Longtime behavior of a homogenized model in viscoelastodynamics
Maurizio Grasselli, Vittorino Pata · Discrete and Continuous Dynamical Systems · 1998
A material with heterogeneous structure at microscopic level isconsidered. The microscopic mechanical behavior is described by astress-strain law of Kelvin-Voigt type. It has beenshown that a homogenization process leads to a macroscopic stress-strainrelation containing a time convolution term which accounts for memory effects.Consequently, the displacement field $\mathbf{u}$ obeys to a Volterraintegrodifferential motion equation. The longtime behavior of $\mathbf{u}$ ishere investigated proving the existence of a uniform attractor when the bodyforces vary in a suitable metric space.