广义多相固体是指基体中含有异质体，即含有不同几何形状的增强相、夹杂、孔洞甚至裂纹（在几何上裂纹可视为退化的孔洞）的固体材料，广义相占据的区域定义为子域。遵循Eshelby的思路，抛弃子域本征应变为常量的假定，建立本征变量边界积分方程的计算模型。通过近场群和远场群的划分及合理有效的离散方式，以全新的方式构建反映近场群内在特性和子域相互作用的局部Eshelby矩阵，研究反映远场群影响的数值迭代算法。发展计算精度与效率统一的、能够兼顾局部细节与整体性能的高性能计算方法，实现广义多相固体材料的大规模数值模拟与性能表征。通过计算分析，探讨广义多相固体细观结构参数与整体性能的关系，考察代表性体积单元（RVE）的选择与材料结构多尺度特性的关系，为实现材料性能的研究、预报与元器件结构设计的集成打下基础，促进计算材料科学及相关领域的发展和工程应用。

The generalized multi-phase solids in this application denote the solid materials containing inhomogeneity including reinforcements, inclusions, cavities, etc. with various geometric shapes or crack (a crack can be looked as a degraded cavity). The subdomain is defined as the zone occupied by the multi-phase. Following Eshelby’s idea and by getting rid of the assumption of constant eigenstrains, the computational model of the eigen-variable boundary integral equations will be established. With the aid of dividing the subdomains into the near-field and the far-field groups using reasonable and effective discrete manners, construct the local Eshelby matrix in a new way, reflecting the intrinsic characteristics and mutual effects of subdomains of the near-field group. Study the numerical iteration procedures reflecting the effects of the far-field group. Based on them, develop the high-performance computational methods with both accuracy and efficiency to guarantee both the overall properties and local details to effectuate the large-scale numerical simulation and the property characterization of the generalized multi-phase solids. Through the analysis of computation, investigate the correlations between the meso-structural parameters and the overall properties as well as the correlations between the reasonable choice of the representative volume element (RVM) and the material characteristics with respect to the multi-scaled structures of the generalized multiphase materials. Lay a solid foundation to realize the integration between the research and prediction of materials property and the design of structural components to enhance the advances in the computational materials sciences and their application in engineering.