TY - JOUR
T1 - Nonlocal-to-local limit in linearized viscoelasticity
AU - Seitz, Manuel
AU - Stefanelli, Ulisse
AU - Friedrich, Manuel
PY - 2024/5/25
Y1 - 2024/5/25
N2 - 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.
AB - 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.
KW - evolutionary Γ-convergence
KW - Kelvin-Voigt rheology
KW - nonlocal-to-local limit
KW - Peridynamics
KW - viscoelasticity
UR - http://www.scopus.com/inward/record.url?scp=85194475698&partnerID=8YFLogxK
U2 - 10.2478/caim-2024-0001
DO - 10.2478/caim-2024-0001
M3 - Article
SN - 2038-0909
VL - 15
SP - 1
EP - 26
JO - Communications in Applied and Industrial Mathematics
JF - Communications in Applied and Industrial Mathematics
IS - 1
ER -