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Title: An asymptotically compatible treatment of traction loading in linearly elastic peridynamic fracture

Abstract

Meshfree discretizations of state-based peridynamic models are attractive due to their ability to naturally describe fracture of general materials. However, two factors conspire to prevent meshfree discretizations of state-based peridynamics from converging to corresponding local solutions as resolution is increased: quadrature error prevents an accurate prediction of bulk mechanics, and the lack of an explicit boundary representation presents challenges when applying traction loads. Herein, we develop a reformulation of the linear peridynamic solid (LPS) model to address these shortcomings, using improved meshfree quadrature, a reformulation of the nonlocal dilatation, and a consistent handling of the nonlocal traction condition to construct a model with rigorous accuracy guarantees. In particular, these improvements are designed to enforce discrete consistency in the presence of evolving fractures, whose a priori unknown location render consistent treatment difficult. In the absence of fracture, when a corresponding classical continuum mechanics model exists, our improvements provide asymptotically compatible convergence to corresponding local solutions, eliminating surface effects and issues with traction loading which have historically plagued peridynamic discretizations. When fracture occurs, our formulation automatically provides a sharp representation of the fracture surface by breaking bonds, avoiding the loss of mass. We provide rigorous error analysis and demonstrate convergence for amore » number of benchmarks, including manufactured solutions, free-surface, nonhomogeneous traction loading, and composite material problems. Finally, we validate simulations of brittle fracture against a recent experiment of dynamic crack branching in soda-lime glass, providing evidence that the scheme yields accurate predictions for practical engineering problems.« less

Authors:
 [1];  [1];  [2]
  1. Lehigh Univ., Bethlehem, PA (United States)
  2. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Publication Date:
Research Org.:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); USDOE National Nuclear Security Administration (NNSA); National Science Foundation (NSF)
OSTI Identifier:
1769919
Alternate Identifier(s):
OSTI ID: 1776288
Report Number(s):
SAND-2021-2115J
Journal ID: ISSN 0045-7825; 694002
Grant/Contract Number:  
AC04-94AL85000; NA0003525; DMS 1753031
Resource Type:
Accepted Manuscript
Journal Name:
Computer Methods in Applied Mechanics and Engineering
Additional Journal Information:
Journal Volume: 377; Journal ID: ISSN 0045-7825
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
42 ENGINEERING; Peridynamics; Neumann boundary condition; Fracture; Asymptotic compatibility; Meshfree method; Nonlocal models

Citation Formats

Yu, Yue, You, Huaiqian, and Trask, Nathaniel Albert. An asymptotically compatible treatment of traction loading in linearly elastic peridynamic fracture. United States: N. p., 2021. Web. doi:10.1016/j.cma.2021.113691.
Yu, Yue, You, Huaiqian, & Trask, Nathaniel Albert. An asymptotically compatible treatment of traction loading in linearly elastic peridynamic fracture. United States. https://doi.org/10.1016/j.cma.2021.113691
Yu, Yue, You, Huaiqian, and Trask, Nathaniel Albert. Tue . "An asymptotically compatible treatment of traction loading in linearly elastic peridynamic fracture". United States. https://doi.org/10.1016/j.cma.2021.113691. https://www.osti.gov/servlets/purl/1769919.
@article{osti_1769919,
title = {An asymptotically compatible treatment of traction loading in linearly elastic peridynamic fracture},
author = {Yu, Yue and You, Huaiqian and Trask, Nathaniel Albert},
abstractNote = {Meshfree discretizations of state-based peridynamic models are attractive due to their ability to naturally describe fracture of general materials. However, two factors conspire to prevent meshfree discretizations of state-based peridynamics from converging to corresponding local solutions as resolution is increased: quadrature error prevents an accurate prediction of bulk mechanics, and the lack of an explicit boundary representation presents challenges when applying traction loads. Herein, we develop a reformulation of the linear peridynamic solid (LPS) model to address these shortcomings, using improved meshfree quadrature, a reformulation of the nonlocal dilatation, and a consistent handling of the nonlocal traction condition to construct a model with rigorous accuracy guarantees. In particular, these improvements are designed to enforce discrete consistency in the presence of evolving fractures, whose a priori unknown location render consistent treatment difficult. In the absence of fracture, when a corresponding classical continuum mechanics model exists, our improvements provide asymptotically compatible convergence to corresponding local solutions, eliminating surface effects and issues with traction loading which have historically plagued peridynamic discretizations. When fracture occurs, our formulation automatically provides a sharp representation of the fracture surface by breaking bonds, avoiding the loss of mass. We provide rigorous error analysis and demonstrate convergence for a number of benchmarks, including manufactured solutions, free-surface, nonhomogeneous traction loading, and composite material problems. Finally, we validate simulations of brittle fracture against a recent experiment of dynamic crack branching in soda-lime glass, providing evidence that the scheme yields accurate predictions for practical engineering problems.},
doi = {10.1016/j.cma.2021.113691},
journal = {Computer Methods in Applied Mechanics and Engineering},
number = ,
volume = 377,
place = {United States},
year = {2021},
month = {2}
}

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