Finite element computation of discrete configurational forces in crystal plasticity

Abstract

In this contribution the theory of configurational forces is applied to a viscoplastic material model with plastic slip in the basal and prismatic slip systems of an hcp crystal structure. Thereby the derivation of the configurational force balance is related to a translational invariance of the underlying energetics. The computation of configurational forces in this dissipative media requires the computation of gradients of the internal variables. In the context of the finite element method, this usually requires a projection of integration point data to the global mesh nodes. Alternatively, the gradients can be computed using a rather unknown subelement technique. The numerical accuracy of the different methods is qualitatively and quantitatively analyzed from a configurational force point of view. In a final example, the influence of the crystal orientation and plastic slip in multiple slip systems on the loading of a mode I crack is discussed with the help of the computed configurational forces. Furthermore, the influence of hardening is considered in this scenario.