Advanced High-Contrast Metamaterial Analysis

Project Description Composite materials with periodic microstructures are widely used to engineer materials with tailored mechanical, thermal, or acoustic properties. A class of advanced composites called high-contrast composites (or metamaterials)- where the constituent material phases exhibit large differences in stiffness,density,or conductivity-are of particular interest as they display complex 'non- standard' wave [login to view URL] mathematical study of the high-contrast regime results in non-local or frequency-dependent effective models that model rich dynamic behaviour that cannot be captured by the standard continuum approximations. This project aims to mathematically investigate such high-contrast periodic composites, focusing on how scale interactions lead to non-trivial wave phenomena, such as dispersion, localisation, and band-gap formation. Objectives ·Model wave propagation (elastic, acoustic, or electromagnetic) in a periodic composite with strongly contrasting material properties. ·Utilise two-scale scale asymptotic expansion methods to derive effective equations that capture the influence of the microscale geometry and the high-contrast material properties. ·Analyse scale interactions to identify how the coupling between the microstructure and macroscopic fields leads to non-local effects or frequency-dependent responses. ·Characterise non-trivial wave phenomena, including slow or trapped waves and band gaps. Methodology ·Formulate governing partial differential equations (e.g. wave equation, elastodynamic or Maxwell equations) with periodic coefficients representing a two-phase periodic composite. ·Introduce a small-scale parameter (ε) representing the length scale of the microstructure and apply asymptotic expansions. with respect to this small period parameter, to derive homogenised models. · Introduce high-contrast scaling regimes, where material parameters differ by several orders of magnitude critically coupled with small period parameter ε, leading to degenerate problems. · Investigate how such scale-coupling effects give rise to highly dispersive or non-local macroscopic homogenisation models. Expected outcomes ·Derivation of effective macroscopic models capturing high-contrast and multiscale interactions. · Identification of non-trivial wave behaviour, such as dispersion curves, stop bands, and localised resonance modes. ·Comparison between classical and high-contrast homogenisation. Skills developed ·Mastery of multi-scale asymptotic analysis techniques. ·Understanding of wave propagation and dispersion phenomena in highly heterogeneous anisotropic media.

Project ID: 40385132