A hybrid meshfree discretization to improve the numerical performance of peridynamic models

Journal Article · 16 January 2022 · Computer Methods in Applied Mechanics and Engineering

DOI: https://doi.org/10.1016/j.cma.2021.114544 · OSTI ID:1841481

Shojaei, Arman  ^[1]; Hermann, Alexander ^[1]; Cyron, Christian J.  ^[2]; Seleson, Pablo  ^[3]; Silling, Stewart A. ^[4]

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1. Helmholtz-Zentrum Hereon, Geesthacht (Germany). Inst. of Material Systems Modeling
2. Helmholtz-Zentrum Hereon, Geesthacht (Germany). Inst. of Material Systems Modeling; Hamburg Univ. of Technology (Germany). Inst. of Continuum and Material Mechanics
3. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
4. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Center for Computing Research

Efficient and accurate calculation of spatial integrals is of major interest in the numerical implementation of peridynamics (PD). The standard way to perform this calculation is a particle-based approach that discretizes the strong form of the PD governing equation. This approach has rapidly been adopted by the PD community since it offers some advantages. Additionally, it is computationally cheaper than other available schemes, can conveniently handle material separation, and effectively deals with nonlinear PD models. Nevertheless, PD models are still computationally very expensive compared with those based on the classical continuum mechanics theory, particularly for large-scale problems in three dimensions. This results from the nonlocal nature of the PD theory which leads to interactions of each node of a discretized body with multiple surrounding nodes. Here, we propose a new approach to significantly boost the numerical efficiency of PD models. We propose a discretization scheme that employs a simple collocation procedure and is truly meshfree; i.e., it does not depend on any background integration cells. In contrast to the standard scheme, the proposed scheme requires a much smaller set of neighboring nodes (keeping the same physical length scale) to achieve a specific accuracy and is thus computationally more efficient. Our new scheme is applicable to the case of linear PD models and within neighborhoods where the solution can be approximated by smooth basis functions. Therefore, to fully exploit the advantages of both the standard and the proposed schemes, a hybrid discretization is presented that combines both approaches within an adaptive framework. The high performance of the developed framework is illustrated by several numerical examples, including brittle fracture and corrosion problems in two and three dimensions.

• Research Organization: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)
• Sponsoring Organization: USDOE; German Research Foundation (DFG)
• Grant/Contract Number: AC05-00OR22725
• OSTI ID: 1841481
• Journal Information: Computer Methods in Applied Mechanics and Engineering, Journal Name: Computer Methods in Applied Mechanics and Engineering Journal Issue: N/A Vol. 391; ISSN 0045-7825
• Publisher: ElsevierCopyright Statement
• Country of Publication: United States
• Language: English