Peridynamics is a nonlocal reformulation of classical continuum mechanics suitable for material failure and damage simulation. Governing equations in peridynamics are based on spatial&nbsp;integration rather than spatial&nbsp;differentiation, allowing natural representation of material discontinuities, such as cracks. Peridynamics is nonlocal since every point in a material body interacts with all other points in the body up to a finite distance, called the horizon. A meshfree approach was proposed in [1], which&nbsp;﻿discretizes peridynamic domains by a set of nodes, each associated with a nodal cell with a characteristic volume, leading to a particle-based description of continuum systems. The aforementioned integral operator is also discretized as a finite sum over the discretization nodes and their associated cell volumes are employed as quadrature weights. This meshfree discretization approach is simple, computationally efficient compared to other discretization approaches, and has been demonstrated to be an effective discretization method for large-scale engineering simulations, particularly those involving large deformation and complex fractures. However, this approach has been shown to suffer from convergence issues in static simulations and simulations of dynamic wave propagations. In particular, oscillations were observed in the convergence behaviour of the discrete meshfree system to the nonlocal continuum solution. Such oscillatory behaviour was linked to the quadrature error associated with the use of the nodal volumes for the numerical quadrature of the integral operator. For the above-mentioned class of problems, then, mitigation strategies such as the use of smoothly-decaying influence functions and the so-called partial volume approaches lead to improved convergence behaviour. Nonetheless, a robust quantitative assessment of the performance of this meshfree method, particularly in fracture scenarios, is lacking. In [2], the convergence of meshfree numerical solutions of static peridynamic problems has been investigated. Related convergence studies for peridynamic wave propagation problems appeared in [3]. In this talk, we will discuss recent convergence studies of wave propagation and extensions to dynamic crack propagation in meshfree peridynamic simulations, under different choices of influence functions and integration weights.References[1] S. A. Silling and E. Askari, A meshfree method based on the peridynamic model of solid&nbsp;mechanics, Computers &amp; Structures, 83, 1526-1535, 2005.[2] P. Seleson and D. J. Littlewood, Convergence studies in meshfree peridynamic simulations,&nbsp;Computers and Mathematics with Applications, 71, 2432-2448, 2016.[3] P. Seleson and D. J. Littlewood, Numerical tools for improved convergence of meshfree&nbsp;peridynamic discretizations, in Handbook of Nonlocal Continuum Mechanics for Materials&nbsp;and Structures, G.Voyiadjis (ed.), Springer, Cham, 2018.

Convergence Studies in Meshfree Peridynamic Wave and Crack Propagation

Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2021/volume/85543

ASME 2021 International Mechanical Engineering Congress and Exposition (IMECE2021)

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