A nonlocal homogenization model for wave dispersion in dissipative composite materials

This manuscript presents a nonlocal homogenization model for the analysis of wave dispersion and energy dissipation in bimaterial viscoelastic composites subjected to dynamic loading conditions. The proposed model is derived based on the asymptotic homogenization method with multiple spatial scales applied in the Laplace domain. Asymptotic expansions of the associated response fields up to fourth order are employed to account for wave dispersions induced by the microscopic heterogeneities. The solution of the nonlocal homogenization approach is obtained in semi-analytical form in the Laplace domain and discrete inverse Laplace transform method is employed to approximate the response fields in the time domain. Numerical examinations are carried out to verify the proposed model and assess its capabilities compared to the standard (i.e., local) homogenization and the analytical solutions of composite beams subjected to dynamic loading conditions. Investigations reveal that the nonlocal model accurately accounts for wave dispersions and heterogeneity induced attenuation. A parametric analysis is conducted to identify the relationship between microstructure and heterogeneity induced attenuation under high-frequency loading.