Grasselli, Maurizio; Pata, Vittorino Long-time behavior of a homogenized model in viscoelastodynamics. (English) Zbl 0972.74058 Discrete Contin. Dyn. Syst. 4, No. 2, 339-358 (1998). 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. Cited in 3 Documents MSC: 74Q10 Homogenization and oscillations in dynamical problems of solid mechanics 74D05 Linear constitutive equations for materials with memory 45D05 Volterra integral equations Keywords:Kelvin-Voigt model; Volterra integro-differential equation; existence of uniform attractor; heterogeneous structure; microscopic mechanical behavior; homogenization; macroscopic stress-strain relation; time convolution term; memory effects; metric space PDFBibTeX XMLCite \textit{M. Grasselli} and \textit{V. Pata}, Discrete Contin. Dyn. Syst. 4, No. 2, 339--358 (1998; Zbl 0972.74058) Full Text: DOI