A ten node tetrahedral Macro-Cosserat Point Element (MCPE): Part II: Nonlinear elastic-viscoplastic materials

Abstract

Abstract In Part I of this two-part paper, a Macro-Cosserat Point Element (MCPE) was developed based on a Lagrangian formulation of a ten node macro-tetrahedral element. The MCPE provides ten nodal forces as functions of ten nodal positions, similar to standard finite elements. In previous work, it has been shown that a Eulerian formulation of plasticity can remove unphysical arbitrariness of the reference configuration, an intermediate configuration, total deformation measures and plastic deformation measures that are used in the standard Lagrangian formulation of plasticity. The main objective of this Part II is to develop a Eulerian formulation of the MCPE which is implemented for elastic-viscoplastic response. The resulting MCPE satisfies a nonlinear form of a patch test for plasticity. The examples in Parts I and II of this paper indicate that the MCPE is a robust element that can be used with confidence for modeling general material response.