多晶材料损伤和失效微结构模拟的计算框架
A computational framework for microstructural modelling of polycrystalline materials with damage and failure
摘要：
在本论文中，提出了一个用于分析多晶材料在微观尺度上的变形和损伤现象的计算框架。由于有限元法的通用性和鲁棒性，通常使用该方法进行细观力学研究。然而，有限元公式通常会导致所考虑的微结构的自由度非常高，从而使得替代公式具有很大的工程意义。其中，边界元法（BEM）代表了FEM方法的可行替代方案，因为它允许仅用边界值来表达问题，从而减少了自由度的总数。本论文的计算框架是基于一般各向异性材料的非线性多域边界元方法，并致力于分析三维多晶微结构。本文研究了多晶问题边界元法的不同理论和数值方面的问题：首先，基于控制方程的积分表示，提出了一种新的、更紧凑的积分核表达式，它能够表示一般各向异性材料的多场行为;第二，多晶分析的高计算成本的来源通过不同的策略被识别和适当地处理，开发特殊的晶界网格技术来解决多晶微观形态的巨大统计变异性;第三，非线性变形和破坏机制，如晶间和跨-颗粒裂纹和一般各向异性晶体塑性进行了研究，整个论文的数值结果表明，发展框架。
英文摘要：
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.
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