Formulation and numerical treatment of incompressibility constraints in large strain elastic-plastic analysis

Abstract

The present paper is concerned with an efficient framework for a nonlinear finite element procedure for the rate-independent finite strain analysis of solids undergoing large elastic-isochoric plastic deformations. The formulation relies on the introduction of a mixed-variant metric deformation tensor which will be multiplicatively decomposed into a plastic and an elastic part. This leads to the definition of an appropriate logarithmic strain measure which can be additively decomposed into the exact isochoric (deviatoric) and volumetric (spheric) strain measures. This fact may be seen as the basic idea in the formulation of appropriate mixed finite elements which guarantee the accurate computation of isochoric strains. The mixed-variant logarithmic elastic strain tensor provides a basis for the definition of a local isotropic hyperelastic stress response whereas the plastic material behavior is assumed to be governed by a generalized J2 yield criterion and rate-independent isochoric plastic strain rates are computed using an associated flow rule. On the numerical side, the computation of the logarithmic strain tensors is based on higher-order Pade approximations. To be able to take into account the plastic incompressibility constraint a modified mixed variational principle is considered which leads to a quasi-displacement finite element procedure. Finally, the numerical solution of finite strain elastic-plastic problems is presented to demonstrate the efficiency and the accuracy of the algorithm. Copyright © 1999 John Wiley & Sons, Ltd.