A space-time discretization of a nonlinear peridynamic model on a 2D lamina

Peridynamics is a nonlocal theory for dynamic fracture analysis consisting in second order time partial integro-differential equation. In this paper, we consider nonlinear model of peridynamics two-dimensional spatial domain. We implement spectral method the space discretization based on Fourier expansion solution while Newmark-? marching. This computational approach takes advantages from convolutional form peridynamic operator and use discrete transform. show convergence result fully approximation study stability applied to linear model. Finally, perform several numerical tests comparisons validate our results provide simulations implementing volume penalization technique avoid limitation periodic boundary conditions due approach.