NURBS plasticity: non-associated plastic flow

Abstract

This paper extends the non-uniform rational basis spline (NURBS) plasticity framework of Coombs et al. (2016) and Coombs and Ghaffari Motlagh (2017) to include non-associated plastic flow. The NURBS plasticity approach allows any smooth isotropic yield envelope to be represented by a NURBS surface whilst the numerical algorithm (and code) remains unchanged. This paper provides the full theoretical and algorithmic basis of the non-associated NURBS plasticity approach and demonstrates the predictive capability of the plasticity framework using both small and large deformation problems. Wherever possible errors associated with the constitutive formulation are specified analytically and if not numerical analyses provide this information. The rate equations within the plasticity framework are integrated using an efficient and stable implicit stress update algorithm which allows for the derivation of the algorithmic consistent tangent which ensures optimum convergence of the global out of balance force residual when used in boundary value simulations. The important extension provided by this paper is that the evolution of plastic strain is decoupled from the yield surface normal. This allows the framework to model more realistic material behaviour, particularly in the case of frictional plasticity models where an associated flow rule is known to significantly overestimate volumetric dilation leading to spurious results. This paper therefore opens the door for the NURBS plasticity formulation to be used for a far wider class of material behaviour than is currently possible.