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Title: Convergence studies in meshfree peridynamic simulations

Meshfree methods are commonly applied to discretize peridynamic models, particularly in numerical simulations of engineering problems. Such methods discretize peridynamic bodies using a set of nodes with characteristic volume, leading to particle-based descriptions of systems. In this article, we perform convergence studies of static peridynamic problems. We show that commonly used meshfree methods in peridynamics suffer from accuracy and convergence issues, due to a rough approximation of the contribution to the internal force density of nodes near the boundary of the neighborhood of a given node. We propose two methods to improve meshfree peridynamic simulations. The first method uses accurate computations of volumes of intersections between neighbor cells and the neighborhood of a given node, referred to as partial volumes. The second method employs smooth influence functions with a finite support within peridynamic kernels. Numerical results demonstrate great improvements in accuracy and convergence of peridynamic numerical solutions, when using the proposed methods.
 [1] ;  [2]
  1. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
  2. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Publication Date:
Report Number(s):
Journal ID: ISSN 0898-1221; PII: S0898122115005891
Grant/Contract Number:
AC04-94AL85000; AC05-00OR22725; ERKJE45
Accepted Manuscript
Journal Name:
Computers and Mathematics with Applications (Oxford)
Additional Journal Information:
Journal Name: Computers and Mathematics with Applications (Oxford); Journal Volume: 71; Journal Issue: 11; Journal ID: ISSN 0898-1221
Research Org:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Sponsoring Org:
USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)
Country of Publication:
United States
97 MATHEMATICS AND COMPUTING; peridynamics; meshfree method; convergence; partial volumes; influence functions
OSTI Identifier:
Alternate Identifier(s):
OSTI ID: 1311292; OSTI ID: 1351648