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Personne# Vladimir Dorodnitsyn

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Porous medium

In materials science, a porous medium or a porous material is a material containing pores (voids). The skeletal portion of the material is often called the "matrix" or "frame". The pores are typica

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Metamaterials are often defined as artificial compositions designed to exhibit desired physical properties. These materials attract a lot of research attention due to unusual behavior that may not yet have been seen in nature. Although there is no commonly accepted definition for metamaterials, they are typically associated with peculiar macroscale properties resulting from their substructure. The electromagnetic metamaterial concept was first developed in 1968. As the wave theory is similar in every field, the achievements in optics were reflected in acoustics several decades later. This allowed developing acoustic metamaterials with such extraordinary properties as negative refractive index, negative bulk modulus and mass density, acoustic lensing, sound wave spectral decomposition, and acoustic bandgaps. All of those features are not only attractive scientifically, but are of interest for plenty of potential applications, including sound and vibration insulation, waveguiding, audible and high-frequency filtering, and even seismic absorption. On the other hand, cellular solids and saturated porous media have been studied for a long time. These media are abundant in nature as granular soils, wood, rocks, bones, and foams. Wave analysis in such environments typically requires some crucial assumptions which do not allow extending a theory to other configurations. An example of such a constraint is the openness of the cells in a medium. Many porous media applications are found in geophysics - particularly gas and oil extractions - the permeability of the cells plays an important role. The ad-hoc dynamic models for such media operate only with open-cell configuration. Moreover, the study is limited to the low-frequency analysis, omitting the influence of wave scattering. The latter, however, is the key source of dispersion in acoustic metamaterials. Scattering may have two origins, geometrical or resonant. Bragg's scattering is determined by the geometrical configuration, such that constructive interference occurs only when the incident wave matches the characteristic size of a unit cell. This makes such systems practically inconvenient. The concept of resonant scattering, introduced about a decade ago, has much fewer limitations and is mostly determined by the dynamics of matrix inclusions. In this thesis, a closed-cell cellular solid with thin vibrating walls and fluid-filled cells is proposed as a new class of acoustic metamaterials. First, the dynamics of a prototypical square cell is investigated numerically considering periodic boundary conditions and taking into account fluid-structure interaction. The results are compared to Biot's theory of saturated porous media in the limit of a closed-cells system. The proposed configuration is studied with respect to dispersion sources, showing the presence of local resonant behavior for different combinations of relative density and entrained fluid. Surprisingly, semi-analytical models can be used to provide a bottom-up explanation of the structure's dynamic behavior. The presence of two pressure waves, slow and fast, is confirmed numerically and analytically. Finally, an experimental proof-of-concept was carried out. Periodic cellular solids represent a versatile acoustic metamaterial platform characterized by low cost, simple, scalable design, which makes possible achieving the desired macroscopic behavior using different types of fluids and bulk materials.

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Vladimir Dorodnitsyn, Alessandro Spadoni

Internal degrees of freedom and periodic structure are critical requirements in the design of acoustic/elastic metamaterials since they can give rise to extraordinary properties like negative effective mass and stiffness. However, they are challenging to realize in three dimensions. Closed-cell, crystalline foams are a particularly advantageous basis to develop metamaterials as they intrinsically have a complex microstructure, exhibiting internal resonances. Recently self-assembly techniques have been implemented to produce such foams: a Kelvin (body centered cubic) foam, a face centered cubic foam, and a Weaire-Phelan structure. Numerical models are employed to demonstrate that such foams are superanisotropic, selectively behaving as a fluid or a solid, pentamode solids as a result of fluid-structure interaction, in addition to having regimes characterized by film resonances and high density of states. Microstructural deformations obtained from numerical models allow the derivation of equivalent mechanical models. (C) 2014 Acoustical Society of America.

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Wave propagation in cellular and porous media is widely studied due to its abundance in nature and industrial applications. Biot's theory for open-cell media predicts the existence of two simultaneous pressure waves, distinguished by its velocity. A fast wave travels through the solid matrix, whereas a much slower wave is carried by fluid channels. In closed-cell materials, the slow wave disappears due to a lack of a continuous fluid path. However, recent finite element (FE) simulations done by the authors of this paper also predict the presence of slow pressure waves in saturated closed-cell materials. The nature of the slow wave is not clear. In this paper, an equivalent unit cell of a medium with square cells is proposed to permit an analytical description of the dynamics of such a material. A simplified FE model suggests that the fluid-structure interaction can be fully captured using a wavenumber-dependent spring support of the vibrating cell walls. Using this approach, the pressure wave behavior can be calculated with high accuracy, but with less numerical effort. Finally, Rayleigh's energy method is used to investigate the coexistence of two waves with different velocities. (C) 2016 Acoustical Society of America.