Finite element implementation of a generalised non-local rate-dependent crystallographic formulation for finite strains

This work describes the finite element implementation of a generalised stra in gradient and rate-dependent crystallographic formulation for finite stra ins and general anisothermal conditions based on a multiplicative decomposi tion of the deformation gradient. The implementation involved the developme nt of both a novel finite element formulation to determine the spatial slip rate gradients at each material point, and an implicit numerical integrati on scheme at the constitutive level to update the stresses and solution dep endent variables. The time-integration procedure uses a Newton-Raphson sche me with a single level of iteration to solve the incremental non-linear equ ations associated with the non-local constitutive formulation. Closed-form solutions for the relevant fourth-order Jacobian tensors are given. The pro posed numerical scheme is formulated in a general form and hence should be applicable to most existing crystallographic models. The crystallographic f ormulation is then used to investigate the effect of the morphology and vol ume fraction of the reinforcing phase of a two-phase single crystal on its macroscopic behaviour. (C) 2001 Published by Elsevier Science Ltd.