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

The present paper is concerned with an e cient framework for a nonlinear nite element procedure for the rate-independent nite 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 de nition 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 nite elements which guarantee the accurate computation of isochoric strains. The mixed-variant logarithmic elastic strain tensor provides a basis for the de nition 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 ow rule. On the numerical side, the computation of the logarithmic strain tensors is based on higher-order Pad e approximations. To be able to take into account the plastic incompressibility constraint a modi ed mixed variational principle is considered which leads to a quasi-displacement nite element procedure. Finally, the numerical solution of nite strain elasticplastic problems is presented to demonstrate the e ciency and the accuracy of the algorithm