Evolution of the stiffness tetrad in fiber-reinforced materials under large plastic strain

Holm Altenbach,Rainer Glüge,Martin Weber

doi:10.1007/s00419-020-01827-8

Abstract

The main aim of this work is to track the evolution of the stiffness tetrad during large plastic strain. Therefore, the framework of a general finite plasticity theory is developed. Some special cases are examined, and the case of a material plasticity theory is considered more closely. Its main feature is that the elasticity law changes during plastic deformations, for which we develop an approach. As sample materials, we use three types of fiber-reinforced composites. For numerical experiments and verification of the model’s predictions, finite element simulations of representative volume elements for uni-, bi- and tri-directional reinforced materials with periodic boundary conditions are used. From these, we extract the stiffness tetrads before and after large deformations of the material. We quantify the change of the stiffness tetrads due to the fiber reorientation. Finally, we propose an analytical evolution with three parameters that account reasonably well for the evolution of the stiffness tetrad.

Highlights

The objective of this article is to develop a phenomenological finite plasticity theory which describes the evolution of the elastic anisotropy
The results show that the stiffness tetrad changes significantly, and that this change cannot be predicted by the plastic transformation PC of the isomorphy concept
We start with the multiplicative decomposition of the deformation gradient

Summary

Introduction

The objective of this article is to develop a phenomenological finite plasticity theory which describes the evolution of the elastic anisotropy. We use a linear law for the elastic part of our modeling approach. This is reasonable because the focus of this work lies in the evolution of anisotropic behavior during large plastic deformations. One can resort to a single crystal elasticity reference law and needs to consider only orientation changes, summarized as texture evolution in polycrystals. The crystal orientation distribution evolves due to the lattice spin, and the effective elasticity is estimated by orientation averages of the single crystal stiffness. For this setting, textbook knowledge is available, e.g., [8,25,27]

Objectives

Results

Conclusion