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

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.