Finite element analysis of textured materials

The rate-independent formulation of crystal plasticity based on yield surfaces with rounded-off corners is applied to the elastic-plastic FEM analysis of polycrystals. For an assumed finite element mesh of a macroscopic member, a number of crystalline grains are considered in a neighbourhood of each of the integration points. The approach enables analysis of an elastic-plastic behaviour of the material – on the macroscopic level, and a collateral texture development, and slip systems hardening – on the microscopic one. However, a large number of the considered grains require time-consuming computations. To speed up the calculations, the model of a textured continuum is introduced instead of that for the aggregate of grains. In this model, all local fields are continuous functions of six variables describing the position of a macroscopic point and the orientation of a microscopic crystalline frame. The FEM procedure is the same as that for the discrete model, but the number of numerical operations decreases about 50 times. The model is fully constrained, i.e. it works under the Taylor assumption, when the local deformation fields are the same as the global one.