Asymptotic analysis for the Kelvin–Voigt model for a thin laminate

A two dimensional Kelvin–Voigt model of a visco-elastic thin stratified strip with Neumann condition at the lateral boundary is considered. The dimension reduction combined with the homogenization procedure allows us to construct a complete asymptotic expansion of the solution and to justify the limit one dimensional model containing the long-fading memory term while the initial model corresponds to the short memory.