A computational framework for microstructural modelling of polycrystalline materials with damage and failure

TL;DR

This thesis presents a novel boundary element method framework for simulating microstructural deformation and damage in polycrystalline materials, effectively capturing non-linear failure mechanisms with reduced computational cost.

Contribution

It introduces a compact integral kernel formulation and a specialized meshing strategy for efficient, accurate analysis of anisotropic polycrystalline microstructures using BEM.

Findings

Effective modeling of inter-granular and trans-granular cracking.

Reduced degrees of freedom compared to FEM approaches.

Demonstrated capability to simulate complex failure mechanisms.

Abstract

In the present thesis, a computational framework for the analysis of the deformation and damage phenomena occurring at the micro-scale of polycrystalline materials is presented. Micro-mechanics studies are commonly performed using the Finite Element Method (FEM) for its versatility and robustness. However, finite element formulations usually lead to an extremely high number of degrees of freedom of the considered micro-structures, thus making alternative formulations of great engineering interest. Among the others, the Boundary Element Method (BEM) represents a viable alternative to FEM approaches as it allows to express the problem in terms of boundary values only, thus reducing the total number of degrees of freedom. The computational framework developed in this thesis is based on a non-linear multi-domain BEM approach for generally anisotropic materials and is devoted to the analysis of three-dimensional polycrystalline microstructures. Different theoretical and numerical aspects of the polycrystalline problem using the boundary element method are investigated: first, being the formulation based on a integral representation of the governing equations, a novel and more compact expression of the integration kernels capable of representing the multi-field behaviour of generally anisotropic materials is presented; second, the sources of the high computational cost of polycrystalline analyses are identified and suitably treated by means of different strategies including an ad-hoc grain boundary meshing technique developed to tackle the large statistical variability of polycrystalline micro-morphologies; third, non-linear deformation and failure mechanisms such as inter-granular and trans-granular cracking and generally anisotropic crystal plasticity are studied and the numerical results presented throughout the thesis demonstrate the potential of the developed framework.