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Journal articles on the topic '(finite deformation theory)'

Author: Grafiati

Published: 4 June 2021

Last updated: 6 September 2023

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1

WATANABE, Osamu. "Finite deformation theory of elastoplasicity." Transactions of the Japan Society of Mechanical Engineers Series A 54, no. 501 (1988): 992–1001. http://dx.doi.org/10.1299/kikaia.54.992.

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2

Meggyes, �. "Multiple decomposition in finite deformation theory." Acta Mechanica 146, no. 3-4 (September 2001): 169–82. http://dx.doi.org/10.1007/bf01246731.

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3

Frishter, Lyudmila, and Al-Gburi Noora Saad Subhi. "Uniform Domain Equilibrium Equation with Finite Deformations." E3S Web of Conferences 410 (2023): 03007. http://dx.doi.org/10.1051/e3sconf/202341003007.

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In corner areas of structures, high stress values and gradients occur, and lead to stress concentrations. Infinite stress and deformations are determined by a solution of the linear elasticity theory problem in the area with a wedge-shape boundary notch. Infinite solutions of the elasticity problem occur under impact of forced deformations, when a surge of the deformation value reaches beyond the area boundary. Relative values of stress concentrations for corner area zones make no more sense. At finite displacements, high deformation and stress values occur in the corner zones of the area. For a linear statement of the elasticity theory problem, at minor deflections, not only first-order, but also second-order derivatives of the displacements function are significant. To account for finite deformations of such corner zones of the area, correct formulations of elasticity problems are required. Study objective: influence determination of the infinitesimal order of the deformation on the appearance of equilibrium equations of an area with induced (temperature) deformations. This allows for the analysis of the influence of linear, shear deformations, and of the swing on the solution of the elasticity problem with induced deformations.

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4

Hu, Yi, Yong Zhao, and Haopeng Liang. "Refined Beam Theory for Geometrically Nonlinear Pre-Twisted Structures." Aerospace 9, no. 7 (July 6, 2022): 360. http://dx.doi.org/10.3390/aerospace9070360.

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This paper proposes a novel fully nonlinear refined beam element for pre-twisted structures undergoing large deformation and finite untwisting. The present model is constructed in the twisted basis to account for the effects of geometrical nonlinearity and initial twist. Cross-sectional deformation is allowed by introducing Lagrange polynomials in the framework of a Carrera unified formulation. The principle of virtual work is applied to obtain the Green–Lagrange strain tensor and second Piola–Kirchhoff stress tensor. In the nonlinear governing formulation, expressions are given for secant and tangent matrices with linear, nonlinear, and geometrically stiffening contributions. The developed beam model could detect the coupled axial, torsional, and flexure deformations, as well as the local deformations around the point of application of the force. The maximum difference between the present deformation results and those of shell/solid finite element simulations is 6%. Compared to traditional beam theories and finite element models, the proposed method significantly reduces the computational complexity and cost by implementing constant beam elements in the twisted basis.

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5

Saxena, Prashant, Mokarram Hossain, and Paul Steinmann. "A theory of finite deformation magneto-viscoelasticity." International Journal of Solids and Structures 50, no. 24 (November 2013): 3886–97. http://dx.doi.org/10.1016/j.ijsolstr.2013.07.024.

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6

Frishter, Ludmila. "INFINITESIMAL AND FINITE DEFORMATIONS IN THE POLAR COORDINATE SYSTEM." International Journal for Computational Civil and Structural Engineering 19, no. 1 (March 29, 2023): 204–11. http://dx.doi.org/10.22337/2587-9618-2023-19-1-204-211.

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The deformation problem of elasticity theory with regard to nonlinear deformations is examined. The expressions of deformations through displacements in the orthogonal curvilinear coordinate system are recorded. The relations for finite deformations in cylindrical and polar coordinate systems are derived. Physical relations for finite deformations and corresponding generalized stresses are recorded.

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7

Liu, Zong Min, Ji Ze Mao, and Hai Yan Song. "Path-Independent Ĵ-Integral Based on Finite Deformation Theory." Key Engineering Materials 577-578 (September 2013): 189–92. http://dx.doi.org/10.4028/www.scientific.net/kem.577-578.189.

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For a finite deformation body, there are large strains and displacements on the crack tip. So it is necessary to study-integral based on finite deformation theory. Base forces theory is a new theory for describing finite deformation. In this paper, -integral based on base forces theory are presented. This work provides a new theoretical foundation for studying dynamic crack propagation.

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8

Lin, Wen Shan. "Plastic Deformation Theory Application in Finite Element Analysis." Advanced Materials Research 594-597 (November 2012): 2723–26. http://dx.doi.org/10.4028/www.scientific.net/amr.594-597.2723.

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In the present study, the constitutive law of the deformation theory of plasticity has been derived. And that develop the two-dimensional and three-dimensional finite element program. The results of finite element and analytic of plasticity are compared to verify the derived the constitutive law of the deformation theory and the FEM program. At plastic stage, the constitutive laws of the deformation theory can be expressed as the linear elastic constitutive laws. But, it must be modified by iteration of the secant modulus and the effective Poisson’s ratio. Make it easier to develop finite element program. Finite element solution and analytic solution of plasticity theory comparison show the answers are the same. It shows the derivation of the constitutive law of the deformation theory of plasticity and finite element analysis program is the accuracy.

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9

CHRISTMANN, JULIA, RALF MÜLLER, and ANGELIKA HUMBERT. "On nonlinear strain theory for a viscoelastic material model and its implications for calving of ice shelves." Journal of Glaciology 65, no. 250 (March 12, 2019): 212–24. http://dx.doi.org/10.1017/jog.2018.107.

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ABSTRACTIn the current ice-sheet models calving of ice shelves is based on phenomenological approaches. To obtain physics-based calving criteria, a viscoelastic Maxwell model is required accounting for short-term elastic and long-term viscous deformation. On timescales of months to years between calving events, as well as on long timescales with several subsequent iceberg break-offs, deformations are no longer small and linearized strain measures cannot be used. We present a finite deformation framework of viscoelasticity and extend this model by a nonlinear Glen-type viscosity. A finite element implementation is used to compute stress and strain states in the vicinity of the ice-shelf calving front. Stress and strain maxima of small (linearized strain measure) and finite strain formulations differ by ~ 5% after 1 and by ~ 30% after 10 years, respectively. A finite deformation formulation reaches a critical stress or strain faster, thus calving rates will be higher, despite the fact that the exact critical values are not known. Nonlinear viscosity of Glen-type leads to higher stress values. The Maxwell material model formulation for finite deformations presented here can also be applied to other glaciological problems, for example, tidal forcing at grounding lines or closure of englacial and subglacial melt channels.

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10

ISHIDA, Ryohei. "Finite Element Analysis of Circular Plate Based on Finite Deformation Theory." Proceedings of Ibaraki District Conference 2002 (2002): 91–92. http://dx.doi.org/10.1299/jsmeibaraki.2002.91.

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11

Steinmann, Paul. "A micropolar theory of finite deformation and finite rotation multiplicative elastoplasticity." International Journal of Solids and Structures 31, no. 8 (April 1994): 1063–84. http://dx.doi.org/10.1016/0020-7683(94)90164-3.

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12

KOBAYASHI, Michiaki. "Acoustoelastic theory for finite plastic deformation of solids." Transactions of the Japan Society of Mechanical Engineers Series A 57, no. 534 (1991): 346–53. http://dx.doi.org/10.1299/kikaia.57.346.

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13

Hwang, K. C., H. Jiang, Y. Huang, H. Gao, and N. Hu. "A finite deformation theory of strain gradient plasticity." Journal of the Mechanics and Physics of Solids 50, no. 1 (January 2002): 81–99. http://dx.doi.org/10.1016/s0022-5096(01)00020-5.

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14

Geiss, Christoff, and José Antonio de la Peña. "On the deformation theory of finite dimensional algebras." manuscripta mathematica 88, no. 1 (December 1995): 191–208. http://dx.doi.org/10.1007/bf02567817.

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15

KOBAYASHI, Michiaki. "Acoustoelastic Theory for Finite Plastic Deformation of Solids." JSME international journal. Ser. 1, Solid mechanics, strength of materials 35, no. 1 (1992): 45–52. http://dx.doi.org/10.1299/jsmea1988.35.1_45.

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16

Chambon, René, Denis Caillerie, and Claudio Tamagnini. "A finite deformation second gradient theory of plasticity." Comptes Rendus de l'Académie des Sciences - Series IIB - Mechanics 329, no. 11 (November 2001): 797–802. http://dx.doi.org/10.1016/s1620-7742(01)01400-3.

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17

Liu, Jing, Zhifeng Shi, Yimin Shao, and Huifang Xiao. "Effects of spall edge profiles on the edge plastic deformation for a roller bearing." Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications 233, no. 5 (May 15, 2017): 850–61. http://dx.doi.org/10.1177/1464420717710276.

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A clear understanding of the plastic deformations at the spall edges is a primary task for the edge propagation predictions in rolling element bearings. This work proposed an elastic–plastic two-dimensional finite element model for calculating the contact stress and plastic deformation between the rolling element and raceway. This model includes a rolling element and one raceway. The rectangular plane strain solid elements are used to formulate the finite element model. The Coulomb model is used to formulate the friction force between the rolling element and raceway. A bilinear kinematic hardening material model is used in the finite element model, which can formulate the elastic–plastic deformations. The studied spall edge profiles are assumed to be sharp and cylindrical ones. To validate the finite element model, the contact deformations between the rolling element and the raceway from the proposed model and Hertzian contact theory are compared. Effects of spall edge profiles on the edge plastic deformations at the edge are analyzed, as well as the edge plastic deformation zone width. Based on the numerical results, the relationship between the edge plastic deformation and the spall edge profile, and that between the edge plastic deformation zone width and the spall edge profile are established. The results show that the edge plastic deformation is significantly influenced by the spall edge profiles, as well as the edge plastic deformation zone width. This paper provides a clear understanding of the effects of the edge profiles on the plastic deformations and propagation at the spall edge.

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18

Klochkov, Yuriy V., Anatoliy P. Nikolaev, Olga V. Vakhnina, and Mikhail Yu Klochkov. "Variants of determining correlations of deformation theory of plasticity in the calculation of shell of rotation on the basis of finite element method." Structural Mechanics of Engineering Constructions and Buildings 15, no. 4 (December 15, 2019): 315–22. http://dx.doi.org/10.22363/1815-5235-2019-15-4-315-322.

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Relevance. The problems of decline of resource-demanding of objects of building and engineer dictate the necessity of consideration of processes of deformation of constructions at the resiliently-plastic state. The widely in-use theory of account of practical properties of material is a deformation theory of plasticity. The aim of the research is development of variants of receipt of determining correlations on the step of ladening at deformation of material outside a resiliency. Methods. Algorithms over of receipt of determining correlations of theory of small resiliently-plastic deformations are brought on the step of ladening in two variants. In the first they turn out differentiation of expressions of tensions as functions of deformations on the basis of deformation theory of plasticity; in the second determining correlations turn out on the basis of hypothesis about the proportion of components of deviators increases of tensions to components of deviators increases of deformations. Results. On the test example of calculation of the jammed cylindrical shell realization of the got determining correlations is presented.

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19

Bayoumi, A. E., R. B. Joshi, and H. M. Zbib. "Investigation of Finite Deformations and Shear Banding: Theory and Experiment." Applied Mechanics Reviews 44, no. 11S (November 1, 1991): S20—S26. http://dx.doi.org/10.1115/1.3121356.

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An experimental method using a digital image processing technique is developed for the purpose of characterizing material behavior at large elastoplastic deformations and the associated phenomenon of localization of plastic flow into shear bands. This allows for a detailed description of the evolution of the nonuniform deformation pattern in the post-localization regime. The experimental results are utilized to calibrate a recently developed gradient-dependent constitutive equation which takes into account the effect of heterogeneous plastic flow, anisotropy and large deformations. The measured values of the gradient coefficients are of small magnitude suggesting that higher order gradients are important only in the highly inhomogeneous region as expected. Moreover, it is found that anisotropic effects become significant in the post-localization regime where the anisotropy ratio changes considerably.

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20

Shao, Xin Yan, Xian Zhang Ling, Wei Zhang, Liang Tang, Li Na Wang, and Min Wang. "Finite Element Analysis on Instantaneous Deformation and Consolidation Deformation of Saturated Soft Clay Foundation." Advanced Materials Research 250-253 (May 2011): 3198–203. http://dx.doi.org/10.4028/www.scientific.net/amr.250-253.3198.

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Deformation analysis of foundation is an important research field in geotechnical engineering, especially analysis on instantaneous deformation and consolidation deformation of saturated soft clay foundations. In this paper, a computation model of instantaneous deformation and consolidation deformation was built on the basis of Biot Consolidation Theory and consideration of mechanism of instantaneous deformation and consolidation deformation and consideration of interrelation of both deformations. A method was proposed to determine initial pore water pressure in soil. Nonlinearity of soil deformation under drainage conditions was considered by combining Duncan-Zhang model with compaction curve of soil, and failure soil elements were processed by Mohr-Coulomb Failure Criteria. By numerical simulation, a nonlinear axi-symmetric FEM program was complied to solve foundation deformation and applied in calculation of soft ground tank settlement. Results show that the method presented in this paper is efficient and suitable to analyze instantaneous deformation and consolidation deformation.

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21

Levin, V. A., and K. M. Zingermann. "Effective Constitutive Equations for Porous Elastic Materials at Finite Strains and Superimposed Finite Strains." Journal of Applied Mechanics 70, no. 6 (November 1, 2003): 809–16. http://dx.doi.org/10.1115/1.1630811.

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A method is developed for derivation of effective constitutive equations for porous nonlinear-elastic materials undergoing finite strains. It is shown that the effective constitutive equations that are derived using the proposed approach do not change if a rigid motion is superimposed on the deformation. An approach is proposed for the computation of effective characteristics for nonlinear-elastic materials in which pores are originated after a preliminary loading. This approach is based on the theory of superimposed finite deformations. The results of computations are presented for plane strain, when pores are distributed uniformly.

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22

Surana, K. S., A. D. Joy, and J. N. Reddy. "A finite deformation, finite strain nonclassical internal polar continuum theory for solids." Mechanics of Advanced Materials and Structures 26, no. 5 (November 17, 2017): 381–93. http://dx.doi.org/10.1080/15376494.2017.1387327.

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23

Balbi, Valentina, Tom Shearer, and William J. Parnell. "A modified formulation of quasi-linear viscoelasticity for transversely isotropic materials under finite deformation." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 474, no. 2217 (September 2018): 20180231. http://dx.doi.org/10.1098/rspa.2018.0231.

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The theory of quasi-linear viscoelasticity (QLV) is modified and developed for transversely isotropic (TI) materials under finite deformation. For the first time, distinct relaxation responses are incorporated into an integral formulation of nonlinear viscoelasticity, according to the physical mode of deformation. The theory is consistent with linear viscoelasticity in the small strain limit and makes use of relaxation functions that can be determined from small-strain experiments, given the time/deformation separability assumption. After considering the general constitutive form applicable to compressible materials, attention is restricted to incompressible media. This enables a compact form for the constitutive relation to be derived, which is used to illustrate the behaviour of the model under three key deformations: uniaxial extension, transverse shear and longitudinal shear. Finally, it is demonstrated that the Poynting effect is present in TI, neo-Hookean, modified QLV materials under transverse shear, in contrast to neo-Hookean elastic materials subjected to the same deformation. Its presence is explained by the anisotropic relaxation response of the medium.

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24

You, L. H., J. J. Zhang, H. B. Wu, and R. B. Sun. "Regular papers / Articles ordinaires A numerical approach for the static analysis of the body of pressurized dry gas holders." Canadian Journal of Civil Engineering 30, no. 2 (April 1, 2003): 381–90. http://dx.doi.org/10.1139/l02-095.

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In this paper, a numerical method is developed to calculate deformations and stresses of the body of dry gas holders under gas pressure. The deformations of the wall plates are decomposed into out-of-plane bending and in-plane deformation. The out-of-plane bending of the wall plates is described by the theory of orthotropic plates and the in-plane deformation by the biharmonic equation of flat plates under plane stress. The theories of beam columns and beams are employed to analyze the columns and corridors, respectively. By considering compatibility conditions between the members and boundary conditions, equations for the determination of deformations and stresses of dry gas holders under gas pressure are obtained. Both the proposed approach and the finite element method are used to investigate the deformations and stresses of the body of a dry gas holder under gas pressure. The results from the proposed method agree with those from the finite element method. Because far fewer unknowns are involved, the proposed method is computationally more efficient than both the finite element method and the series method developed from the theory of stiffened plates.Key words: numerical approach, body of dry gas holders, gas pressure.

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25

Eriksen, Eivind. "Computing Noncommutative Deformations of Presheaves and Sheaves of Modules." Canadian Journal of Mathematics 62, no. 3 (June 1, 2010): 520–42. http://dx.doi.org/10.4153/cjm-2010-015-6.

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AbstractWe describe a noncommutative deformation theory for presheaves and sheaves of modules that generalizes the commutative deformation theory of these global algebraic structures and the noncommutative deformation theory of modules over algebras due to Laudal.In the first part of the paper, we describe a noncommutative deformation functor for presheaves of modules on a small category and an obstruction theory for this functor in terms of global Hochschild cohomology. An important feature of this obstruction theory is that it can be computed in concrete terms in many interesting cases.In the last part of the paper, we describe a noncommutative deformation functor for quasi-coherent sheaves of modules on a ringed space (X,𝒜). We show that for any good A-affine open cover U of X, the forgetful functor QCoh𝒜 → PreSh(U,𝒜) induces an isomorphism of noncommutative deformation functors.Applications. We consider noncommutative deformations of quasi-coherent 𝒜-modules on X when (X,𝒜) = (X,𝒪X) is a scheme or (X,𝒜) = (X,𝒟) is a D-scheme in the sense of Beilinson and Bernstein. In these cases, we may use any open affine cover of X closed under finite intersections to compute noncommutative deformations in concrete terms using presheaf methods. We compute the noncommutative deformations of the left 𝒟X-module 𝒟X when X is an elliptic curve as an example.

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26

Liu, Zong Min, Ji Ze Mao, and Hai Yan Song. "J-Integral and its Dual Form Based on Finite Deformation Theory." Key Engineering Materials 525-526 (November 2012): 313–16. http://dx.doi.org/10.4028/www.scientific.net/kem.525-526.313.

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In general, there are large strains and displacements on the crack tip. So it is necessary to study-integral and its dual form based on finite deformation theory. Base forces theory is a new theory for describing finite deformation. -integral and its dual form based on base forces theory are presented in the paper. This work provides theoretical foundation for studying crack propagation.

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27

Oliynyk, Kateryna, and Claudio Tamagnini. "Finite deformation hyperplasticity theory for crushable, cemented granular materials." Open Geomechanics 2 (November 16, 2020): 1—None. http://dx.doi.org/10.5802/ogeo.8.

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28

Carroll, M. M. "A Rate-Independent Constitutive Theory for Finite Inelastic Deformation." Journal of Applied Mechanics 54, no. 1 (March 1, 1987): 15–21. http://dx.doi.org/10.1115/1.3172952.

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A rate-independent constitutive theory for finite inelastic deformation is formulated in terms of the symmetric Piola-Kirchhoff stress, the Lagrangian strain, and a kinematic tensor which describes inelastic or microstructural effects. Assumptions of (a) continuity in the transition from loading to neutral loading, (b) consistency, and (c) nonnegative work in closed cycles of deformation, lead to simplification of the theory. The response is described by two scalar functions — a stress potential and a loading function. The theory can describe isotropic or anisotropic response, and allows for hardening, softening, or ideal behavior. It may also be appropriate to describe the response of porous materials, such as metals, rocks and ceramics, and also the evolution of damage.

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29

Gao, Ya Nan, Feng Gao, M. R. Yeung, and Qing Hui Jiang. "A Development of 3D-DDA with Finite Deformation Theory." Applied Mechanics and Materials 29-32 (August 2010): 1402–7. http://dx.doi.org/10.4028/www.scientific.net/amm.29-32.1402.

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A post-adjustment method that makes DDA coupled with finite deformation theory was presented in this paper. The displacement post-adjustment equations were derived. We also calculated two examples to illustrate this method. The method was also compared with original DDA and reference’s. It shows that the method in this paper can work well on the block rotation error problems.

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30

Huang, Z. P. "A constitutive theory in thermo-viscoelasticity at finite deformation." Mechanics Research Communications 26, no. 6 (November 1999): 679–86. http://dx.doi.org/10.1016/s0093-6413(99)00078-6.

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31

Ya-nan, Gao, and Gao Feng. "Analysis of slope stability based on finite deformation theory." Procedia Earth and Planetary Science 1, no. 1 (September 2009): 460–64. http://dx.doi.org/10.1016/j.proeps.2009.09.073.

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32

Kulikov, G. M., and S. V. Plotnikova. "Finite deformation plate theory and large rigid-body motions." International Journal of Non-Linear Mechanics 39, no. 7 (September 2004): 1093–109. http://dx.doi.org/10.1016/s0020-7462(03)00099-4.

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33

Hwang, K. C., Y. Guo, H. Jiang, Y. Huang, and Z. Zhuang. "The finite deformation theory of Taylor-based nonlocal plasticity." International Journal of Plasticity 20, no. 4-5 (April 2004): 831–39. http://dx.doi.org/10.1016/j.ijplas.2003.08.001.

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34

Yanqi, Song, and Chen Zhida. "Variational principles of asymmetric elasticity theory of finite deformation." Applied Mathematics and Mechanics 20, no. 11 (November 1999): 1200–1206. http://dx.doi.org/10.1007/bf02463787.

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35

Atkinson, C., and B. Peltier. "The finite deformation of a reinforced packer, membrane theory." Journal of Engineering Mathematics 27, no. 4 (September 1993): 443–54. http://dx.doi.org/10.1007/bf00128766.

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36

Vertin, K. D., and S. A. Majlessi. "Finite Element Analysis of the Axisymmetric Upsetting Process Using the Deformation Theory of Plasticity." Journal of Engineering for Industry 115, no. 4 (November 1, 1993): 450–58. http://dx.doi.org/10.1115/1.2901789.

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The deformation theory of plasticity is extended to the analysis of bulk metal forming problems. An elastic-plastic finite element formulation is developed and used to simulate solid cylinder and ring upsetting processes. The intent of this analysis is to demonstrate that the deformation theory yields solutions equivalent to the incremental theory, and requires less computation time. Predicted results are compared with published incremental finite element solutions and experimental measurements. Deformation theory results are in agreement with published data for many forming conditions. The performance of the formulation gradually degraded with increasing deformation and friction, and possible causes for this behavior are discussed.

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37

Li, Mingrui, Zhe Zhou, and Wenbin Huang. "Plastic theory for the multi-crystal metals —From infinitesimal deformation to finite deformation." Progress in Natural Science 13, no. 1 (January 1, 2003): 25–30. http://dx.doi.org/10.1080/10020070312331343080.

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LI, Mingrui. "Plastic theory for the multi-crystal metals---From infinitesimal deformation to finite deformation." Progress in Natural Science 13, no. 1 (2003): 25. http://dx.doi.org/10.1360/03jz9004.

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39

Mukherjee, Goutam, and Raj Bhawan Yadav. "Equivariant one-parameter deformations of associative algebras." Journal of Algebra and Its Applications 19, no. 06 (June 18, 2019): 2050114. http://dx.doi.org/10.1142/s0219498820501145.

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40

Nishiguchi, I., T. L. Sham, and E. Krempl. "A Finite Deformation Theory of Viscoplasticity Based on Overstress: Part II—Finite Element Implementation and Numerical Experiments." Journal of Applied Mechanics 57, no. 3 (September 1, 1990): 553–61. http://dx.doi.org/10.1115/1.2897058.

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A one-step time integration method is developed for the finite deformation theory of viscoplasticity based on overstress (FVBO) described in Part I. This time integration method is based on a forward gradient approximation and it leads to explicit expressions of the tangent operators suitable for finite element implementation. Numerical experiments and closed-form solutions for a hypoelastic material in homogeneous deformation states are presented. The FVBO is applied to the modeling of second-order effects in torsion. The numerical results show that a modification of the Jaumann rate and second-order terms of the inelastic rate of deformation are necessary to model the observed effects.

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41

Hussein, Bassam A., Hiroyuki Sugiyama, and Ahmed A. Shabana. "Coupled Deformation Modes in the Large Deformation Finite-Element Analysis: Problem Definition." Journal of Computational and Nonlinear Dynamics 2, no. 2 (November 17, 2006): 146–54. http://dx.doi.org/10.1115/1.2447353.

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In the classical formulations of beam problems, the beam cross section is assumed to remain rigid when the beam deforms. In Euler–Bernoulli beam theory, the rigid cross section remains perpendicular to the beam centerline; while in the more general Timoshenko beam theory the rigid cross section is permitted to rotate due to the shear deformation, and as a result, the cross section can have an arbitrary rotation with respect to the beam centerline. In more general beam models as the ones based on the absolute nodal coordinate formulation (ANCF), the cross section is allowed to deform and it is no longer treated as a rigid surface. These more general models lead to new geometric terms that do not appear in the classical formulations of beams. Some of these geometric terms are the result of the coupling between the deformation of the cross section and other modes of deformations such as bending and they lead to a new set of modes referred to in this paper as the ANCF-coupled deformation modes. The effect of the ANCF-coupled deformation modes can be significant in the case of very flexible structures. In this investigation, three different large deformation dynamic beam models are discussed and compared in order to investigate the effect of the ANCF-coupled deformation modes. The three methods differ in the way the beam elastic forces are calculated. The first method is based on a general continuum mechanics approach that leads to a model that includes the ANCF-coupled deformation modes; while the second method is based on the elastic line approach that systematically eliminates these modes. The ANCF-coupled deformation modes eliminated in the elastic line approach are identified and the effect of such deformation modes on the efficiency and accuracy of the numerical solution is discussed. The third large deformation beam model discussed in this investigation is based on the Hellinger–Reissner principle that can be used to eliminate the shear locking encountered in some beam models. Numerical examples are presented in order to demonstrate the use and compare the results of the three different beam formulations. It is shown that while the effect of the ANCF-coupled deformation modes is not significant in very stiff and moderately stiff structures, the effect of these modes can not be neglected in the case of very flexible structures.

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42

Gomaa, S., T. L. Sham, and E. Krempl. "Finite element formulation for finite deformation, isotropic viscoplasticity theory based on overstress (FVBO)." International Journal of Solids and Structures 41, no. 13 (June 2004): 3607–24. http://dx.doi.org/10.1016/j.ijsolstr.2004.01.016.

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Sigaeva, Taisiya, and Aleksander Czekanski. "Finite bending of a multilayered cylindrical nanosector with residual deformations." Mathematics and Mechanics of Solids 23, no. 5 (January 31, 2017): 715–26. http://dx.doi.org/10.1177/1081286516689296.

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This paper deals with the universal model describing plane strain bending of a multilayered sector of a cylindrical tube which can have residual deformations as well as nano-scale effects. In order to model the response of the sector at the nano-scale, the Gurtin–Murdoch theory is employed. Residual deformations of the layers, such as prestretch or precompression, are introduced into the model of finite bending using the multiplicative decomposition rule for corresponding deformation gradients. Numerous coupled nonlinear effects exhibited by the sector are discussed.

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Kołakowski, Zbigniew, and Jacek Jankowski. "Effect of Membrane Components of Transverse Forces on Magnitudes of Total Transverse Forces in the Nonlinear Stability of Plate Structures." Materials 13, no. 22 (November 20, 2020): 5262. http://dx.doi.org/10.3390/ma13225262.

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For an isotropic square plate subject to unidirectional compression in the postbuckling state, components of transverse forces in bending, membrane transverse components and total components of transverse forces were determined within the first-order shear deformation theory (FSDT), the simple first-order shear deformation theory (S-FSDT), the classical plate theory (CPT) and the finite element method (FEM). Special attention was drawn to membrane components of transverse forces, which are expressed with the same formulas for the first three theories and do not depend on membrane deformations. These components are nonlinearly dependent on the plate deflection. The magnitudes of components of transverse forces for the four theories under consideration were compared.

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Li, Hong Yang, Song Yu, and Jian Hui Li. "Crystal Plasticity Finite Element Simulation of Aluminium Deformation." Materials Science Forum 1001 (July 2020): 127–32. http://dx.doi.org/10.4028/www.scientific.net/msf.1001.127.

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Crystal plasticity deformation of aluminium plays an important role on the investigation of macro deformation. In this paper, to discuss the effect ot crystal plasticity on the aluminium material behavior, crystal plasticity theory and macro finite element was combined together. The basic theory of crystal plasticity and finite element was introduce and the simulation result of aluminium was given. The stress and strain distribution was discussed and the efficient of the method was shown. It is shown that the orientation of the material and other micro character of the materials all influence the plasticity behavior of the material greatly.

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Zhao, Pengbing, Jin Huang, and Yaoyao Shi. "A formulation of tooth deformation and its error compensation for worm gear transmission mechanisms." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 231, no. 8 (September 28, 2016): 1518–39. http://dx.doi.org/10.1177/0954406216672498.

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Milling head and rotary table are the key components in five-axis CNC machine tools. However, tracking and positioning precision of these rotary axes based on worm gear mechanisms are affected by the backlash, friction, elastic deformation, and other nonlinearities. Therefore, finding out a simple and universal principle to predict the tooth deformation in an initial design is quite significant. A novel deformation calculation and compensation method with finite element analysis and circular plate theory is proposed for the worm gear transmissions. When the relationship (form factor) between the solutions of circular plate theory and finite element analysis is derived, deformation calculation with finite element analysis can be replaced by multiplying the solution of circular plate theory and the form factor. Analysis and calculation results show that the presented method can provide a reference for the compensation control of the positioning errors.

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DEMCHENKO, OLEG, and ALEXANDER GUREVICH. "GROUP ACTION ON THE DEFORMATIONS OF A FORMAL GROUP OVER THE RING OF WITT VECTORS." Nagoya Mathematical Journal 235 (December 20, 2017): 42–57. http://dx.doi.org/10.1017/nmj.2017.43.

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A recent result by the authors gives an explicit construction for a universal deformation of a formal group $\unicode[STIX]{x1D6F7}$ of finite height over a finite field $k$ . This provides in particular a parametrization of the set of deformations of $\unicode[STIX]{x1D6F7}$ over the ring ${\mathcal{O}}$ of Witt vectors over $k$ . Another parametrization of the same set can be obtained through the Dieudonné theory. We find an explicit relation between these parameterizations. As a consequence, we obtain an explicit expression for the action of $\text{Aut}_{k}(\unicode[STIX]{x1D6F7})$ on the set of ${\mathcal{O}}$ -deformations of $\unicode[STIX]{x1D6F7}$ in the coordinate system defined by the universal deformation. This generalizes a formula of Gross and Hopkins and the authors’ result for one-dimensional formal groups.

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Freed, Alan D. "Transverse-Isotropic Elastic and Viscoelastic Solids." Journal of Engineering Materials and Technology 126, no. 1 (January 1, 2004): 38–44. http://dx.doi.org/10.1115/1.1631030.

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A set of invariants are presented for transverse-isotropic materials whose gradients produce strain fields, instead of deformation fields as is typically the case. Finite-strain theories for elastic and K-BKZ-type viscoelastic solids are derived. Shear-free and simple shearing deformations are employed to illustrate the constitutive theory.

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Kulikov, R. G., T. G. Kulikova, and Nikolai A. Trufanov. "Numerical Method for Solving the Problem of Thermomechanics of Polymeric Environment in Conditions of Phase Transition." Solid State Phenomena 243 (October 2015): 139–45. http://dx.doi.org/10.4028/www.scientific.net/ssp.243.139.

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A methodology and a numerical algorithm of solving boundary problems of mechanics of deformable crystallizing elastic polymer media have been developed. A class of problems describing processes taking place in polymer products during their manufacturing is considered. Due to the significance of shrinking deformations the problem is considered within finite deformations theory. Constitutive relations are built on base of Peng-Landel potential. A ‘weak’ variation problem statement based on Galerkin approach is used. The offered algorithm is based on linearization methodology when small deformations are applied to finite ones. Deformation process is considered as a sequence of transitions through intermediate configurations. This approach makes possible to bring the received solution to the sequence of linearized boundary problems for which effective numerical algorithms have been designed. Numerical procedure is based on the technology of finite element method. Increments of displacements on the considered time step are taken to be nodal unknowns. The offered algorithm is applied to solution of the problem concerning the polyethylene pipe deformation during its manufacturing. Main advantages of the proposed algorithm have been defined.

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Khaldjigitov, Abduvali, Uchkunbek Adambaev, and Mumin R. Babadjanov Mumin R. Babadjanov. "FINITE DIFFERENCE METHOD FOR SOLVING THE ELASTOPLASTIC PROBLEMS OF ANISOTROPIC BODIES." Applied Mathematics and Control Sciences, no. 4 (December 30, 2019): 9–25. http://dx.doi.org/10.15593/2499-9873/2019.4.01.

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Usually, for the numerical solution of elastoplastic boundary value problems based on deformation theory of plasticity is used an elastic solutions method proposed by A.A. Ilyushin. In literatures the method of elastic solutions relative to boundary value problems of the theory of plastic flow is called the method of initial stresses or the method of initial deformations. In this paper, to solve the boundary value problems of the deformation theory of plasticity of transversally isotropic bodies, it is used relatively “simple” finite-difference method considered in combination with the iterative method, that is, the elastic solution method. The essence of the method is to construct symmetric finite-difference equations, separately for internal and boundary nodes of the area under consideration, and to solve them with respect to “central” or boundary node displacements and the organization of the iterative process. Elastoplastic problems are solved numerically for isotropic and transversely isotropic parallelepipeds under various boundary and boundary conditions. The obtained results are consistent with the known solutions, which shows the validity of the applied methodology. It is explored the spreading of the zone of plasticity and the effect of anisotropy on their distribution.

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