Investigation of different influence functions in peridynamics

Peridynamics is a non–local numerical method for solving fracture problems based on integral equations. It is assumed that particles in a continuum are endowed with volume and interact with each other at a finite distance, as in molecular dynamics. The influence function in peridynamic models is used to limit the force acting on a particle and to adjust the bond strength depending on the distance between the particles. It satisfies certain continuity conditions and describes the behavior of non-local interaction. The article investigates various types of influence function in peridynamic models on the example of three-dimensional problems of elasticity and fracture. In the course of the work done, the bond-based and state-based fracture models used in the Sandia Laboratory are described, 6 types of influence functions for the bond-based model and 2 types of functions for the state-based model are presented, and the corresponding formulas for calculating the stiffness of the bond are obtained. For testing, we used the problem of propagation of a spherically symmetric elastic wave, which has an analytical solution, and a qualitative problem of destruction of a brittle disk under the action of a spherical impactor. Graphs of radial displacement are given, raster images of simulation results are shown.