Numerical Methods for the Stochastic Nonlocal Model – Peridynamics Model for Mechanics

Abstract

Mathematical modeling and computer simulations are nowadays widely used tools for the prediction of the behavior of scientific and engineering systems. Our interest is in how uncertainty propagates through the recently developed nonlocal, derivative free, continuum peridynamics model for material mechanics. In con- trast to classical partial differential equation models, peridynamics is an integro- differential equation that does not involve spatial derivatives of the displacement field. We focus on the peridynamics model whose forcing terms are described by a finite-dimensional random vector, which is often called finite-dimensional noise assumption. Numerical methods based on this stochastic peridynamics model are implemented. Preliminary results for the one-dimensional problem will be pro- vided and compared.