Anisotropic finite elastoplastic analysis of shells: simulation of earing in deep-drawing of single- and polycrystalline sheets by Taylor-type micro-to-macro transitions

Abstract

The paper presents new aspects of anisotropic elastoplastic analyses of shells at finite strains. On the side of the computational shell analysis we design a surface-orientated brick-type mixed finite shell element in a setting relative to the parameter space of the shell equipped with shell-typical assumed strain modifications and an additive definition of an enhanced current metric in the Lagrangian representation. For this element we outline an interface to strain-driven constitutive stress update algorithms of multiplicative plasticity for single crystals and polycrystals at finite strains. On the side of computational plasticity we outline details of a constitutive model for finite single crystal plasticity. Here, we consider a distinct incremental variational formulation of the local constitutive elasto–visco-plastic response of single crystals in a multisurface format, where a quasi-hyperelastic stress potential is obtained from a local minimization problem with respect to the internal variables. It is shown that this local minimization problem determines the internal state of the material for finite increments of time. The proposed nonlinear shell formulation is applied to the simulation of earing in deep-drawing of anisotropic sheets. We present finite element simulations of cup-drawings of f.c.c. single crystal sheets and previously rolled polycrystalline f.c.c. sheets. The anisotropic polycrystal is modeled by a Taylor-type texture analysis based on an assumed microstructure of single crystal grains. A comparison with experiments underlines the performance of the simulation.