A collocation approach for spatial discretization of stochastic peridynamic modeling of fracture

Abstract

In this paper a collocation approach is presented for spatial discretization of the partial integrodifferential equation arising in a peridynamic formulation in stochastic fracture mechanics. In the formulation nodes are distributed inside the domain forming a grid, and the inverse multiquadric radial basis functions are used as interpolation functions inside the domain. Due to this discretization the peridynamic stiffness is generated in a manner similar to the finite element method. Further, any discontinuity in the domain is included in this discretized form and affects only the peridynamic stiffness of the adjacent nodes. Using this approach as a tool, the probability density function of the energy release rate can be determined at a given crack tip point for all possible crack paths. Thus, the crack propagation direction can be probabilistically identified. This is accomplished by numerical evaluation of the requisite Neumann expansion using pertinent Monte Carlo simulations. Specific examples of applications are included. © 2011 by Mathematical Sciences Publishers.