Analysis of large elastic-plastic deformations: Integration algorithm and numerical examples

L.U. Sultanov

Kazan Federal University, Kazan, 420008 Russia

E-mail:  Lenar.Sultanov@kpfu.ru

Received August 29, 2017

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Abstract

An algorithm for investigation of elastic-plastic solids with regard to finite deformations has been developed. The kinematics of elastic-plastic deformations is based on multiplicative decomposition of the deformation gradient into elastic and inelastic parts. The stress state is determined by the Cauchy stress tensor. The constitutive equations have been obtained from the second law of thermodynamics with the introduction of the elastic free energy function. The elastic free energy function is formulated in an invariant form of the left Cauchy–Green tensor. The von Mises yield criterion with isotropic hardening has been used. The radial return method with an iterative refinement of the current state of deformation has been applied for dividing the elastic and plastic deformations. The principle of virtual work in terms of the virtual velocity has been used. The numerical implementation is based on the finite element method. The solution of the necking of a circular bar has been presented.

Keywords: nonlinear elasticity, finite deformations, plasticity

Acknowledgments. The study was supported by the Russian Science Foundation (project no. 16-11-10299).

Figure Captions

Fig. 1. Force-displacement graph. Solid line – a dependence obtained with the help of the developed algorithm, □ – [20],  – [22].

Fig. 2. Plastic deformation intensity.

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For  citation: Sultanov L.U. Analysis of large elastic-plastic deformations: Integration algorithm and numerical examples. Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2017, vol. 159, no. 4, pp. 509–517. (In Russian)

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