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Analysis of finite elasto-plastic strains: integration algorithm and numerical examples. (English. Russian original) Zbl 1409.74010
Lobachevskii J. Math. 39, No. 9, 1478-1483 (2018); translation from Uch. Zap. Kazan. Univ., Ser. Fiz.-Mat. Nauki 159, No. 4, 509-517 (2017).
Summary: The paper is devoted to the development of a calculation technique for elasto-plastic solids with regard to finite strains. The kinematics of elasto-plastic strains is based on the multiplicative decomposition of the total deformation gradient into elastic and inelastic (plastic) components. The stress state is described by the Cauchy stress tensor. Physical relations are obtained from the equation of the second law of thermodynamics supplemented with a free energy function. The free energy function is written in an invariant form of the left Cauchy-Green elastic strain tensor. An elasto-plasticity model with isotropic strain hardening is considered. Based on an analog of the associated rule of plastic flows and the von Mises yield criterion, we develop the method of stress projection onto the yield surface (known as the radial return method) with an iterative refinement of the current stress-strain state. The iterative procedure is based on the introduction of additional virtual stresses to the resolving power equation. The constitutive relations for the rates and increments of the true Cauchy stresses are constructed. In terms of the incremental loading method, the variational equation is obtained on the basis of the principle of possible virtual powers. Spatial discretization is based on the finite element method; an octanodal finite element is used. We present the solution to the problem of tension of a circular bar and give a comparison with results of other authors.
MSC:
74C05 Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials)
74A20 Theory of constitutive functions in solid mechanics
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[1] Sultanov, L. U., Analysis of finite elastoplastic deformations. Kinematics and constitutive equations, Uchen. Zap. Kazan. Univ., Ser. Fiz.-Mat. Nauki, 157, 158-165, (2015)
[2] Eidel, B.; Gruttmann, F., Elastoplastic orthotropy at finite strains: multiplicative formulation and numerical implementation, Comput. Mater. Sci., 28, 732-742, (2003)
[3] Schröder, J.; Gruttmann, F.; Löblein, J., A simple orthotropic finite elasto-plasticity model based on generalized stress-strain measures, Comput. Mech., 30, 48-64, (2002) · Zbl 1058.74025
[4] Simo, J. S., A framework for finite strain elastoplasticity based on maximum plastic dissipation and the multiplicative decomposition: Part I. Continuumformulation, Comput. Methods Appl. Mech. Eng., 66, 199-219, (1988) · Zbl 0611.73057
[5] Miehe, C., A theory of large-strain isotropic thermoplasticity based on metric transformation tensors, Arch. Appl. Mech., 66, 45-64, (1995) · Zbl 0844.73027
[6] Basar, Y.; Itskov, M., Constitutive model and finite element formulation for large strain elasto-plastic analysis of shell, Comput. Mech., 23, 466-481, (1999) · Zbl 0943.74035
[7] Meyers, A.; Schievbe, P.; Bruhns, O. T., Some comments on objective rates of symmetric Eulerian tensors with application to Eulerian strain rates, Acta Mech., 139, 91-103, (2000) · Zbl 0984.74004
[8] Xiao, H.; Bruhns, O. T.; Meyers, A., A consistent finite elastoplasticity theory combining additive and multiplicative decomposition of the stretching and deformation gradient, Int. J. Plasticity, 16, 143-177, (2000) · Zbl 1005.74015
[9] J. Bonet and R. D. Wood, Nonlinear Continuum Mechanics for Finite Element Analysis (Cambridge Univ. Press, Cambridge, 1997). · Zbl 0891.73001
[10] Rouainia, M.; Wood, D. M., Computational aspects in finite strain plasticity analysis of geotechnical materials, Mech. Res. Commun., 33, 123-133, (2006) · Zbl 1192.74361
[11] Simo, J. S.; Ortiz, M., A unified approach to finite deformation elastoplastic analysis lased on the use of hyperelastic constitutive equations, Comput. Methods. Appl. Mech. Eng., 49, 221-245, (1985) · Zbl 0566.73035
[12] Eterovic, A. L.; Bathe, K.-J., A hyperelastic-based large strain elasto-plastic constitutive formulation with combined isotropic-kinematic hardening using the logarithmic stress and strain measures, Int. J. Numer. Meth. Eng., 30, 1099-1114, (1990) · Zbl 0714.73035
[13] Davydov, R. L.; Sultanov, L. U., Numerical algorithm of solving the problem of large elastic-plastic deformation by FEM, Vestn. Perm. Politekh. Univ., Mekh., No., 1, 81-93, (2013)
[14] Davydov, R. L.; Sultanov, L. U., Numerical algorithm for investigating large elasto-plastic deformations, J. Eng. Phys. Thermophys., 88, 1280-1288, (2015)
[15] Golovanov, A. I.; Sultanov, L. U., Numerical investigation of large elastoplastic strains of threedimensional bodies, Int. Appl. Mech., 41, 614-620, (2005) · Zbl 1089.74506
[16] Abdrakhmanova, A. I.; Sultanov, L. U., Numerical modelling of deformation of hyperelastic incompressible solids, Mater. Phys. Mech., 26, 30-32, (2016)
[17] Golovanov, A. I.; Konoplev, Yu. G.; Sultanov, L. U., Numerical investigation of finite deformations of hyperelastic bodies. IV. Finite-element implementation. Examples of the solution of problems, Uch. Zap. Kazan. Univ., Ser. Fiz.-Mat. Nauki, 152, 115-126, (2010)
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