Material plasticity – Development of stiffness tetrads in fiber‐reinforced materials with large plastic deformations

Abstract

AbstractThe main objective of this work is to follow the evolution of the stiffness tetrad during large plastic strains. For this purpose, the framework of a general theory of finite plasticity is developed. Some special cases are investigated and the case of a material plasticity theory is considered in more detail. Its main feature is that the elasticity law changes during plastic deformations, for which we develop an approach. We use three types of fiber‐reinforced composites as example materials. Finite element simulations of representative volume elements for uni‐, bi‐ and tri‐directionally reinforced materials with periodic boundary conditions are used for numerical experiments and verification of the model's predictions. From these, we extract the stiffness tetrads before and after large deformations of the material. We quantify the change in stiffness tetrads due to fiber reorientation. Finally, we propose an analytical evolution with three parameters that reproduces reasonably well the evolution of the stiffness tetrads.