Nonlocal-to-local limit in linearized viscoelasticity

Manuel Friedrich; Manuel Seitz; Ulisse Stefanelli

doi:10.2478/caim-2024-0001

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Nonlocal-to-local limit in linearized viscoelasticity

Communications in Applied and Industrial Mathematics

Volume 15 (2024): Issue 1 (January 2024)

By: Manuel Friedrich, Manuel Seitz and Ulisse Stefanelli

Open Access

|May 2024

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.

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Articles in this issue

DOI: https://doi.org/10.2478/caim-2024-0001 | Journal eISSN: 2038-0909

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Language: English

Page range: 1 - 26

Submitted on: Feb 29, 2024

Accepted on: Mar 27, 2024

Published on: May 25, 2024

Published by: Italian Society for Applied and Industrial Mathemathics

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Keywords:

Peridynamics,

viscoelasticity,

Kelvin-Voigt rheology,

nonlocal-to-local limit,

evolutionary Γ-convergence

Related subjects:

Mathematics,

Numerical and computational mathematics,

Applied mathematics

© 2024 Manuel Friedrich, Manuel Seitz, Ulisse Stefanelli, published by Italian Society for Applied and Industrial Mathemathics
This work is licensed under the Creative Commons Attribution 4.0 License.

Volume 15 (2024): Issue 1 (January 2024)