Nonstandard micro-inertia terms in the relaxed micromorphic model: well-posedness for dynamics

TL;DR

This paper establishes the well-posedness of dynamic relaxed micromorphic models with novel micro-inertia terms, which are crucial for accurately modeling band-gap responses in meta-materials.

Contribution

It introduces and proves the existence of solutions for new relaxed micromorphic models incorporating micro-inertia terms, enhancing the modeling of meta-material dynamics.

Findings

Existence of solutions proven using Banach fixed point theorem.

Novel micro-inertia terms improve band-gap response modeling.

Enhanced understanding of generalized continuum theories.

Abstract

We study the existence of solutions arising from the modelling of elastic materials using generalized theories of continua. In view of some evidence from physics of meta-materials we focus our effort on two recent nonstandard relaxed micromorphic models including novel micro-inertia terms. These novel micro-inertia terms are needed to better capture the band-gap response. The existence proof is based on the Banach fixed point theorem.