Associated People

J. Schröder, L. Scheunemann, M. Sarhil, P. Neff

Abstract

Mechanical metamaterials are a fast-growing field in industrial applications due to their specially tailored macroscopic behavior. The analysis and modelling of metamaterials, which exhibit exotic properties including band gaps, negative refraction, dispersion or cloaking, requires higher-order continua to capture size effects arising from complex microstructures. In this research project, we follow a new and promising approach based on the relaxed micromorphic model [1], which is able to describe "exotic" properties on the macroscopic scale in a variationally consistent way. The relaxed micromorphic model reduces the complexity of the general micromorphic theory utilizing fewer material parameters by implementing the Curl of the micro-distortion field with keeping the full kinematics of the micromorphic theory. We aim to analyze macroscopic boundary value problems with fully resolved microstructures and compare it to the macroscopic relaxed micromorphic model using H(Curl) conforming finite elements [2]. Then suitable formulations are extracted from these evidence-based findings for an extension of a macro-homogeneity (Hill-Mandel) condition. This allows for a rigorous energetically and mathematically consistent scale-dependent homogenization scheme, connecting the relaxed micromorphic continuum (macroscale) with the associated Cauchy continuum (microscale).

References

[1] P. Neff, I.D. Ghiba, A. Madeo, L. Placidi, G. Rosi. A unifying perspective: the relaxed linear micromorphic continuum. Continuum Mech. Thermodyn. 26,639-681(2014).
[2] J.C. Nédélec, Mixed finite elements in R3, Numer. Math. 35,315-341(1980).