Convergence results for finite element and finite difference approximation of nonlocal fracture models
Abstract
We consider a nonlocal fracture model and study the convergence properties of the finite element and the finite difference approximation. The model is a nonlinear state-based peridynamic model. We show the well-posedness of the model and show a priori convergence rate for the finite element and the finite difference approximation. We perform numerical experiments with fracture and numerically compute the rate of convergence. We show the good agreement between theoretical convergence rate and numerically computed convergence rate. The peridynamic model is designed such that the nonlocal fracture energy and the classical Griffith’s fracture energy agree for any given size of horizon. This is demonstrated through numerical examples.
Prashant K. Jha
Assistant Professor
My research uses mechanics, applied mathematics, and computational science to understand and represent the complex behavior of materials, e.g., multiphysics effects in materials, material damage, crack propagation, and high-fidelity simulation of granular media involving arbitrarily shaped particles and particle breakage. My interests include the mechanics of smart materials, focusing on functional soft and granular materials.