Reducing computational efforts in linear and nonlinear analysis of peridynamic models under impact loads

Peridynamic theory with a new formulation in the equations of motion, replaces the partial differential equations with integral equations. Due to this capability, it is possible to model crack initiation in any direction without the need to consider crack-growth criteria. One of the main problems in peridynamic theory is its high computational efforts due to its dynamic nature. If the critical time step of the numerical integration is greater than the loading time step, it will increase the cost of calculations. In this paper, using wavelet transform, peridynamic problems under irregular and random impact loads are analyzed. The aim of this study is to increase the computational speed for these problems. The method presented in this paper is investigated on two material models, namely Prototype brittle material and micro-plastic material. In this regard, structures with linear and nonlinear behavior have been analyzed considering the effects of discontinuities (such as cracks) and without considering the effects of discontinuities. The selected structures include two beams. Each beam is subjected to two types of irregular impact loading. The beams are analyzed once with the main impact (wave) function and once with the approximate impact (waves) functions obtained using wavelet transform. Based on the results of linear and nonlinear analyses of this study, it can be judged that the presented method reduces the computational cost by 87% in perdynamic models with linear behavior. It also bring a 94% reduction in computational costs in predynamic models with nonlinear behavior.