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.

Date
Oct 6, 2018 12:00 AM
Event
SIAM TX LA Meeting 2018
Location
Baton Rouge, USA
Prashant K. Jha
Prashant K. Jha
Research Associate

My research is driven by the application of mathematics and computational science to present-day relevant and challeng- ing problems. Specific areas of interest include mechanics of solids and granular media, computational oncology, and multiscale modeling.