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Homogenization and mechanical dissipation in thermoviscoelasticity. (English) Zbl 0621.73044
In this paper the authors investigate the macroscopic mechanical and thermal behaviour of a medium composed of nonhomogeneous viscoelastic materials of Kelvin-Voigt type. The study demonstrates that the classical theories of viscoelasticity with short range memory can be related to the theories of viscoelasticity with fading memory, through homogenization theory. In this contest the microstructure is supposed of periodic type, with a reference cell which contains all the relevant information on the microstructure. The composite materials is described as the composition of scaled versions of the cell by a small scaling parameter \(\epsilon\). When \(\epsilon\) goes to zero, the displacement field is found to converge (weakly) to the displacement of a body, with the same configuration, made of a homogeneous material which is no longer of Kelvin-Voigt type but rather a material with fading memory. A result of strong convergence for the strain rate field is also obtained.
Reviewer: M.Codegone

MSC:
74D99 Materials of strain-rate type and history type, other materials with memory (including elastic materials with viscous damping, various viscoelastic materials)
74A15 Thermodynamics in solid mechanics
35B40 Asymptotic behavior of solutions to PDEs
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
35A15 Variational methods applied to PDEs
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