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

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