<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>We study the quasistatic evolution of a linear peridynamic Kelvin-Voigt viscoelastic material. More specifically, we consider the gradient flow of a nonlocal elastic energy with respect to a nonlocal viscous dissipation. Following an evolutionary Γ-convergence approach, we prove that the solutions of the nonlocal problem converge to the solution of the local problem, when the peridynamic horizon tends to 0, that is, in the nonlocal-to-local limit.</p>
</abstract>

We study the quasistatic evolution of a linear peridynamic Kelvin-Voigt viscoelastic material. More specifically, we consider the gradient flow of a nonlocal elastic energy with respect to a nonlocal viscous dissipation. Following an evolutionary Γ-convergence approach, we prove that the solutions of the nonlocal problem converge to the solution of the local problem, when the peridynamic horizon tends to 0, that is, in the nonlocal-to-local limit.

Nonlocal-to-local limit in linearized viscoelasticity

Friedrich-Alexander Universit¨at Erlangen-Nürnberg

Communications in Applied and Industrial Mathematics

This work is licensed under the Creative Commons Attribution 4.0 International License.

{"article-title":"Nonlocal-to-local limit in linearized viscoelasticity"}

We study the quasistatic evolution of a linear peridynamic Kelvin-Voigt viscoelastic material. More specifically, we consider the gradient flow of a nonlocal...

Nonlocal-to-local limit in linearized viscoelasticity

Published Online: May 25, 2024

Page range: 1 - 26

Received: Feb 29, 2024

Accepted: Mar 27, 2024

DOI: https://doi.org/10.2478/caim-2024-0001

Keywords
AMS subject classification: 74A70, 70G75, 35Q74, 49J45, 74D05

© 2024 Manuel Friedrich et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Nonlocal-to-local limit in linearized viscoelasticity

Published Online: May 25, 2024

Page range: 1 - 26

Received: Feb 29, 2024

Accepted: Mar 27, 2024

DOI: https://doi.org/10.2478/caim-2024-0001

KeywordsAMS subject classification: 74A70, 70G75, 35Q74, 49J45, 74D05

© 2024 Manuel Friedrich et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Keywords
AMS subject classification: 74A70, 70G75, 35Q74, 49J45, 74D05