Numerical Algorithm of Solving the Problem of Large Elastic-Plastic Deformation by FEM

A numerical algorithm of the investigation of stress-strain state of the solids with large elastic-plastic deformations is described. The constitutive equations are obtained using the free energy function and yield function. The general radial return method is applied. Calculation algorithm is based on the linearized equation of virtual work, defined to actual state. The continuation method is used. The von Mises yield criterion with isotropic hardening is considered. A spatial discretization is based on the finite element method. The developed algorithm of investigation of large elastic-plastic deformations is tested on the solution of the necking of circular bar problem and a conical shell subjecting to a constant ring load. The results of solutions and comparison with results obtained by other authors are presented.