Finite-strain formulation and FE implementation of a constitutive model for powder compaction

Abstract

A finite-strain formulation is developed, implemented and tested for a constitutive model capable of describing the transition from granular to fully dense state during cold forming of ceramic powder. This constitutive model (as well as many others employed for geomaterials) embodies a number of features, such as pressure-sensitive yielding, complex hardening rules and elastoplastic coupling, posing considerable problems in a finite-strain formulation and numerical implementation. A number of strategies are proposed to overcome the related problems, in particular, a neo-Hookean type of modification to the elastic potential and the adoption of the second Piola-Kirchhoff stress referred to the intermediate configuration to describe yielding. An incremental scheme compatible with the formulation for elastoplastic coupling at finite strain is also developed, and the corresponding constitutive update problem is solved by applying a return mapping algorithm.