The National Natural Science Foundation of China, grant No. 11102036, 2012.1-2014.12
This project will be devoted to develop efficient high-order meshfree methods for the evolution from continuum to broken body in saturated porous media based on the Biot and Cosserat/Micro-polar theories. Its engineering background is the geological hazard/disaster such as landslides. The evolution is characterized by plasticity, damage, strain localization and fracture. The constitutive behavior of the porous media is described by elastic-plastic-damage model. The high order meshfree approximation is used to accurately capture the large deformation and high gradient field presented in the shear band. To improve the computational efficiency, this project will develop new methods to “correct” nodal derivatives for high order approximations such that the required number of quadrature points can be substantially decreased. The h-adaptivity for meshfree methods by simply inserting new nodes (not elements) will be implemented to resolve the shear band more efficiently. The fracture of the porous media is described by introducing discontinuity in meshfree approximation and using phantom node technique to avoid increasing the number of nodal degrees of freedom. This project will establish the framework of high-order meshfree methods for the Cosserat porous media with discontinuity and achieve the numerical simulation for the progressive failure in the saturated porous media.