本书全面系统地论述了材料性能多尺度分析方法与摄动展开渐进均匀化方法的基本理论，建立了以概率随机数值方法为基础的等效弹性力学性能分析方法实现过程，较为全面地实现了对材料二维、三维弹性应力场的随机模拟。另外，本书还探讨了多孔材料、多相复合材料随机等效弹性力学性能统计分布特征，并提出了其相应的模型。 本书适合作为普通高等学校力学专业或土木工程专业的教材，也可作为材料性能多尺度分析方法的参考书，还可供相关专业技术人员参考。

Chapter 1Overview 1.1Motivation 1.2Purpose and approach 1.3Organization of thesis Chapter 2Background and theoretical fundamentals 2.1Micromechanics of composite material 2.2Homogenization and localization theory 2.3Conventional heterogeneous material design 2.4Literature review on coated particulate composite material 2.4.1Application and characteristics performance 2.4.2Manufacturing 2.4.3Numerical approach for multiscale modeling Chapter 3Firstorder perturbation based probabilistic multiscale theory 3.1Introduction 3.2Problem setting of threephase composite material 3.3Firstorder perturbation based stochastic homogenization 3.4Computer implementation 3.5Simplification case of porous material 3.6Extensionof firstorder perturbation based stochastic homogenization to nphase constituent material Chapter 4Computational material design methods 4.1Introduction 4.2Parameterization modeling 4.3Probabilistic sensitivity considering manufacturing based random field modeling 4.4Update of prediction Chapter 5Numerical example for coated particulate composite material 5.1Introduction 5.2Microstructure generation algorithm for coated particulate composite material 5.3Result and discussion on probabilistic homogenized property for coated particulate composite material 5.4Result and discussion on probabilistic sensitivity for coated particulate composite material Stochastic Multiscale Simulation Method and Application for Composite Material Chapter 6Numerical example for spherical porous material 6.1Introduction 6.2Numerical example setting for spherical porous material 6.3Microstructure generation algorithm 6.4Regression curve of probabilistic homogenized elastic property for spherical porous material 6.5Update of prediction by experimental data Chapter 7Numerical example for lattice structure by selective laser sintering 7.1Introduction 7.2Definition of lattice structure and process parameters of selective laser sintering 7.3Geometrical imperfections 7.4Compression test 7.5Stochastic homogenization analysis and discussion 7.5.1Firstorder perturbation based stochastic homogenization method 7.5.2Statistical finite element models with geometrical imperfections 7.5.3Numerical results and discussion Chapter 8Discussions on theoretical framework of firstorder perturbation based stochastic homogenization method 8.1Findings 8.2List of assumptions and limitations 8.3Future works 8.3.1Potential application to Fiber reinforced plastics 8.3.2Extension touncertainty propagation 8.3.3Reduction of computational time Appendix ANomenclature Appendix BMicroscopic stress analysis and verification of probabilistic sensitivity for strength prediction of coated particulate composite material Appendix CMicroscopic stress concentration check for spherical porous material Reference