Main topics of the project include: 1) Framework of symplectic theory and the corresponding computational algorithm. 2) Molecular dynamics method to investigate nanometer-scale interfacial mechanical behavior and interfacial failure and fracture mechanisms of composite materials. 3) Multiscale method for nonlinear analysis of heterogeneous materials and the higher order computational theory and model for failure prediction of materials based on the modern mechanics theory. 4) Integrated design optimization of materials and structures, numerical modeling and design optimization for composite materials and structural systems considering interrelations of meso-macro scale with multi-physics coupling effects. 5) Effective numerical algorithm and technique for the development of large scale software system in engineering science computation.