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Journal articles on the topic 'Stress invariants'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

Sadegh, A. M., and S. C. Cowin. "The Proportional Anisotropic Elastic Invariants." Journal of Applied Mechanics 58, no. 1 (March 1, 1991): 50–57. http://dx.doi.org/10.1115/1.2897178.

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There are two proportional invariants for a linear isotropic material, the hydrostatic invariant, and the deviatoric invariant. The former is proportional to the trace of the tensor and the latter is proportional to the trace of the square of the associated deviatoric tensor. The hydrostatic stress and strain and the von Mises stress and strain are directly related to the hydrostatic and deviatoric proportional invariants, respectively, for an isotropic, linear elastic material. For each anisotropic linear elastic material symmetry there are up to six proportional invariants. In this paper we illustrate the six proportional invariants of an orthotropic elastic material using the elastic constants for spruce as the numerical example. The proportional elastic invariants play a role in anisotropic linear elasticity similar to the roles played by the hydrostatic stress and strain and the von Mises stress and strain in isotropic elasticity. They are the unique parameters whose contours represent both the stress and the strain distributions. They also have potential for representing failure or fracture criteria.

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2

Schajer, G. S. "Mohr-Coulomb Failure Criterion Expressed in Terms of Stress Invariants." Journal of Applied Mechanics 65, no. 4 (December 1, 1998): 1066–68. http://dx.doi.org/10.1115/1.2791905.

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A polynomial expression for the Mohr-Coulomb criterion for failure of brittle or frictional materials in terms of stress invariants is derived. The form of the polynomial expression corresponds to the pyramidal shape of the failure surface in principal stress space. The pressure-sensitive character of the failure of a Mohr-Coulomb material is indicated by a linear influence of the first stress invariant I1 in the polynomial expression.

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3

Kuznetsov, V. V. "Thin-shell stress-strain state invariants." Strength of Materials 26, no. 8 (August 1994): 598–603. http://dx.doi.org/10.1007/bf02209434.

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4

Pejkowski, Łukasz, and Dariusz Skibicki. "Multiaxial Fatigue Life Assessment Method Based on the Mean Value of Modified Second Invariant of the Deviatoric Stress." Solid State Phenomena 224 (November 2014): 15–20. http://dx.doi.org/10.4028/www.scientific.net/ssp.224.15.

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Stress invariants approach to the multiaxial fatigue life estimation is generally based on the root mean square value of second invariant of the deviatoric stress amplitude and the value of hydrostatic stress. Such an approach omits a significant part of the information about multiaxial load history. It is particularly noticeable in case of non-proportional loadings, which lead to a reduction of fatigue life (i.e. [1–3]). In this work a new method based on the mean value of modified second invariant of the deviatoric stress has been presented.

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5

Yang, Qiang, Xin Chen, and Wei-Yuan Zhou. "Microplane-damage-based Effective Stress and Invariants." International Journal of Damage Mechanics 14, no. 2 (April 2005): 179–91. http://dx.doi.org/10.1177/1056789505048602.

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6

Murti, V., W. Zhang, and S. Valliappan. "Stress invariants in an orthotropic damage space." Engineering Fracture Mechanics 40, no. 6 (January 1991): 985–90. http://dx.doi.org/10.1016/0013-7944(91)90164-v.

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7

Iyer, Saiganesh K., and Cliff J. Lissenden. "Inelastic Anisotropy of Inconel 718: Experiments and Mathematical Representation." Journal of Engineering Materials and Technology 122, no. 3 (March 15, 2000): 321–26. http://dx.doi.org/10.1115/1.482804.

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A generalized threshold function for viscoplastic materials, which can also serve as a yield function in rate-independent plasticity, is suggested for materials that exhibit a strength differential and/or a permanent volume change. The motivation for this type of a threshold function is that experiments, at both 25 and 650°C, on the nickel-based alloy Inconel 718 indicate that higher stresses occur in compression than in tension. Similar results have been obtained for martensitic steels and other metallic alloys at 25°C. A general approach for determining the inelastic flow dependence on each of the three stress invariants (I1,J2, and J3) is to follow stress paths where only one invariant is changing. Two classical experiments that do this are hydrostatic pressure and pure torsion, however many others are possible. Unfortunately, these stress paths generally require three-dimensional stress states, which are difficult to obtain in the laboratory. Thus, for experimental expediency, tests involving axial-torsional loading of thin-walled tubes can be used to determine the significance of the first and third stress invariants, I1 and J3, respectively. [S0094-4289(00)01303-7]

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8

Haoyun, Liang. "On the stationary behaviour of the stress invariants." Mechanics Research Communications 13, no. 4 (July 1986): 203–7. http://dx.doi.org/10.1016/0093-6413(86)90020-0.

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9

ZHANG, TINGTING, XIAOSHENG GAO, BRYAN A. WEBLER, BRIAN V. COCKERAM, MATTHEW HAYDEN, and STEPHEN M. GRAHAM. "APPLICATION OF THE PLASTICITY MODELS THAT INVOLVE THREE STRESS INVARIANTS." International Journal of Applied Mechanics 04, no. 02 (June 2012): 1250021. http://dx.doi.org/10.1142/s1758825112500214.

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Increasing experimental evidence shows that the classical J2 plasticity theory may not fully describe the plastic response of many materials, including some metallic alloys. In this paper, the effect of stress state on plasticity and the general forms of the yield function and flow potential for isotropic materials are assumed to be functions of the first invariant of the stress tensor (I1) and the second and third invariants of the deviatoric stress tensor (J2 and J3). A 5083 aluminum alloy, Nitronic 40 (a stainless steel), and Zircaloy-4 (a zirconium alloy) were tested under tension, compression, torsion, combined torsion–tension and combined torsion–compression at room temperature to demonstrate the applicability of a proposed I1-J2-J3 dependent model. The I1-J2-J3 dependent plasticity model was implemented in ABAQUS via a user defined subroutine. The model parameters were determined and validated by comparing the numerically predicted and experimentally measured load versus displacement and/or torque versus twist angle curves. The results showed that the proposed model incorporating the I1-J2-J3 dependence produced output that matched experimental data more closely than the classical J2 plasticity theory for the loading conditions and materials tested.

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10

Shariff, Mohd Halim Bin Mohd, and Jose Merodio. "Residually Stressed Fiber Reinforced Solids: A Spectral Approach." Materials 13, no. 18 (September 14, 2020): 4076. http://dx.doi.org/10.3390/ma13184076.

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We use a spectral approach to model residually stressed elastic solids that can be applied to carbon fiber reinforced solids with a preferred direction; since the spectral formulation is more general than the classical-invariant formulation, it facilitates the search for an adequate constitutive equation for these solids. The constitutive equation is governed by spectral invariants, where each of them has a direct meaning, and are functions of the preferred direction, the residual stress tensor and the right stretch tensor. Invariants that have a transparent interpretation are useful in assisting the construction of a stringent experiment to seek a specific form of strain energy function. A separable nonlinear (finite strain) strain energy function containing single-variable functions is postulated and the associated infinitesimal strain energy function is straightforwardly obtained from its finite strain counterpart. We prove that only 11 invariants are independent. Some illustrative boundary value calculations are given. The proposed strain energy function can be simply transformed to admit the mechanical influence of compressed fibers to be partially or fully excluded.

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11

Zhang, Ji, Zhong Xian Zhang, and Cai Ping Huang. "Representation Based Classification of Strength Theories of Concrete." Advanced Materials Research 168-170 (December 2010): 74–77. http://dx.doi.org/10.4028/www.scientific.net/amr.168-170.74.

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This paper proposes a new classification of strength theories of concrete based on mathematical representation. First, stress invariants in strength criteria are classified according to their geometrical meanings in the stress space. Then, strength criteria of concrete are classified according to the categories of stress invariants employed in their representations and subclassified according to the nonlinear terms involved. By this formal classification, the mathematical properties of strength theories of concrete can be analyzed more clearly for constitutive formulation.

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12

Revuzhenko, A. F. "Rock failure criteria based on new stress tensor invariants." Journal of Mining Science 50, no. 3 (May 2014): 437–42. http://dx.doi.org/10.1134/s1062739114030053.

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13

Nogueira, Carnot L. "Nonlinear Elastic Effects on High-Strength Concrete Stress Invariants." Advances in Civil Engineering Materials 8, no. 3 (March 1, 2019): 20190017. http://dx.doi.org/10.1520/acem20190017.

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14

Prasad, K. Guru, and J. H. Kane. "Boundary formulations for sensitivities of three-dimensional stress invariants." Computers & Structures 43, no. 6 (June 1992): 1165–74. http://dx.doi.org/10.1016/0045-7949(92)90016-s.

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15

Loginov, Yuriy, and Yuliya Zamaraeva. "Invariant stress state parameters for forging upsetting of magnesium in the shell." Metal Working and Material Science 23, no. 1 (March 15, 2021): 79–88. http://dx.doi.org/10.17212/1994-6309-2021-23.1-79-88.

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Introduction. For pressure treatment of low-plastic metals, it is necessary to develop special techniques for increasing plasticity. In the cold state, an increase in plastic properties is possible due to an increase in the level of compressive stresses during deformation. In the processes of forging precipitation, this is achieved by using shells or clips of various types. At the same time, the configuration of the precipitation tool also matters. To create additional compressive stresses and increase the ductility of the metal, the working surface of the tool can be configured differently than with a normal free draft, where it is obviously larger than the contact surface area of the workpiece, so that metal broadening can occur. The stress state has a great influence on the plasticity of the processed material. This state is described by methods of tensor representation, but to assess the situation, it is customary to use invariants of tensors in one form or another, which eliminates the influence of coordinates on the results of the analysis. In the sections of deformable body mechanics dealing with the influence of the stress state on plasticity, the first, but sometimes other invariants of the stress tensor are used, the invariants themselves are transformed into the stress state indicator and the lode coefficient. The aim of the work: mathematical evaluation of invariant parameters of the stress state of the magnesium precipitation process at room temperature, according to the results of which it is possible to obtain a positive result in real experiments. Research methods: finite element simulation using the DEFORM software module. Results and discussion. The theoretical justification of increasing the plasticity of the magnesium billet in the process of precipitation in the cage without its compression is carried out. An increase in the stress state index modulo 2...5 times is revealed, which contributes to an increase in the plasticity of the metal. At the same time, a zone with a lode coefficient close to zero is identified. It is adjacent to the middle of the height of the workpiece at the point of contact with the cage and can be a dangerous cross-section from the position of crack formation.

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16

Li, Dong Xia, and Yan Zhi Zhu. "Analysis of the Stress Invariants Criterions for I-II Mixed Mode Crack Initiation Angles." Advanced Materials Research 97-101 (March 2010): 1194–97. http://dx.doi.org/10.4028/www.scientific.net/amr.97-101.1194.

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Crack propagation in practical engineering problems is often of mixed-mode type. The analysis of mixed-mode I–II crack initiation angles under different loading conditions is presented using stress invariants criteria. Where I1 and I2 are the first and the second stress invariants, IP-criterion postulates that crack will propagate along the direction defined by a maximum value of IP along the elastic–plastic boundary defined by von Mises. The mixed-mode I-II crack initiation angle is predicted successfully and is agree well with experimental data.

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17

Shariff, Mohd Halim Bin Mohd. "Anisotropic stress softening of residually stressed solids." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 477, no. 2252 (August 2021): 20210289. http://dx.doi.org/10.1098/rspa.2021.0289.

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Residual stress in purely elastic solids has been extensively studied in the literature. However, to the best of the author’s knowledge, the influence of residual stresses on anisotropic Mullins materials has not been studied. Hence, the aim of this paper is to propose an anisotropic phenomenological model to describe the Mullins phenomena for residually stressed elastomers; taking note that most materials are not purely elastic and some of them exhibit an anisotropic stress-softening phenomenon widely known as the Mullins effect. The anisotropic model is based on the use of direction-dependent damage parameters and a set of anisotropic spectral invariants presented recently in the literature by the author. The spectral invariants have a clear physical meaning that is useful in aiding the design of a rigorous experiment to construct a specific form of constitutive equation. Since boundary value results for residually stressed Mullins material are not found in the literature, the effect of residual stresses on the Mullins phenomena in simple tension, torsion and equibiaxial deformations is discussed in this paper.

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18

Martirosian, Marina. "Coping Behavior: Personality Invariants of Professional Stress in Legal Activity." Psychological Prospects Journal 32 (2018): 182–92. http://dx.doi.org/10.29038/2227-1376-2018-32-182-192.

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19

Zolochevskii, A. A. "Determining equations of nonlinear deformation with three stress-state invariants." Soviet Applied Mechanics 26, no. 3 (March 1990): 277–82. http://dx.doi.org/10.1007/bf00937216.

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20

Vu, Q. H., D. Halm, and Y. Nadot. "Multiaxial fatigue criterion for complex loading based on stress invariants." International Journal of Fatigue 32, no. 7 (July 2010): 1004–14. http://dx.doi.org/10.1016/j.ijfatigue.2009.11.006.

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21

Bardet, J. P. "Lode Dependences for Isotropic Pressure-Sensitive Elastoplastic Materials." Journal of Applied Mechanics 57, no. 3 (September 1, 1990): 498–506. http://dx.doi.org/10.1115/1.2897051.

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Experimental investigations indicate that the third stress invariant; Lode angle α affects significantly the behavior of pressure sensitive materials. The present communication presents a formulation to account for α in isotropic pressure-sensitive elastoplastic materials. Seven Lode dependences are reviewed. A new one, referred to as LMN, in proposed to generalize Lade and Duncan, and Matsuoka and Nakai failure surfaces. The formulation is general enough to introduce α into the isotropic elastoplastic modes which are only developed in terms of first and second-stress invariants. As an illustration, several Lode dependences are introduced into Roscoe and Burland model. The performance of the modified model is estimated by comparing experimental and analytical results in the case of true triaxial loadings on normally consolidated clay.

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22

Formanowicz, Dorota, Adam Kozak, and Piotr Formanowicz. "A Petri net based model of oxidative stress in atherosclerosis." Foundations of Computing and Decision Sciences 37, no. 2 (October 1, 2012): 59–78. http://dx.doi.org/10.2478/v10209-011-0005-x.

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Abstract. In this paper a Petri net based model of the process of oxidative stress in atherosclerosis is presented and analyzed. Model expressed in the language of Petri net theory have, on one hand, an intuitive graphical representation, and on the other hand their formal properties can be analyzed using rigorous mathematical methods. Moreover, the behavior of a net can be simulated what supports the process of model development and an interpretation of the results of the analysis. Both the analysis and the simulation can be supported by many freely available software tools. In the case of biological systems an analysis the t-invariants is especially important since they correspond to some elementary biological subprocesses. In this paper the results of such an analysis are presented. In particular, minimal t-invariants, MCT-sets and t-clusters are calculated, their biological meaning is determined and some biological conclusions are drawn.

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23

ANDREOPOULOS, YIANNIS, and ANANT HONKAN. "An experimental study of the dissipative and vortical motion in turbulent boundary layers." Journal of Fluid Mechanics 439 (July 23, 2001): 131–63. http://dx.doi.org/10.1017/s0022112001004475.

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The experimental data of Honkan & Andreopoulos (1997a) have been further analysed and some new statistical results obtained. In the present work, particular emphasis is given to the time-dependent behaviour of the kinematic shear stress, vorticity, enstrophy, dissipation rate, vorticity stretching and several of the matrix invariants of the velocity-gradient tensor, strain-rate tensor and rotation-rate tensor. The invariants are linked with terms appearing in the transport equations of enstrophy and dissipation rate. Indicative of the existence of extremely high fluctuations is that all r.m.s. values are considerably larger than the corresponding mean values. All invariants exhibit a very strong intermittent behaviour, which is characterized by large amplitude of bursts, which may be of the order of 10 times the r.m.s. values. A substantial qualitative agreement is found between the present experimentally obtained statistical properties of the invariants and those obtained from direct numerical simulation data. Patterns with high rates of turbulent kinetic energy dissipation and high enstrophy suggest the existence of strong shear layers in the near-wall region. In many instances, locally high values of the invariants are also associated with peaks in the shear stress. Conditional analysis provides some evidence of the existence of sequences of several vortices during strong vortical activities, with an average frequency of appearance four times higher than the frequency of appearance of hairpin vortices.

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24

CHACIN, JUAN M., and BRIAN J. CANTWELL. "Dynamics of a low Reynolds number turbulent boundary layer." Journal of Fluid Mechanics 404 (February 10, 2000): 87–115. http://dx.doi.org/10.1017/s002211209900720x.

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The generation of Reynolds stress, turbulent kinetic energy and dissipation in the turbulent boundary layer simulation of Spalart (1988) is studied using the invariants of the velocity gradient tensor. This technique enables the study of the whole range of scales in the flow using a single unified approach. In addition, it also provides a rational basis for relating the flow structure in physical space to an appropriate statistical measure in the space of invariants. The general characteristics of the turbulent motion are analysed using a combination of computer-based visualization of flow variables together with joint probability distributions of the invariants. The quantities studied are of direct interest in the development of turbulence models. The cubic discriminant of the velocity gradient tensor provides a useful marker for distinguishing regions of active and passive turbulence. It is found that the strongest Reynolds-stress and turbulent-kinetic-energy generating events occur where the discriminant has a rapid change of sign. Finally, the time evolution of the invariants is studied by computing along particle paths in a Lagrangian frame of reference. It is found that the invariants tend to evolve toward two distinct asymptotes in the plane of invariants. Several simplified models for the evolution of the velocity gradient tensor are described. These models compare well with several of the important features observed in the Lagrangian computation. The picture of the turbulent boundary layer which emerges is consistent with the ideas of Townsend (1956) and with the physical picture of turbulent structure set forth by Theodorsen (1955).

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25

Shariff, MHBM, Roger Bustamante, and Jose Merodio. "A nonlinear electro-elastic model with residual stresses and a preferred direction." Mathematics and Mechanics of Solids 25, no. 3 (December 23, 2019): 838–65. http://dx.doi.org/10.1177/1081286519891769.

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In this communication, a spectral model is developed for a residually stressed electro-elastic body with a preferred direction. The model uses a total energy function that depends on the right stretch tensor, the residual stress tensor, a preferred direction structural tensor and one of the electric variables. The proposed spectral invariants have a clear physical meaning; using these invariants, we prove that only [Formula: see text] of the [Formula: see text] classical invariants in the corresponding minimal integrity basis are independent. A method for exclusion or partial exclusion of compressed fibres is proposed. Some boundary value problems with cylindrical symmetry are studied. Results for the inflation of a hollow sphere, where the residual stress is assumed to depend only on the radial position, are also given. The spectral constitutive formulation is useful in a rigorous construction of a specific form of the total energy function via appropriate experiments.

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26

Funai, Takashi, Hiroyuki Kataoka, Hideo Yokota, and Taka-aki Suzuki. "Proposal and validation of polyconvex strain-energy function for biological soft tissues." Bio-Medical Materials and Engineering 32, no. 3 (May 18, 2021): 131–44. http://dx.doi.org/10.3233/bme-196015.

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BACKGROUND: Mechanical simulations for biological tissues are effective technology for development of medical equipment, because it can be used to evaluate mechanical influences on the tissues. For such simulations, mechanical properties of biological tissues are required. For most biological soft tissues, stress tends to increase monotonically as strain increases. OBJECTIVE: Proposal of a strain-energy function that can guarantee monotonically increasing trend of biological soft tissue stress-strain relationships and applicability confirmation of the proposed function for biological soft tissues. METHOD: Based on convexity of invariants, a polyconvex strain-energy function that can reproduce monotonically increasing trend was derived. In addition, to confirm its applicability, curve-fitting of the function to stress-strain relationships of several biological soft tissues was performed. RESULTS: A function depending on the first invariant alone was derived. The derived function does not provide such inappropriate negative stress in the tensile region provided by several conventional strain-energy functions. CONCLUSIONS: The derived function can reproduce the monotonically increasing trend and is proposed as an appropriate function for biological soft tissues. In addition, as is well-known for functions depending the first invariant alone, uniaxial-compression and equibiaxial-tension of several biological soft tissues can be approximated by curve-fitting to uniaxial-tension alone using the proposed function.

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27

Coppola, T., L. Cortese, and P. Folgarait. "The effect of stress invariants on ductile fracture limit in steels." Engineering Fracture Mechanics 76, no. 9 (June 2009): 1288–302. http://dx.doi.org/10.1016/j.engfracmech.2009.02.006.

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28

Voyiadjis, George Z., S. H. Hoseini, and G. H. Farrahi. "Effects of stress invariants and reverse loading on ductile fracture initiation." International Journal of Solids and Structures 49, no. 13 (June 2012): 1541–56. http://dx.doi.org/10.1016/j.ijsolstr.2012.02.030.

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29

Cao, Trong Son, Christian Bobadilla, Pierre Montmitonnet, and Pierre Olivier Bouchard. "On the Development and Identification of Phenomenological Damage Models - Application to Industrial Wire Drawing and Rolling Processes." Key Engineering Materials 554-557 (June 2013): 213–26. http://dx.doi.org/10.4028/www.scientific.net/kem.554-557.213.

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The continuum thermodynamics-based Lemaitre damage model is nowadays widely used to deal with coupled damage analyses for various mechanical applications (e.g. forming process simulations). However, such a model, which only accounts for the stress triaxiality (the ratio between the first and the second invariants of stress tensor) has been found to give incorrect results under shear dominated loading (in terms of damage location as well as risk of crack). Several recent studies have demonstrated the importance of the third stress invariant in damage prediction; the Lode angle parameter is generally used to include it. The idea is to describe completely the stress state in damage model’s formulations, which is defined by the equivalent stress, the stress triaxiality ratio and the Lode angle parameter. This later parameter has proved to have an important influence on ductile damage under low stress triaxiality. Xue’s coupled damage model accounts for the third invariant of the deviatoric stress tensor, allowing a better balance between respective effects of shear and elongation on damage. Some extensions of more physically based damage models, such as the Gurson-Tvergaard-Needleman model, have also been presented to account for this influence of the third stress invariant. In the present work, the phenomenological damage models have been implemented in Forge® Finite Element (FE) software to investigate ductile damage occurring during industrial forming processes. This paper presents the comparative study of Xue’s model and Lemaitre’s model. A complete procedure is detailed to identify the material and damage parameters from experimental mechanical tests on high carbon steel. This identification process has been carried out both for Lemaitre’s coupled damage model and Xue’s coupled damage model. Application to wire drawing followed by flat rolling shows that in such shear-inducing processes, these models predict damage at different locations, due to their different emphasis on shear with respect to elongational strain damage.

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30

Walker, David T., and Chao-Yi Chen. "Evaluation of Algebraic Stress Modeling in Free-Surface Jet Flows." Journal of Fluids Engineering 118, no. 1 (March 1, 1996): 48–54. http://dx.doi.org/10.1115/1.2817509.

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This study evaluated three algebraic stress models for predicting turbulent stresses near the free surface in a free-surface jet at nonzero Froude number, by comparing to experiments. The models examined included one with no explicit near-surface modeling, one which specified model coefficients in terms of invariants of the anisotropy tensor, and a third model which employed a surface correction with an ad-hoc damping function. Experiment showed that at low Froude number, the anisotropy near the free surface did not attain the limiting behavior characteristic of two-dimensional turbulence and the anisotropy increased with streamwise distance. At high Froude number the surface can have little effect on the anisotropy. Far from the free surface, all the models performed well. For the model with no explicit free-surface modeling, the turbulence near the free surface was predicted to be isotropic. For the “anisotropy-invariant” model, the predicted anisotropy was too small and confined to locations too near the free surface. The model with the ad-hoc damping function captured the anisotropy near the free surface best, but specification of the decay constant in the damping function is an open question.

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31

Morland, L. W. "The general viscous relation for the response of ice and its implications in the reduced model for ice-sheet flow." Journal of Glaciology 53, no. 182 (2007): 435–41. http://dx.doi.org/10.3189/002214307783258413.

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AbstractAnalyses of confined and unconfined compression combined with shear, and of biaxial stress laterally confined or unconfined, are presented for a general deviatoric viscous relation describing the response of an incompressible material. At present, numerical models for ice-sheet flow commonly adopt a very simple viscous law throughout the ice sheet, in which the deviatoric stress is coaxial with the strain rate, and the single response function depends on only one invariant, and is determined by single stress component tests which cannot verify the validity of the simplification. The analysis presented here is concerned with two-stress-component experimental configurations which could determine the general quadratic form of a viscous relation, with two response functions depending on two invariants. It is shown that the two combined compression and shear tests can also check the consistency of a viscous fluid assumption, but not so the biaxial stress tests. Each test allows a direct assessment of the significance of the quadratic term. It is then shown that a significant quadratic term changes the relative stress magnitudes in the commonly adopted reduced model for ice-sheet flow, and that the crucial simplifications are not achieved.

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32

Klipp, Cheryl. "Turbulent Friction Velocity Calculated from the Reynolds Stress Tensor." Journal of the Atmospheric Sciences 75, no. 4 (March 29, 2018): 1029–43. http://dx.doi.org/10.1175/jas-d-16-0282.1.

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Abstract To eliminate the need to correct for instrument tilt, a process that can be problematic in complex terrain, a new way to calculate the turbulent friction velocity is derived based on invariants of the Reynolds stress tensor. In utilizing Reynolds stress tensor invariants, this new method eliminates the need for tilt correction. The friction velocity is calculated without any reference to the wall normal or other terrain features making this method a candidate for future use with data from complex environments. Since this new method is derived from a different theoretical basis than the well-established methods, it is evaluated using data from flat terrain to compare the new method to the standard calculation method, treated here as a baseline truth. For neutral thermal stratification the values calculated using the new method nearly identically match the control values calculated using the standard method. Although for nonneutral stratification the values calculated using the new method do not closely match the values calculated using the standard method, the new friction velocity produces the same dimensionless shear versus dimensionless height Monin–Obukhov scaling relationship over the full range of stabilities as does the standard friction velocity.

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33

IIMORI, Masato, Yoji SHIBUTANI, Hiro TANAKA, and Yang LIU. "Shape optimization analysis of adhesive interface under multiaxial stress state using failure function with stress invariants." Transactions of the JSME (in Japanese) 85, no. 870 (2019): 18–00409. http://dx.doi.org/10.1299/transjsme.18-00409.

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34

Zubchaninov, V. G. "To the Question of Determining Laws of Communication General Mathematical Theory of Plasticity." UNIVERSITY NEWS. NORTH-CAUCASIAN REGION. NATURAL SCIENCES SERIES, no. 2 (206) (June 18, 2020): 48–52. http://dx.doi.org/10.18522/1026-2237-2020-2-48-52.

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The paper discusses the question of the reliability and applicability of the general laws of the mathematical theory of plasticity. In a new direction of the theory of plasticity (the theory of elastic-plastic deformation processes) the isotropy postulate is given, which establishes the invariance of the connection between stresses and strains. However, this invariance during orthogonal transformations of the image of the process and its vectors in the linear coordinate space can be violated due to a change in the invariants of the form of the stress-strain state. However, numerous experiments show that the influence of these invariants is weak and can be neglected. In the theory of flow, the main hypothesis is the assumption of the decomposition of total deformations into elastic and plastic parts. Such decomposition under complex loading is impossible and contradicts the concept of the complete and incomplete plastic states of the material. This article shows that the flow theory is a special case of the theory of processes. An extended version of the theory of flow is obtained, which can be used for medium-curvature deformation trajectories, and which makes it possible to use the hypothesis of decomposition of total deformations in the theory of flow.

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Yoon, Jeong Whan, Yanshan Lou, Jonghun Yoon, and Michael V. Glazoff. "Asymmetric yield function based on the stress invariants for pressure sensitive metals." International Journal of Plasticity 56 (May 2014): 184–202. http://dx.doi.org/10.1016/j.ijplas.2013.11.008.

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Ostrowska-Maciejewska, J., and D. Harris. "Three-dimensional constitutive equations for rigid/perfectly plastic granular materials." Mathematical Proceedings of the Cambridge Philosophical Society 108, no. 1 (July 1990): 153–69. http://dx.doi.org/10.1017/s0305004100069024.

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AbstractA three-dimensional constitutive equation governing the flow of an isotropic rigid/perfectly plastic granular material is presented. The equation relates the strain-rate tensor to the Cauchy stress tensor and to the co-rotational rate of the Cauchy stress. It contains scalar functions of the scalar invariants involving the stress, stress-rate and strain-rate tensors together with parameters which characterize the material. The model generalizes the double-shearing model and its relationship to existing theories is demonstrated.

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Vigdorovich, Igor, and Holger Foysi. "Simultaneous Invariants of Strain and Rotation Rate Tensors and Their Admitted Region." Advances in Mathematical Physics 2015 (2015): 1–7. http://dx.doi.org/10.1155/2015/147125.

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The purpose of this paper is to establish the admitted region for five simultaneous, functionally independent invariants of the strain rate tensorSand rotation rate tensorΩand calculate some simultaneous invariants of these tensors which are encountered in the theory of constitutive relations for turbulent flows. Such a problem, as far as we know, has not yet been considered, though it is obviously an integral part of any problem in which scalar functions of the tensorsSandΩare studied. The theory provided inside this paper is the building block for a derivation of new algebraic constitutive relations for three-dimensional turbulent flows in the form of expansions of the Reynolds-stress tensor in a tensorial basis formed by the tensorsSandΩ, in which the scalar coefficients depend on simultaneous invariants of these tensors.

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38

Kremer, J. M., A. A. Shabana, and G. E. O. Widera. "Application of Composite Plate Theory and the Finite Element Method to the Dynamics and Stress Analysis of Spatial Flexible Mechanical Systems." Journal of Mechanical Design 116, no. 3 (September 1, 1994): 952–60. http://dx.doi.org/10.1115/1.2919475.

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This investigation concerns itself with the dynamic and stress analysis of thin, laminated composite plates consisting of layers of orthotropic laminae. It is assumed that the bonds between the laminae are infinitesimally thin and shear nondeformable. The finite element formulation presented is sufficiently general to accept an arbitrary number of layers and an arbitrary number of orthotropic material property sets. In the dynamic formulation presented, the laminae is assumed to undergo large arbitrary rigid body displacements and small elastic deformations. The nodal shape functions of the laminae are assumed to have rigid body modes that need to describe only large rigid body translations. Using the expressions for the kinetic and strain energies, the lamina mass and stiffness matrices are identified. The nonlinear mass matrix of the lamina is expressed in terms of a set of invariants that depend on the assumed displacement field. By summing the laminae kinetic and strain energies, the body mass and stiffness matrices are identified. It is shown that the body invariants can be expressed explicitly in terms of the invariants of its laminae. Numerical examples of a spatial RSSR mechanism are presented in order to demonstrate the use of the present formulation.

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Akhmedov, E. T. "Curved space equilibration versus flat space thermalization: A short review." Modern Physics Letters A 36, no. 20 (June 28, 2021): 2130020. http://dx.doi.org/10.1142/s0217732321300202.

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We discuss equilibration process in expanding Universes as compared to the thermalization process in Minkowski spacetime. The final goal is to answer the following question: Is the equilibrium reached before the rapid expansion stops and quantum effects have a negligible effect on the background geometry or stress–energy fluxes in a highly curved early Universe have strong effects on the expansion rate and the equilibrium is reached only after the drastic decrease of the spacetime curvature? We argue that consideration of more generic non-invariant states in theories with invariant actions is a necessary ingredient to understand quantum field dynamics in strongly curved backgrounds. We are talking about such states in which correlation functions are not functions of such isometry invariants as geodesic distances, while having correct UV behavior. The reason to consider such states is the presence of IR secular memory effects for generic time-dependent backgrounds, which are totally absent in equilibrium. These effects strongly affect the destiny of observables in highly curved spacetimes.

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Zharikov, I. F., V. N. Zakharov, and B. K. Norel. "Strength certificate and the constraint equation relating stress and strain invariants for inhomogeneous rocks in bulk stress state." Mechanics of Solids 50, no. 6 (November 2015): 641–49. http://dx.doi.org/10.3103/s0025654415060059.

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Orthwein, W. C. "Estimating Fatigue Due to Cyclic Multiaxial Stress." Journal of Vibration and Acoustics 109, no. 1 (January 1, 1987): 97–102. http://dx.doi.org/10.1115/1.3269403.

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A new expression similar to the Huber-von-Mises-Hencky criterion for multiaxial stresses, also known as the distortional energy theory, is derived from the second order stress invariants of the stress tensor, rather than from the deviatoric stress tensor, as in the derivation of the Huber-von Mises-Hencky criterion. It is proposed as a mutually constant design criterion for fatigue resistance under the action of multiaxial cyclic stresses which may be used with either the Gerber-yield criterion or the Goodman-yield (modified Goodman) criterion. As is shown in the following paragraphs, neither of these criteria may be used with the Huber-von Mises-Hencky criterion; it is suited only for the Soderberg criterion which does not involve the ultimate stress.

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Joseph Antony, S., and M. A. Sultan. "Invariants of stress and fabric tensors in charged granular systems subjected to shearing." Mechanics of Materials 41, no. 6 (June 2009): 742–47. http://dx.doi.org/10.1016/j.mechmat.2009.01.004.

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Longo, Sandro, Maria Clavero, Luca Chiapponi, and Miguel Losada. "Invariants of Turbulence Reynolds Stress and of Dissipation Tensors in Regular Breaking Waves." Water 9, no. 11 (November 16, 2017): 893. http://dx.doi.org/10.3390/w9110893.

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Lilley, F. E. M. "Magnetotelluric analysis using Mohr circles." GEOPHYSICS 58, no. 10 (October 1993): 1498–506. http://dx.doi.org/10.1190/1.1443364.

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The Mohr circle, most commonly met in the analysis of mechanical stress, is used to depict magnetotelluric impedance information, taking the real and quadrature parts of magnetotelluric tensors separately. The magnetotelluric concepts of two‐dimensionality, three‐dimensionality, skew and anisotropy are then all given quantitative expression on a diagram, as are various magnetotelluric invariants. In particular, a new invariant, the “central impedance,” becomes evident in a discussion of effective impedances. Some insight is gained into impedance rotations, and an anisotropy angle is defined, analogous to skew angle. Mohr circles are also tested to depict the effects of the shear and twist operations on a regionally two‐dimensional structure. Generally, the application of shear or twist results in an impedance tensor with a Mohr circle of typical three‐dimensional form.

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Alexandrov, Sergei, and Yeau-Ren Jeng. "A method of finding stress solutions for a general plastic material under plane strain and plane stress conditions." Journal of Mechanics 37 (December 18, 2020): 100–107. http://dx.doi.org/10.1093/jom/ufaa001.

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Abstract A general plastic material under plane strain and plane stress is classified by a yield criterion that depends on both the first and second invariants of the stress tensor. The yield criterion together with the stress equilibrium equations forms a statically determinate system. This system is investigated in the principal lines coordinate system (i.e. the coordinate curves of this coordinate system coincide with trajectories of the principal stress directions). It is shown that the scale factors of the principal lines coordinate system satisfy a simple equation. Using this equation, a method for constructing the principal stress trajectories is developed. Therefore, the boundary value problem of plasticity theory reduces to a purely geometric problem. It is believed that the method developed is useful for solving a wide class of boundary value problems in plasticity.

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Usal, Melek. "On Continuum Damage Modeling of Fiber Reinforced Viscoelastic Composites with Microcracks in terms of Invariants." Mathematical Problems in Engineering 2015 (2015): 1–15. http://dx.doi.org/10.1155/2015/624750.

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A continuum damage model is developed for the linear viscoelastic behavior of composites with microcracks consisting of an isotropic matrix reinforced by two arbitrarily independent and inextensible fiber families. Despite the fact that the matrix material is isotropic, the model in consideration bears the characteristic of directed media included in the transverse isotropy symmetry group solely due to its fibers distributions and the existence of microcracks. Using the basic laws of continuum damage mechanics and equations belonging to kinematics and deformation geometries of fibers, the constitutive functions have been obtained. It has been detected as a result of the thermodynamic constraints that the stress potential function is dependent on two symmetric tensors and two vectors, whereas the dissipative stress function is dependent on four symmetric tensors and two vectors. To determine arguments of the constitutive functionals, findings relating to the theory of invariants have been used as a method because of the fact that isotropy constraint is imposed on the material. As a result the linear constitutive equations of elastic stress, dissipative stress, and strain energy density release rate have been written in terms of material coordinate description. Using these expressions, total stress has been found.

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Artemov, A. M., E. S. Baranovskii, A. A. Verlin, and E. V. Syomka. "Thick-walled spherical shell problem." Advanced Engineering Research 21, no. 1 (April 4, 2021): 22–31. http://dx.doi.org/10.23947/2687-1653-2021-21-1-22-31.

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Introduction. Cylindrical and spherical shells are extensively used in engineering. They face internal and/or external pressure and heat. Stresses and strains distribution in elastoplastic shells has been studied by many scientists. Numerous works involve the use of the von Mises yield conditions, maximum shear stress, maximum reduced stress. These condi- tions do not include the dependence on the first invariant of the stress tensor and the sign of the third invariant of the stress deviator. In some cases, it is possible to obtain numerical-analytical solutions for stresses, displacements and de- formations for bodies with spherical and cylindrical symmetry under axisymmetric thermal and force action.Materials and Methods. The problem on the state of a thick-walled elastoplastic shell is solved within the framework of the theory of small deformations. A plasticity condition is proposed, which takes into account the dependence of the stress tensor on three independent invariants, and also considers the sign of the third invariant of the stress deviator and translational hardening of the material. A disconnected thermoelastoplastic problem is being solved. To estimate the stresses in the region of the elastic state of a spherical shell, an equivalent stress is introduced, which is similar to the selected plasticity function. The construction of the stress vector hodograph is used as a method for verification of the stress state.Results. The problem has an analytical solution for linear plasticity functions. A solution is obtained when the strength- ening of the material is taken into account. Analytical and graphical relationships between the parameters of external action for the elastic or elastoplastic states of the sphere are determined. For a combined load, variants are possible when the plastic region is generated at the inner and outer boundaries of the sphere or between these boundaries.Discussion and Conclusions. The calculation results have shown that taking into account the plastic compressibility and the dependence of the plastic limit on temperature can have a significant impact on the stress and strain state of a hollow sphere. In this case, taking into account the first invariant of the stress tensor under the plasticity condition leads to the fact that not only the pressure drop between the outer and inner boundaries of the spherical shell, but the pressure values at these boundaries, can vary within a limited range. In this formulation of the problem, when there is only thermal action, the hollow sphere does not completely pass into the plastic state. The research results provide predicting the behavior of an object (a hollow sphere) that experiences centrally symmetric distributed power and thermal external influences.

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Mazouz, A., L. Labraga, and C. Tournier. "Anisotropy Invariants of Reynolds Stress Tensor in a Duct Flow and Turbulent Boundary Layer." Journal of Fluids Engineering 120, no. 2 (June 1, 1998): 280–84. http://dx.doi.org/10.1115/1.2820645.

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The present study shows that the Reynolds stress anisotropy tensor for turbulent flow depends both on the nature of the surface and the boundary conditions of the flow. Contrary to the case of turbulent boundary layers with k-type surface roughness, the measured anisotropy invariants of the Reynolds stress tensor over a series of spanwise square bars separated by rectangular cavities (k-type) in duct flows show that roughness increases the anisotropy. There is a similarity between the effect of roughness on channel flow turbulence and that on pipe flow turbulence. The present data show that the effect of introducing a surface roughness significantly perturbs the entire thickness of the turbulent flow.

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JONGEN, T., and T. B. GATSKI. "A unified analysis of planar homogeneous turbulence using single-point closure equations." Journal of Fluid Mechanics 399 (November 25, 1999): 117–50. http://dx.doi.org/10.1017/s002211209900631x.

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A unified approach for assessing and characterizing both the non-equilibrium and equilibrium states of planar homogeneous flows is analysed within the framework of single-point turbulence closure equations. The underlying methodology is based on the replacement of the modelled evolution equation for the Reynolds stress anisotropy tensor by an equivalent set of three equations for characteristic scalar invariants or state variables. For stress anisotropy evolution equations which use modelled pressure–strain rate correlations that are quasi-linear, this equivalence then leads to an analytic solution for the time evolution of the Reynolds stress anisotropy. With this analysis, the transient system characteristics can be studied, including the dependence on initial states, the occurrence of limit-cycle behaviour, and the system global stability. In the fixed-point asymptotic limit, these results are consistent with and unify previous equilibrium studies, and provide additional information allowing the resolution of some questions that could not be answered in the framework of previous developments. A new result on constraints applicable to the development of realizable pressure–strain rate models is obtained from a re-examination of the stress anisotropy invariant map. With the analytic solution for the transient behaviour, some recent non-equilibrium models, which incorporate relaxation effects, are evaluated in a variety of homogeneous flows in inertial and non-inertial frames.

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Shams, Moniba, Chaudry Masood Khalique, and Taha Aziz. "Plane Wave Reflection in a Compressible Half Space with Initial Stress." Open Physics 17, no. 1 (August 29, 2019): 438–48. http://dx.doi.org/10.1515/phys-2019-0044.

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Abstract In this paper, the problem of wave propagation in a compressible half-space with an initial stress is considered. General discussion on the speed of wave in the presence of an initial stress is presented. Furthermore, reflection of a homogeneous plane P−wave is also studied. A special strain energy function dependent on this initial stress is used to understand the response of the materials. Explicit formulas for the reflection coefficients are also presented. General nonlinear theory and the theory of invariants are used to derive theoretical results. Graphical illustration of theoretical results for various numerical values of parameters show that initial stress has considerable bearing on the behavior of a plane wave.

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