TY - JOUR
T1 - On the quasi-static approximation in the initial boundary value problem of linearised elastodynamics
AU - Knops, R. J.
AU - Quintanilla, R.
N1 - Funding Information:
The work of R. Quintanilla has been supported by Ministerio de Economía y Competitividad under the research project “Análisis Matemático de Problemas de la Termomecánica” (MTM2016-74934-P), (AEI/FEDER, UE), and Ministerio de Ciencia, Innovación y Universidades under the research project “Análisis matemático aplicado a la termomecánica” (PID2019-105118GB-I00).
Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Nature B.V. part of Springer Nature.
Copyright:
Copyright 2021 Elsevier B.V., All rights reserved.
PY - 2021/2
Y1 - 2021/2
N2 - Continuous data dependence estimates are employed to rigorously derive conditions that validate the quasi-static approximation for the initial homogeneous boundary value problem in the theory of small elastic deformations superposed upon large elastic deformations. This theory imposes no sign-definite assumptions on the linearised elastic moduli and in consequence the requisite estimates are established using methods principally motivated by known Lagrange identity arguments.
AB - Continuous data dependence estimates are employed to rigorously derive conditions that validate the quasi-static approximation for the initial homogeneous boundary value problem in the theory of small elastic deformations superposed upon large elastic deformations. This theory imposes no sign-definite assumptions on the linearised elastic moduli and in consequence the requisite estimates are established using methods principally motivated by known Lagrange identity arguments.
KW - Continuous dependence
KW - Dirichlet boundary conditions
KW - Lagrange identities arguments
KW - Linearised elastodynamics
KW - Quasi-static approximation
UR - http://www.scopus.com/inward/record.url?scp=85100266390&partnerID=8YFLogxK
U2 - 10.1007/s10665-020-10072-5
DO - 10.1007/s10665-020-10072-5
M3 - Article
AN - SCOPUS:85100266390
SN - 0022-0833
VL - 126
JO - Journal of Engineering Mathematics
JF - Journal of Engineering Mathematics
IS - 1
M1 - 11
ER -