Enriched Continua for Finite-sized Metamaterials
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Architectured mechanical metamaterials, which are built from a lattice of unit cells, exhibit very different material behavior than the homogeneous base material from which they are made. This is particularly evident in the dynamic regime, where phenomena such as dispersion, negative group velocity, and band-gaps occur. Modeling the dynamic response of mechanical metamaterials via the reduced relaxed micromorphic model [4, 1] (or any other enriched continuum models) is challenging. This mainly comes down to two problems: • First, fitting the necessary material parameters (independent of frequency and wavenumber) based on the bulk material behavior [6]. • Second, a suitable framework must be discussed to incorporate the correct boundary behavior on a finite-sized specimen [5]. While for the static regime the corresponding material parameters are typically fitted by a range of simple deformation modes, the dynamic response is more involved. In the time-harmonic domain, a Bloch-Floquet analysis of a single unit cell (with periodicity) is performed, and thus considering only the dynamic behaviour of an infinitely big metamaterial. However, this only allows us to fit the correct bulk material behavior. We want to present how we can build on this framework to improve the performance of modelling finite-sized specimens, incorporating Null-Lagrangians [3] and the concept of boundary forces [5]. This is particularly important when considering the impact of different unit-cell cuts in the presence of interfaces or free boundaries [2].
