Interface effects on the effective behavior of some Kelvin–Voigt viscoelastic heterogeneous bodies

Article type: Research Article

Authors: Licht, C.^{; ; ;} | Orankitjaroen, S.^;

Affiliations: LMGC, UMR-CNRS 5508, Université Montpellier II, Case courier 048, Place Eugène Bataillon, 34095 Montpellier cedex 5, France. E-mail: clicht@univ-montp2.fr | Department of Mathematics, Faculty of Science, Mahidol University, Bangkok 10400, Thailand | Centre of Excellence in Mathematics, CHE, Bangkok 10400, Thailand. E-mail: somsak.ora@mahidol.ac.th

Note: [] Corresponding author. E-mail: clicht@univ-montp2.fr

Abstract: The effective behavior of a solid made from a periodic distribution of inclusions in a matrix is investigated. Inclusions and matrix are linearly elastic or viscoelastic of Kelvin–Voigt type (and possibly rigid for the inclusions) while the link between them can be pure adhesion or viscous friction with bilateral contact or involve a very thin viscoelastic layer. As long as one constituent is viscoelastic, the effective behavior is no longer of Kelvin–Voigt type but with memory.

Keywords: homogenization, Kelvin–Voigt viscoelasticity, viscoelasticity with memory, interface effects, semi-groups of operators, Laplace transform, integro-differential equations

DOI: 10.3233/ASY-141247

Journal: Asymptotic Analysis, vol. 90, no. 3-4, pp. 249-265, 2014