On the comparison of two approaches to compute material forces for inelastic materials. Application to single-slip crystal-plasticity Original Research Article

The main goal of this contribution is the application of the material force method to dissipative materials whereby special emphasis is placed on the application to crystal-plasticity. Balance equations on the material manifold, as e.g. the material motion balance of momentum, generally necessitate the computation of the spatial gradient of additional internal degrees of freedom or rather internal variables. We therefore focus in this work on the comparison of two different numerical approaches to compute these gradient fields within a finite element setting, namely a node point based––and an integration point based formulation. Several numerical examples underline that the latter framework, which is the convenient, numerically comparatively cheap and well-established approach in computational inelasticity, turns out to be sufficiently accurate for the problem at hand.