Finite elastic–plastic deformation behaviour of crystalline solids based on a non-associated macroscopic flow rule 1Paper presented at the Sixth International Symposium on Plasticity and Its Current Applications, Juneau, Alaska (U.S.A.), July 14–18, 1997. 1

Abstract

The present paper deals with a nonlinear finite element analysis of the macroscopic elastic–plastic deformation and localization behaviour of crystalline solids. The description includes elastic strains arising from the distortion of the lattice as well as crystallographic deformations due to irreversible microscopic slip along preferred lattice planes and in corresponding lattice directions. In addition, the effect of plastic volume changes on the microstructure is taken into account. Macro- and microscopic stress measures are related to Green’s macroscopic strains via a hyperelastic constitutive law based on a free energy potential function, and the onset of plastic yielding on the microscale is described by a modified yield condition which includes appropriate microscopic stress components. To be able to compute inelastic deformations from plastic potentials, the latter are expressed in terms of work-conjugate microscopic stress and strain measures thus leading to a non-associated flow rule for the macroscopic plastic strain rate. The numerical integration of the rate formulation of the constitutive equations is performed using a plastic predictor-elastic corrector technique. Its implementation into a nonlinear finite element program is discussed, and numerical solutions of finite strain elastic-plastic boundary value problems involving highly localized deformations are presented. They demonstrate both the efficiency of the algorithm and the influence of various model parameters on the deformation and load-carrying behaviour of crystalline solids.