William Prager Professor, Department of Structural Engineering
Director, Center for Extreme Events Research
The failure processes in the materials exhibit distinct characteristics depending on the material ductility, the loading rate, and the environmental conditions. The mathematical models and the associated numerical methods for describing the material failure processes can be classified as the discrete description based on fracture mechanics and the continuum phenomenological description based on damage mechanics. This work first discusses how damage mechanics based models can be formulated by the homogenization of fracture models. The challenges in the numerical approximation and discretization of failure modeling based on fracture mechanics and damage mechanics will then be addressed. The mesh dependent issue in the micro-crack informed damage model remedied by the implicit gradient regularization or scaling laws under the Reproducing Kernel Particle Method (RKPM) will introduced, and stability and convergence of the proposed numerical methods will be discussed. The application of the meshfree RKPM formulation for fracture to damage multiscale mechanics and materials modeling, and their applications to the modeling of extreme events, will be demonstrated. These include the modeling of man-made disasters such as fragment-impact processes, penetration, shock and blast events, as well as natural disasters such as landslide will be presented to demonstrate the effectiveness of the new developments.