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Long-time behavior of a homogenized model in viscoelastodynamics. (English) Zbl 0972.74058

Summary: We consider a material with heterogeneous structure at the microscopic level. The microscopic mechanical behavior is described by a stress-strain law of Kelvin-Voigt type. It is shown that a homogenization process leads to a macroscopic stress-strain relation containing a time convolution term which accounts for memory effects. Consequently, the displacement field \(u\) obeys Volterra integrodifferential equation of motion. We investgate the long-time behavior of \(u\), and prove the existence of a uniform attractor when the body forces vary in a suitable metric space.

MSC:

74Q10 Homogenization and oscillations in dynamical problems of solid mechanics
74D05 Linear constitutive equations for materials with memory
45D05 Volterra integral equations
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