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Volume 32, Issue 5
New Insights on Convergence Properties of Peridynamic Models for Transient Diffusion and Elastodynamics

Zhikun Zhou, Xuhao Peng, Pan Wu, Ziguang Chen & Florin Bobaru

DOI: 10.4208/cicp.OA-2022-0080

Commun. Comput. Phys., 32 (2022), pp. 1257-1286.

Published online: 2023-01

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  • Abstract

Recent analytical solutions for peridynamic (PD) models of transient diffusion and elastodynamics allow us to revisit convergence of 1D PD models to their classical counterparts. We find and explain the reasons for some interesting differences between the convergence behavior for transient diffusion and elastodynamics models. Except for very early times, PD models for transient diffusion converge monotonically to the classical one. In contrast, for elastodynamic problems this convergence is more complex, with some periodic/almost-periodic characteristics present. These special features are investigated for sine waves used as initial conditions. The analysis indicates that the convergence behavior of PD solutions to the classical one can be understood in terms of convergence properties for models using the Fourier series expansion terms of a particular initial condition. The results obtained show new connections between PD models and their corresponding classical versions.

  • Keywords

Convergence, peridynamics, nonlocal models, analytical solutions, transient diffusion, elastodynamics.

  • AMS Subject Headings

45K05, 65M12, 65M22, 74A70, 74H10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-32-1257, author = {Zhou , ZhikunPeng , XuhaoWu , PanChen , Ziguang and Bobaru , Florin}, title = {New Insights on Convergence Properties of Peridynamic Models for Transient Diffusion and Elastodynamics}, journal = {Communications in Computational Physics}, year = {2023}, volume = {32}, number = {5}, pages = {1257--1286}, abstract = {

Recent analytical solutions for peridynamic (PD) models of transient diffusion and elastodynamics allow us to revisit convergence of 1D PD models to their classical counterparts. We find and explain the reasons for some interesting differences between the convergence behavior for transient diffusion and elastodynamics models. Except for very early times, PD models for transient diffusion converge monotonically to the classical one. In contrast, for elastodynamic problems this convergence is more complex, with some periodic/almost-periodic characteristics present. These special features are investigated for sine waves used as initial conditions. The analysis indicates that the convergence behavior of PD solutions to the classical one can be understood in terms of convergence properties for models using the Fourier series expansion terms of a particular initial condition. The results obtained show new connections between PD models and their corresponding classical versions.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2022-0080}, url = {http://global-sci.org/intro/article_detail/cicp/21363.html} }
TY - JOUR T1 - New Insights on Convergence Properties of Peridynamic Models for Transient Diffusion and Elastodynamics AU - Zhou , Zhikun AU - Peng , Xuhao AU - Wu , Pan AU - Chen , Ziguang AU - Bobaru , Florin JO - Communications in Computational Physics VL - 5 SP - 1257 EP - 1286 PY - 2023 DA - 2023/01 SN - 32 DO - http://doi.org/10.4208/cicp.OA-2022-0080 UR - https://global-sci.org/intro/article_detail/cicp/21363.html KW - Convergence, peridynamics, nonlocal models, analytical solutions, transient diffusion, elastodynamics. AB -

Recent analytical solutions for peridynamic (PD) models of transient diffusion and elastodynamics allow us to revisit convergence of 1D PD models to their classical counterparts. We find and explain the reasons for some interesting differences between the convergence behavior for transient diffusion and elastodynamics models. Except for very early times, PD models for transient diffusion converge monotonically to the classical one. In contrast, for elastodynamic problems this convergence is more complex, with some periodic/almost-periodic characteristics present. These special features are investigated for sine waves used as initial conditions. The analysis indicates that the convergence behavior of PD solutions to the classical one can be understood in terms of convergence properties for models using the Fourier series expansion terms of a particular initial condition. The results obtained show new connections between PD models and their corresponding classical versions.

Zhou , ZhikunPeng , XuhaoWu , PanChen , Ziguang and Bobaru , Florin. (2023). New Insights on Convergence Properties of Peridynamic Models for Transient Diffusion and Elastodynamics. Communications in Computational Physics. 32 (5). 1257-1286. doi:10.4208/cicp.OA-2022-0080
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