Advanced High-Contrast Metamaterial Analysis
Budget: $10 – $30 USD
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 phenomena.The 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.
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 phenomena.The 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.