arXiv subjects

A. Madeo

Publications and source records attributed to A. Madeo.

4 recordsLinked to original sources

arXiv2024

Effective surface forces and non-coherent interfaces within the reduced relaxed micromorphic modeling of finite-size mechanical metamaterials

This paper introduces for the first time the concepts of non-coherent interfaces and microstructure-driven interface forces in the framework of micromorphic elasticity. It is shown that such concepts are of paramount importance when studying the response of finite-size mechanical metamaterials at the homogenized macro-scale. The need of introducing interface forces is elucidated through numerical examples comparing reduced relaxed micromorphic simulations to their full-microstructured counterparts. These results provide a milestone for the understanding of metamaterials' modeling at the homogenized scale and for the use of micromorphic-type models to achieve an accurate upscaling towards larger-scale metamaterials' structures.

physics.class-ph↗

arXiv2022

Unfolding engineering metamaterials design: relaxed micromorphic modeling of large-scale acoustic meta-structures

In this paper, we present a unit cell showing a band-gap in the lower acoustic domain. The corresponding metamaterial is made up of a periodic arrangement of this unit cell. We rigorously show that the relaxed micromorphic model can be used for metamaterials' design at large scales as soon as suficiently large specimens are considered. We manufacture the metamaterial via metal etching procedures applied to a titanium plate so as to show that its production for realistic applications is viable. Experimental tests are also carried out confirming that the metamaterials' response is in good agreement with the theoretical design. In order to show that our micromorphic model opens unprecedented possibilities in metastructural design, we conceive a finite-size structure that is able to focus elastic energy in a confined region, thus enabling its possible subsequent re-use. Indeed, thanks to the introduction of a well-posed set of micromorphic boundary conditions, we can combine different metamaterials and classical Cauchy materials in such a way that the elastic energy produced by a source of vibrations is focused in specific collection points. The design of this structure would have not been otherwise possible (via e.g., direct simulations), due to the large dimensions of the metastructure, couting hundreds of unit cells.

physics.app-ph↗

arXiv2014

Band gaps in the relaxed linear micromorphic continuum

In this note we show that the relaxed linear micromorphic model recently proposed by the authors can be suitably used to describe the presence of band-gaps in metamaterials with microstructures in which strong contrasts of the mechanical properties are present (e.g. phononic crystals and lattice structures). This relaxed micromorphic model only has 6 constitutive parameters instead of 18 parameters needed in Mindlin- and Eringen-type classical micromorphic models. We show that the onset of band-gaps is related to a unique constitutive parameter, the Cosserat couple modulus $μ_{c}$ which starts to account for band-gaps when reaching a suitable threshold value. The limited number of parameters of our model, as well as the specific effect of some of them on wave propagation can be seen as an important step towards indirect measurement campaigns.

math-ph↗

arXiv2013

Analytical continuum mechanics à la Hamilton-Piola: least action principle for second gradient continua and capillary fluids

In this paper a stationary action principle is proven to hold for capillary fluids, i.e. fluids for which the deformation energy has the form suggested, starting from molecular arguments, for instance by Cahn and Hilliard. Remark that these fluids are sometimes also called Korteweg-de Vries or Cahn-Allen. In general continua whose deformation energy depend on the second gradient of placement are called second gradient (or Piola-Toupin or Mindlin or Green-Rivlin or Germain or second gradient) continua. In the present paper, a material description for second gradient continua is formulated. A Lagrangian action is introduced in both material and spatial description and the corresponding Euler-Lagrange bulk and boundary conditions are found. These conditions are formulated in terms of an objective deformation energy volume density in two cases: when this energy is assumed to depend on either C and grad C or on C^-1 and grad C^-1 ; where C is the Cauchy-Green deformation tensor. When particularized to energies which characterize fluid materials, the capillary fluid evolution conditions (see e.g. Casal or Seppecher for an alternative deduction based on thermodynamic arguments) are recovered. A version of Bernoulli law valid for capillary fluids is found and, in the Appendix B, useful kinematic formulas for the present variational formulation are proposed. Historical comments about Gabrio Piola's contribution to continuum analytical mechanics are also presented. In this context the reader is also referred to Capecchi and Ruta.

physics.class-ph↗