Numerical fracture experiments using nonlinear nonlocal models

Abstract

We consider a nonlinear peridynamic model and study the fracture dynamics in materials. The model is regularized fracture model and is shown to be wellposed over the space of Hölder continuous functions and the Sobolev space for the appropriate initial conditions and the body forces. The parameters in the model can be calibrated using the elastic properties and the critical energy release rate of a material. We present numerical results which highlight key features of the model. We show the linear rate of convergence, with respect to the mesh size, of finite difference approximation for crack propagation problem. The model is seen to capture the fracture energy accurately. We show that the fracture zone localizes as the nonlocal length scale is refined. Samples with notch and void show the nucleation of crack under different loading conditions. We conclude by talking briefly about our ongoing work on the coupling of local and nonlocal models.