A finite element formulation for finite strain elasto-plastic analysis based on mixed interpolation of tensorial components

Abstract

A quadrilateral finite element formulation for modelling finite strain elasto-plastic deformation processes is presented. The developed formulation is based on Lee's multiplicative decomposition of the deformation gradient and on the hyperelastic expression of the associated Von Mises flow rule. The Hencky or logarithmic strain measure is used in the strain energy function. The quadrilateral element is developed using displacements interpolation and interpolation of the Hencky strain tensor covariant components. A consistent linearization is developed, obtaining a symmetric stiffness matrix.