ANALYSIS OF MESH DEPENDENCE IN RIGID COHESIVE INTERFACE FINITE ELEMENT MODELS

摘要

We consider the use of initially rigid cohesive interface models in a dynamic finite element solution of a fracture process. Our focus is on convergence of finite element solutions using rigid cohesive interfaces to a continuum solution as the mesh spacing △x (and therefore time step △t) tends to zero. We present pinwheel meshes, which possess the "isoperimetric property" that for any curve C in the computational domain, there is an approximation to C using mesh-cell edges that tends to C including a correct representation of its length, as the grid size tends to zero. We suggest that the isoperimetric property is a necessary condition for any possible spatial convergence proof in cohesive zone modeling in the general case that the crack path is not known in advance. Conversely we establish that if the pinwheel mesh is used, the discrete interface first activated in the finite element model will converge (as the mesh size tends to zero) to the continuum initial crack. We carry out mesh refinement experiments to check convergence of both nucleation and propagation. Our preliminary results indicate that the crack path computed in the pinwheel mesh is more stable as the mesh is refined compared to other types of meshes.