Nonlocal-to-local limit in linearized viscoelasticity-Reference-Cited by-同舟云学术

Nonlocal-to-local limit in linearized viscoelasticity

Published:2024-01-01 Issue:1 Volume:15 Page:1-26
ISSN:2038-0909
Container-title:Communications in Applied and Industrial Mathematics
language:en
Short-container-title:

Author:

Friedrich Manuel¹²,Seitz Manuel³⁴,Stefanelli Ulisse⁴⁵⁶

Affiliation:

1. Department of Mathematics , Friedrich-Alexander Universit¨at Erlangen-Nürnberg . Cauerstr. 11, D-91058 Erlangen , Germany

2. Mathematics Münster , University of Münster , Einsteinstr. 62, D-48149 Münster , Germany

3. Vienna School of Mathematics , University of Vienna , Oskar-Morgenstern-Platz 1 , Vienna , Austria

4. Faculty of Mathematics , University of Vienna , Oskar-Morgenstern-Platz 1 , Vienna , Austria

5. Vienna Research Platform on Accelerating Photoreaction Discovery , University of Vienna , W¨ahringerstraße 17 , Vienna , Austria

6. Istituto di Matematica Applicata e Tecnologie Informatiche E. Magenes , via Ferrata 1, I-27100 Pavia , Italy

Abstract

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.

Publisher

Walter de Gruyter GmbH

Link

https://www.sciendo.com/pdf/10.2478/caim-2024-0001

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