Relaxed micromorphic modeling of the interface between a homogeneous solid and a band-gap metamaterial: new perspectives towards meta-structural design

In the present paper, the material parameters of the isotropic relaxed micromorphic model derived for a specific metamaterial in a previous contribution are used to model its transmission properties. Specifically, the reflection and transmission coefficients at an interface between a homogeneous solid and the chosen metamaterial are analyzed by using both the relaxed micromorphic model and a direct FEM implementation of the detailed microstructure. The obtained results show an excellent agreement between the transmission spectra derived via our enriched continuum model and those issued by the direct FEM simulation. Such excellent agreement validates the indirect measure of the material parameters and opens the way towards an efficient meta-structural design.Comment: The paper has been already accepted in Mathematics and Mechanics of Solids as it i

Complete band gaps including non-local effects occur only in the relaxed micromorphic model

In this paper we substantiate the claim implicitly made in previous works that the relaxed micromorphic model is the only linear, isotropic, reversibly elastic, nonlocal generalized continuum model able to describe complete band-gaps on a phenomenological level. To this end, we recapitulate the response of the standard Mindlin-Eringen micromorphic model with the full micro-distortion gradient of P, the relaxed micromorphic model depending only on the Curl P of the micro-distortion P, and a variant of the standard micromorphic model in which the curvature depends only on the divergence Div P of the micro distortion. The Div-model has size-effects but the dispersion analysis for plane waves shows the incapability of that model to even produce a partial band gap. Combining the curvature to depend quadratically on Div P and Curl P shows that such a model is similar to the standard Mindlin-Eringen model which can eventually show only a partial band gap

Considerations on origin and development of the Perlschrift

The paper focuses on the origin of the byzantine minuscule handwriting called Perlschrift by Herbert Hunger in a famous essay published in 1954. The first part is devoted to the analysis of the studies dealt with this handwriting with particular regard to the essay of Herbert Hunger; the second part sheds light on the paleographical characteristics of the Perlschrift and of the earliest examples dating within Xth Century

Relaxed micromorphic model of transient wave propagation in anisotropic band-gap metastructures

In this paper, we show that the transient waveforms arising from several localised pulses in a micro-structured material can be reproduced by a corresponding generalised continuum of the relaxed micromorphic type. Specifically, we compare the dynamic response of a bounded micro-structured material to that of bounded continua with special kinematic properties: (i) the relaxed micromorphic continuum and (ii) an equivalent Cauchy linear elastic continuum. We show that, while the Cauchy theory is able to describe the overall behaviour of the metastructure only at low frequencies, the relaxed micromorphic model goes far beyond by giving a correct description of the pulse propagation in the frequency band-gap and at frequencies intersecting the optical branches. In addition, we observe a computational time reduction associated with the use of the relaxed micromorphic continuum, compared to the sensible computational time needed to perform a transient computation in a micro-structured domain

Relaxed micromorphic broadband scattering for finite-size meta-structures -- a detailed development

The conception of new metamaterials showing unorthodox behaviors with respect to elastic wavepropagation has become possible in recent years thanks to powerful dynamical homogenization techniques. Such methods effectively allow to describe the behavior of an infinite medium generated by periodically architectured base materials. Nevertheless, when it comes to the study of the scattering properties of finite-sized structures, dealing with the correct boundary conditions at the macroscopicscale becomes challenging. In this paper, we show how finite-domain boundary value problems canbe set-up in the framework of enriched continuum mechanics (relaxed micromorphic model) by imposing continuity of macroscopic displacement and of generalized traction when non-local effects areneglected.The case of a metamaterial slab of finite width is presented, its scattering properties are studied viaa semi-analytical solution of the relaxed micromorphic model and compared to numerical simulationsencoding all details of the selected microstructure. The reflection coefficient obtained via the twomethods is presented as a function of the frequency and of the direction of propagation of the incidentwave. We find excellent agreement for a large range of frequencies going from the long-wave limitto frequencies beyond the first band-gap and for angles of incidence ranging from normal to nearparallel incidence. The case of a semi-infinite metamaterial is also presented and is seen to be areliable measure of the average behavior of the finite metastructure. A tremendous gain in termsof computational time is obtained when using the relaxed micromorphic model for the study of theconsidered metastructure

Healing the cosmological constant problem during inflation through a unified quasi-quintessence matter field

We heal the cosmological constant problem by means of a \emph{cancellation mechanism} that adopts a phase transition during which quantum fluctuations are eliminated. To this purpose, we propose that a generalized scalar (dark) matter field with a non-vanishing pressure term can remove the vacuum energy contribution, if its corresponding thermodynamics is written in terms of a \emph{quasi-quintessence} representation. In such a picture, pressure differs from quintessence as it shows a zero kinetic contribution. Using this field, we investigate a metastable transition phase, in which the universe naturally passes through an inflationary phase. To reach this target, we single out a double exponential potential, describing the metastable inflationary dynamics by considering suitable boundaries and thermodynamic conditions. We analyze stability investigating saddle, stable and unstable points and we thus predict a chaotic inflation that mimics the Starobinsky exponential potential. Consequently, the role of the proposed dark matter field is investigated throughout the overall universe evolution. To do so, we provide a physical explanation on unifying the dark sector with inflation by healing the cosmological constant problem.Comment: 12 pages, 3 figures, 2 table