Paper Title
EFFECT OF MICROSTRUCTURE ON WAVE PROPAGATION ANALYSIS IN HOMOGENIZED SECOND GRADIENT MEDIUM

Abstract
In the present work, we develop an effective second-order gradient continuum model for 2D composite materials. The mechanical properties are computed using a variational principle in combination with the Hill macro-homogeneity condition, extended to study wave propagation by investigating the longitudinal and shear waves. Incorporating strain gradient effects into the mechanical formulation enhances the constitutive law by relating the hyperstress tensor to the second-order gradient of displacement. Strain-gradient elasticity is often employed as an alternative to classical continuum Cauchy elasticity to capture elastic size and microstructure effects. The strain-gradient effective moduli are calculated for composite materials exhibiting strong internal strain gradients, demonstrating the proposed approach. We also analyze elastic wave dispersion in periodic composite materials using second-order gradient models derived from the homogenization of the initial composite. A significant increase in natural frequency due to second-order effects is observed. Keywords: homogenization; variational principles; wave propagation; composite materials; microstructure