Homogenized Gradient Elasticity Model for Plane Wave Propagation in Bilaminate Composites

Abstract

Dispersion occurs when a wave propagates through a heterogeneous medium. Such a phenomenon becomes more pronounced when the smallest wavelength of the incoming pulse approaches the size of a unit cell, as well as when the contrast in mechanical impedance of the constituent materials increases. In this contribution focusing on periodic bilaminate composites, the authors seek an accurate description of the wave propagation behavior without the explicit representation of the underlying constituent materials. To this end, a gradient elasticity model based on a novel homogenization strategy is proposed. The intrinsic parameters characterizing the microinertia effect and nonlocal interactions are fully quantified in terms of the constituent materials’ properties and volume fractions. The framework starts with suitable kinematic decompositions within a unit cell. The Hill-Mandel condition is next applied to translate the energy statements from micro to macro. The governing equation of motion and traction definitions are next extracted naturally at the macrolevel via Hamilton’s principle. The ensuing fourth-order governing equation of motion has the same form as a reference gradient model in the literature, which was derived through a fundamentally different homogenization scheme. The predictive capability of the proposed model is demonstrated through four examples, with bilaminate composites encompassing a comprehensive range of material properties and volume fractions. It is furthermore shown that the proposed model performs better than the reference model for bilaminate composites with low to moderate contrast in mechanical impedances.