliminary experiments have shown that small accelerations do not lead to essential settlements, whilst large accelerations cause some phenomena typical for limit states, including a visible appearance of slip lines. All these problems should be well understood for rational planning of experiments. The analysis of these problems is presented in this paper. First, some heuristic considerations about the dynamics of experimental system are presented. Then, the analysis of boundary conditions, expressed as resultants of respective stresses is shown. A particular form of boundary conditions has been chosen, which satisfies the macroscopic boundary conditions and the equilibrium equations. Then, some considerations are presented in order to obtain statically admissible stress field, which does not exceed the Coulomb-Mohr yield conditions. Such an approach leads to determination of the limit base accelerations, which do not cause the plastic state in soil. It was shown that larger accelerations lead to increase of the lateral stresses, and the respective method, which may replace complex plasticity analyses, is proposed. It is shown that it is the lateral stress coefficient K0 that controls the statically admissible stress field during the shaking table experiments.
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Sui, Chuan-Yi, Yu-Sheng Shen, Yu-Min Wen, and Bo Gao. "Application of the Modified Mohr–Coulomb Yield Criterion in Seismic Numerical Simulation of Tunnels." Shock and Vibration 2021 (November 25, 2021): 1–20. http://dx.doi.org/10.1155/2021/9968935.
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To solve the classical problem that the Mohr–Coulomb yield criterion overestimates the tensile properties of geotechnical materials, a modified Mohr–Coulomb yield criterion that includes both maximum tensile stress theory and smooth processing was established herein. The modified Mohr–Coulomb constitutive model is developed using the user-defined material subroutine (UMAT) available in finite element software ABAQUS, and the modified Mohr–Coulomb yield criterion is applied to construct a numerical simulation of a shaking table model test. Compared with the measured data from the shaking table test, the accuracies of the classical Mohr–Coulomb yield criterion and the modified Mohr–Coulomb yield criterion are assessed. Compared to the shaking table test, the classical Mohr–Coulomb model has a relatively large average error (−6.98% in peak acceleration values, −8.47% in displacement values, −23.93% in axial forces), while the modified Mohr–Coulomb model has a smaller average error (+2.71% in peak accelerations value, +3.19% in displacements value, +7.56% in axial forces). The results of numerical simulation using the modified Mohr–Coulomb yield criterion are closer to the measured data.
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Yan, Zhi Xin, Jian Duan, Ping Jiang, and Hou Yu Wang. "A Study on Constitutive Model and Parameters of Rock Slope Stability." Materials Science Forum 575-578 (April 2008): 1210–16. http://dx.doi.org/10.4028/www.scientific.net/msf.575-578.1210.
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In this paper, taking elastic and plastic characteristics of rock into account, the authors have studied the relationship between different constitutive models. By transforming material parameters merely, on the basis of Equivalent Mohr-Coulomb Yield Criterion, the researchers achieved the application of these relationship in the computer program-Ansys5.7. They also have discussed the magnitude relationship between the transformed parameters and the original ones. By analyzing the cases of rock slope with obvious sliding surface, the researchers proved that it is liable to replace Mohr-Coulomb Yield Criterion with Equivalent Mohr-Coulomb Yield Criterion. We can use Equivalent Mohr-Coulomb Yield Criterion to simulate rock material, the results are smaller and more conservative than the standard ones. Meanwhile, the authors indicate that it is beneficial to apply Equivalent Mohr-Coulomb Yield Criterion to simulate rock material in rock slope projects with obvious sliding surface which have accurate standard requirements about displacement.
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Liu, Jian Hua, and Wei Shen Zhu. "A New Elastic-Plasticity Yield Criterion for Rock and Soil." Advanced Materials Research 250-253 (May 2011): 1342–47. http://dx.doi.org/10.4028/www.scientific.net/amr.250-253.1342.
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In this present paper a new yield criterion called M-D criterion is established based on the average of Mohr-Coulomb and Drucker-Prager criterion. The new M-D criterion is integrated with a revised FLAC3D method for mechanical analysis. Comparisons between the results of M-D, Mohr-Coulomb and Drucker-Prager are made by cases study. The study shows that results of M-D criterion are basically between the results of Mohr-Coulomb and Drucker-Prager and have the feature of being medial in quantity.
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Hu, Xiao Rong, and Xiao Mei Fan. "The Triple-Shear Unified Yield Criterion and its Applications." Applied Mechanics and Materials 94-96 (September 2011): 1129–40. http://dx.doi.org/10.4028/www.scientific.net/amm.94-96.1129.
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By taking account of the functions of shear stress couples acting on the dodecahedron element, a triple-shear unified yield criterion for materials is proposed to interpret a series of criteria, especially the commonly used criteria such as the Tresca’s yield criterion, the Von Mises’s yield criterion and the Mohr-Coulomb’s failure criterion through changing its contributive coefficient of the intermediate principal shear stress couples b and the tensile to compressive yield limit ratio α . In spite of that, problems of the limit inner pressures for thin and thick-wall cylinders are analyzed and the new unified solutions are deduced under the hypothesis of the perfectly elasto-plastic materials. The classical solutions based on the Tresca’s yied criterion, the Von Mises’s yield criterion and the Mohr-Coulomb’s failure yield criterion are only the special cases of the new unified solutions. Detailed analyses show that both the contributive coefficient of the intermediate principal shear stress couples b and the tensile to compressive yield limit ratio α have influences on the limit inner pressures for thin and thick-wall cylinders
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Wang, Shui Lin, Yu Yong Jiao, Haibin Xiao, and Chun Guang Li. "Discussion on the Use of Parameters of Drucker-Prager Criterion." Key Engineering Materials 306-308 (March 2006): 1449–54. http://dx.doi.org/10.4028/www.scientific.net/kem.306-308.1449.
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There are several different yield surfaces of Drucker-Prager yield criterion which corresponds to Mohr-Coulomb yield criterion in principal stress space. The different yield surfaces are determined by parameters in Drucker-Prager criterion. The influence of the different parameters on computational results is discussed in the paper, and the use of the equivalent Drucker-Prager criterion to Mohr-Coulomb criterion is suggested when elastoplastic analysis is performed in engineering problems.
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Alexandrov, Sergei E., and Elena A. Lyamina. "A New Method of Calculating the State of Stress in Granular Materials under Plane Strain Conditions." Transportation systems and technology 3, no. 4 (2017): 89–106. http://dx.doi.org/10.17816/transsyst20173489-106.
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The system of equations comprising the Mohr-Coulomb yield condition and the stress equilibrium equations may be studied independently of the flow law. This system of equations is hyperbolic. Accordingly, to solve the aforementioned system of equations, it is reasonable to apply the method of characteristics. In the special case of plasticity theory for materials whose yield criterion does not depend on the average stress, two methods are used to construct an orthogonal net of characteristics and to determine the stress field: the R-S method and Mikhlin’s coordinate method. In the case of the Mohr-Coulomb yield condition, the angle between the characteristic directions depends on the internal friction angle. Therefore, the above-mentioned methods should be generalised in accordance with this property of characteristics. Purpose. In the case of Plasticity theory for materials whose yield strength does not depend on the average stress, to calculate the stress filed, Mikhlin’s coordinate method is widely used. The purpose of this study is to generalise this method for the equation system consisting of the Mohr-Coulomb yield criterion and the pressure equilibrium equations. Methods. The geometrical properties of the characteristics of the equations’ system consisting of the Mohr-Coulomb yield condition and the equilibrium equations are used to introduce the generalised Mikhlin coordinates. Results. It’s been pointed out that solving equation system consisting of the MohrCoulomb yield condition and equilibrium equation comes to solving equation of telegraphy and to subsequent integration. Practical Significance. The developed method of system of equations’ solution, consisting of the Mohr-Coulomb yield condition and equilibrium equation enables obtaining high precision solutions at insignificant computer time expenditures.
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Gesualdo, A., V. Minutolo, and L. Nunziante. "Failure in MohrCoulomb soil cavities." Canadian Geotechnical Journal 38, no. 6 (2001): 1314–20. http://dx.doi.org/10.1139/t01-043.
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In many cavities, resulting from both natural excavation and anthropic action, the phenomenon of the collapse of blocks from the cavity roof presents a serious safety hazard. In a previous publication the authors proposed a method to calculate the shape and dimensions of the collapsing block by means of the upper bound theorem of the plasticity theory. The soft rock material was modelled by means of the MohrCoulomb yield criterion, and the associated flow rule was considered for strain plastic velocity. The linear yield criterion was suitably regularized by means of a circle in the tensile zone. The boundary of the collapsing block is described by a paraboloid surface. An optimization procedure formulated in standard KuhnTucker form and an analytical solution were obtained. The above-mentioned algorithm has been successfully applied to common soils of southern Italy. To validate the theoretical formulation, several numerical tests are performed. These tests show an optimal agreement with the closed-form solution. Therefore the proposed modelling may be used as an efficient guideline for the cavity-strengthening design.Key words: roof stability, regularized MohrCoulomb material, limit analysis, failure mechanics.
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Crisfield, M. A. "Plasticity computations using the Mohr—Coulomb yield criterion." Engineering Computations 4, no. 4 (1987): 300–308. http://dx.doi.org/10.1108/eb023708.
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WANG, Hong-Cai, Wei-Hua ZHAO, Dong-Sheng SUN, and Bin-Bin GUO. "Mohr-Coulomb Yield Criterion in Rock Plastic Mechanics." Chinese Journal of Geophysics 55, no. 6 (2012): 733–41. http://dx.doi.org/10.1002/cjg2.1767.
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Wang, Ruofan, Feitao Zeng, and Li Li. "Applicability of Constitutive Models to Describing the Compressibility of Mining Backfill: A Comparative Study." Processes 9, no. 12 (2021): 2139. http://dx.doi.org/10.3390/pr9122139.
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The compressibility of mining backfill governs its resistance to the closure of surrounding rock mass, which should be well reflected in numerical modeling. In most numerical simulations of backfill, the Mohr–Coulomb elasto-plastic model is used, but is constantly criticized for its poor representativeness to the mechanical response of geomaterials. Finding an appropriate constitutive model to better represent the compressibility of mining backfill is critical and necessary. In this paper, Mohr–Coulomb elasto-plastic model, double-yield model, and Soft Soil model are briefly recalled. Their applicability to describing the backfill compressibility is then assessed by comparing numerical and experimental results of one-dimensional consolidation and consolidated drained triaxial compression tests made on lowly cemented backfills available in the literature. The comparisons show that the Soft Soil model can be used to properly describe the experimental results while the application of the Mohr–Coulomb model and double-yield model shows poor description on the compressibility of the backfill submitted to large and cycle loading. A further application of the Soft Soil model to the case of a backfilled stope overlying a sill mat shows stress distributions close to those obtained by applying the Mohr–Coulomb model when rock wall closure is absent. After excavating the underlying stope, rock wall closure is generated and exercises compression on the overlying backfill. Compared to the results obtained by applying the Soft Soil model, an application of the Mohr–Coulomb model tends to overestimate the stresses in the backfill when the mine depth is small and underestimate the stresses when the mine depth is large due to the poor description of fill compressibility. The Soft Soil model is recommended to describe the compressibility of uncemented or lightly cemented backfill with small cohesions under external compressions associated with rock wall closure.
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Yang, Cai, and Tu Gen Feng. "Study on the Development of Plastic Zone Based on Strain Expressed Mohr- Coulomb Yield Condition." Applied Mechanics and Materials 580-583 (July 2014): 195–200. http://dx.doi.org/10.4028/www.scientific.net/amm.580-583.195.
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At present, there is a lot of research for slope stability, the inherent reason of slope instability is geotechnical material will get plastic deformation under load. In this paper, Mohr- Coulomb yield condition is transformed strain expressed to stress expressed.Based on this, analysis the effects that geotechnical material parameters internal friction angle ,cohesion c and Poisson's ratio to Mohr- Coulomb yield condition and the development of soil plastic zone.In addition, using the strength reduction FEM simulating the change of plastic zone distribution caused by change of the geotechnical materials parameters .The results show that the internal friction angle , cohesion c are reducted, the plastic zone expand;Increasing the Poisson’s ratio , narrowing the slope’s plastic zone;Plastic zone’s different distribution is caused by different material parameters affect the yield surface.
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Navale, Avinash V., Sagar D. Turkane, Kiran B. Ladhane, Chandresh H. Solanki, and Vishwas A. Sawant. "Analysis of Pile Group in Square Arrangement Embedded in Clayey Soil." Indian Journal Of Science And Technology 17, no. 45 (2024): 4765–77. https://doi.org/10.17485/ijst/v17i45.2685.
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Objective: The purpose of this study is to simulate and compare the response of the 3 × 3 pile group, embedded in clay, subjected to static lateral load, in terms of lateral deflection when soil is represented by different elastoplastic yield criteria. The effect of geometrical and material parameters is also investigated. Methods: In the developed finite element formulation, 20 node isoparametric elements have been used to model piles and pile caps. Surrounding soil has been modeled using 8-node isoparametric elements. The code is being developed in FORTRAN 90. Findings: The parametric study revealed the impact of the constitutive model to represent soil, pile spacing, pile length, pile diameter, and soil properties on the lateral deflection of the pile group. Mohr-Coulomb criterion predicts the lowest lateral displacement and maximum bending moment. An increase in spacing-to-diameter ratio from 2 to 6 causes a decrease in pile displacement by 80.13% in Von Misses, 70.3% in Drucker-Prager outer, 76.68% in Drucker-Prager inner, and 56.62% in Mohr-Coulomb yield criteria. An increase in the elastic modulus of soil from 20000 kPa to 60000 kPa results in a reduction in lateral displacement by 43.12% and an increase in pile diameter from .6 m to 1.0 m causes a reduction in lateral displacement by 82.73% when Von Mises criterion is used. The change in length-to-diameter ratio from 10 to 25 reduces pile displacement by 23.91%. Novelty: Among the Von – Mises, Mohr-Coulomb, Drucker–Prager (outer), and Drucker–Prager (inner) criteria, the Mohr-Coulomb criterion predicts the lowest lateral response for the 3 × 3 pile group. However, as the s/D ratio increases from 2 to 6, the difference in response is minimized. A marginal difference is found at the L/D ratio of more than 15. Applications: The developed three-dimensional finite element software can be used by pile designers to predict the response of laterally loaded pile groups. Keywords: Lateral load, Pile group, Pile spacing, Von Misses criterion, Mohr-Coulomb criterion, Drucker-Prager criterion, Lateral pile deflection
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Yang, Cheng Zhong, and Wen Jie Wan. "Finite Element Analysis on High Embankment of Widened Road." Applied Mechanics and Materials 63-64 (June 2011): 770–74. http://dx.doi.org/10.4028/www.scientific.net/amm.63-64.770.
Full textAbstract:
By means of finite element method software simulation analysis, using strength reduction finite element method analyse factor of safety of embankments. Nowadays most finite element program is analyzed in the perfect elasto-plastic with the Mohr-Coulomb not equiangular hexagon circumcircle Drucker-Prager yield criterion, it have margin of error with not equiangular hexagon in π-plane, so we use Mohr-Coulomb equivalent area circle D-P yield criterion instead of it. Calculate conversion coefficient of two safety factor under different yield criterion. Using safety factor through finite element software by strength reduction multiply by conversion coefficient, get new safety factor. Through the example of high embankment of old road widened in Shanghai-Chengdu expressway Hejiaping cable section K2+ 710~890, validation of this method calculated the accuracy of the safety factor, the results show that the new factor of safety closer to the true value.