Enriched homogenized model for viscoelastic plane wave propagation in periodic layered composites

Abstract

Abstract An enriched homogenized model is developed based on a proposed homogenization strategy, to describe the wave propagation behaviour through periodic layered composites. The intrinsic parameters characterising the micro-inertia effect and non-local interactions are defined transparently in terms of the constituent materials’ properties and volume fractions. The framework starts with the introduction of an additional kinematic field to characterise the displacement of the stiff layer, before setting up macro kinematic fields to account for the average deformation of the constituent materials within a segmented unit cell. Relationships between these macro average strain fields are determined based on suitable micro-mechanical arguments. The Hill–Mandel condition is next applied to translate the energy statements from micro to macro. A system of coupled governing equations of motion is finally extracted naturally at the macro level via Hamilton’s Principle. Through a series of benchmark examples, it is shown that the proposed model exhibits excellent predictive capabilities over a broad range of loading frequencies.

Keywords

• Homogenization
• Wave propagation
• Viscoelasticity
• Dispersion
• Local resonance