Hp-Meshless Cloud Method for Dynamic Fracture in Fluid Structure Interaction

COMCO proposes to develop a new, meshless computational methodology for dynamic fracture simulation in fluid-structural interaction. Our approach is based on a new class of methods which eliminate all need for computational mesh of finite elements. This is accomplished by covering the computational domain by a cloud of points and using these points for discretiz- ation of the mathematical problem. We will introduce h-andp-adaptivity, where new points will be adaptively added and removed in the domain, and the local order of approximation will be adaptively selected to assure high accuracy of approximation near the crack tip. This new approach will eliminate classical restrictions on modeling of crack propagation imposed by the finite element methods, where cracks can only propagate along element boundaries. Moreover, by introducing adaptiv- ity, it will allow for accurate resolution of stress around the crack tip and tracking of crack propagation. Importantly, the method will allow for a high degree of parallelization on MPP machines. In Phase I we will extend the meshless computational capabilities exist- ing at COMCO to hp-adaptive modeling of crack propagation problems in two- dimensional domains. We will explore and compare various methods of meshless discretization, and select an approach optimal for fracture problems. Also, we will develop a research-type code and allow for coupling with existing hydrodynamic software used for prediction of dynamic loading. We will perform relevant numerical computations to demonstrate viability of the new technology. The results of Phase I will be a basis for the Phase II effort, which will extend these capabilties to three-dimensional problems (including shells), full dynamic solutions, large-scale problems and various types of crack propagation criteria.