A large-deformation multiplicative framework for anisotropic elastoplastic materialswith application to sheet metal forming

Abstract

In this work, we discuss the derivation and the numerical implementation of a finite strain material model for plastic anisotropy and nonlinear kinematic and isotropic hardening. The model is derived in a thermodynamic setting and is based on the multiplicative split of the deformation gradient in the context of hyperelasticity. Introducing the socalled structure tensors as additional tensor-valued arguments, plastic anisotropy can bemodelled by representing the yield surface and the plastic flow rule as functions of the structure tensors. The evolution equations are integrated by a recentlydeveloped form of the exponential map that preserves plastic incompressibility and uses the spectral decomposition to evaluate the exponential tensor functions in closed form. The model has been validated based on experimental data and its applicability for earing prediction has been demonstrated by performing simulations of cylindrical cup drawing and comparisons with experiments.