Simulation of Cracks in a Cosserat Medium using the eXtended Finite Element Method

Abstract

This research investigates fracture behaviour in the Cosserat materials. The Cosserat elasticity description of the materials incorporates a characteristic length scale (e.g. grains, particles, fibres, etc.) into the model. The characteristic length scale in such materials is known to significantly influence the macroscopic behaviour of the whole body. Simulation of the fracture processes, such as crack opening and propagation, in Cosserat materials still remains a challenge for the scientific community. The goal of this thesis is to propose and validate a two dimensional extended finite element method model of edge cracks within the Cosserat elasticity theory framework.

The crack modelling was conducted using the Finite Element Method (FEM) and eXtended Finite Element Method (XFEM) implemented in the Matlab code. The strong and weak formulations of the problem and the discrete XFEM equations are presented in the thesis. Mode I and II edge crack models in a Cosserat medium are discussed and verified through a series of patch and convergence tests. In addition, the numerical evaluation of the J-integral for the Cosserat medium is presented, and the J-integral for the Cosserat medium is compared to the J-integral for the classical elasticity.

The XFEM/Cosserat method is shown to be robust and able to effectively model the edge crack problems in a Cosserat medium. Moreover, the Cosserat elastic parameter is found to be a powerful coupling tool between the microrotations and the translations. The Cosserat J-integral differs from the classical J-integral by 2% to 40%, for a given crack depending on the micropolar elastic coupling constant.