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

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

Comparison of two 2-D numerical models for snow avalanche simulation

Snow avalanches are gravitational processes characterised by the rapid movement of a snow mass, threatening inhabitants and damaging infrastructure in mountain areas. Such phenomena are complex events, and for this reason, different numerical models have been developed to reproduce their dynamics over a given topography. In this study, we focus on the two-dimensional numerical simulation tools RAMMS::AVALANCHE and FLO-2D, aiming to compare their performance in predicting the deposition area of snow avalanches. We also aim to assess the employment of the FLO-2D simulation model, normally used in water flood or mud/debris flow simulations, in predicting the motion of snow avalanches. For this purpose, two well-documented avalanche events that occurred in the Province of Bolzano (IT) were analyzed (Knollgraben, Pichler Erschbaum avalanches). The deposition area of each case study was simulated with both models through back-analysis processes. The simulation results were evaluated primarily by comparing the simulated deposition area with the observed one through statistical indices. Subsequently, the maximum flow depth, velocity and deposition depth were also compared between the simulation results. The results showed that RAMMS::AVALANCHE generally reproduced the observed deposits better compared to FLO-2D simulation. FLO-2D provided suitable results for wet and dry snow avalanches after a meticulous calibration of the rheological parameters, since they are not those typically considered in avalanche rheology studies. The results showed that FLO-2D can be used to study the propagation of snow avalanches and could also be adopted by practitioners to define hazard areas, expanding its field of application