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

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.

On the statics and dynamics of granular-microstructured rods with higher order effects

“…In Equation ( 2), c 11 and c 111 are functions of x and t only, and account for the local deformation within the VE. We note that although for systems with a small number of particles (or layers in composites modeled as 1D) a more accurate approximation of displacement can be made by subdividing the VE into different regions with different strain regimes (e.g., see [51,52]), for a large number of particles (or layers), such approaches become increasingly complicated and a linear or quadratic approximation within the whole domain of VE remains the most feasible (e.g., see [53]). We note here that efforts at formal homogenization (continualization) of mass-spring systems, such as in [54,55], also propose multiscale decomposition of the displacement field among the possible approaches for developing continuum models.…”

“…Equation ( 51) enforces that the macro-scale displacement f and the micro-scale kinematic measure c11 are identically fixed at both ends. Enforcing Equation (51), and by using Equation ( 50), the following set of algebraic equations result from Equation ( 48)…”

Analysis on the Dynamic Wave Attenuation Properties of Metaconcrete Considering a Quasi-Random Arrangement of Inclusions

“…Viscous behavior of metaconcrete has been considered within a homogenization strategy from micro-to-macro scale to analyze plane waves dispersion in multi-layered viscoelastic periodic composites Tan and Poh (2020). The formulation includes micro-inertial effects and non local interaction mechanism between materials, proposing an unifying approach to study the response of metaconcrete under high energy excitations, where Bragg scattering and local resonators cooperate to signal mitigation.…”