含界面相的颗粒增强复合材料裂纹损伤分析的多相Voronoi单元有限元方法研究

研究含界面相颗粒增强复合材料（PRCS）的裂纹损伤行为是细观力学的前沿研究。由于采用传统有限元建模，界面相薄层导致纤维和基体的单元数量巨大，无法计算含大量夹杂的复合材料，因此构建含界面相的裂纹损伤模型并高效模拟计算真实材料至关重要。本项目拟依据界面裂纹向基体转化贯穿的机理，建立同时包含颗粒相、界面相、基体相和裂纹的细观模型，推导新泛函，提出含有界面相并能够刻划裂纹萌生扩展的新型多相Voronoi单元有限元法（VCFEM）。构建裂纹由一个单元向另一个单元扩展的网格重划分方法，分析PRCS界面相及细观裂纹的空间分布对材料局部损伤破坏和宏观特性的影响，并利用新方法探讨含大量夹杂的PRCS在复杂载荷下的损伤破坏机理。研究结果将为PRCS的优化设计提供指导。

Research on the behavior of cracked particles-reinforced composites (PRCS) with interphase is important in mesomechanics. Owing to the thin interphase of the traditional finite element model, the number of fiber and matrix elements is large, which makes it challenging to calculate composite materials with a large number of inclusions. Therefore, it is important to construct a crack damage model with interphase to simulate the behavior of materials. Based on the mechanism of the transformation from interfacial cracks propagated into the matrix, this project proposes a mesoscopic model containing particle phases, interface phases, matrix phases, and cracks, derives functionals, and develops a multiphase Voronoi element finite element method (VCFEM) featuring the interphase to describe crack initiation and propagation. A mesh repartition method for crack propagation from one element to another is also established. The effects of the interphase of PRCS, and the spatial distribution of mesoscopic cracks on local damage to the material and its macroscopic characteristics are analyzed. The proposed method is used to explore the mechanisms of damage to and failure of PRCS featuring a large number of inclusions under complex loads. The results of this study can help guide the optimal design of PRCS.