Forward and inverse problems for creep models in viscoelasticity.
Philos Trans A Math Phys Eng Sci
; 382(2277): 20230295, 2024 Aug 23.
Article
em En
| MEDLINE
| ID: mdl-39005012
ABSTRACT
This study examines a class of time-dependent constitutive equations used to describe viscoelastic materials under creep in solid mechanics. In nonlinear elasticity, the strain response to the applied stress is expressed via an implicit graph allowing multi-valued functions. For coercive and maximal monotone graphs, the existence of a solution to the quasi-static viscoelastic problem is proven by applying the Browder-Minty fixed point theorem. Moreover, for quasi-linear viscoelastic problems, the solution is constructed as a semi-analytic formula. The inverse viscoelastic problem is represented by identification of a design variable from non-smooth measurements. A non-empty set of optimal variables is obtained based on the compactness argument by applying Tikhonov regularization in the space of bounded measures and deformations. Furthermore, an illustrative example is given for the inverse problem of isotropic kernel identification. This article is part of the theme issue 'Non-smooth variational problems with applications in mechanics'.
Texto completo:
1
Coleções:
01-internacional
Base de dados:
MEDLINE
Idioma:
En
Revista:
Philos Trans A Math Phys Eng Sci
/
Philos. trans. - Royal Soc., Math. phys. eng. sci. (Online
/
Philosophical transactions - Royal Society. Mathematical, physical and engineering sciences (Online)
Assunto da revista:
BIOFISICA
/
ENGENHARIA BIOMEDICA
Ano de publicação:
2024
Tipo de documento:
Article
País de afiliação:
Japão
País de publicação:
Reino Unido