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International audience; Engineered elastic structures (often referred to as metastructures) are promising in applications where filtering, focusing or channeling of elastic waves is required. Besides academic research interest, metastructures are gradually permeating the industrial sector and several associated modelling notions are entering engineering practice. Spatially-resolved finite-element models of large collections of unit-cells inevitably call for mathematical approximations and accurate reduction schemes. In this talk, we exploit well-known finite-element model order reduction techniques: an exact superelement, an eigenmode based superelement and an asymptotic based superelement. We show how the latter two can be obtained from the exact superelement. In the context of metastructural design, we highlight their benefits in terms of reduced computational time with respect to standard full-size finite-element solutions. Specifically, we define the superelements starting from unit cells of three-dimensional metastructures and use those to solve mathematical problems of general interest: (i) polynomial Bloch-Floquet eigenvalue problems associated with complex dispersion diagrams (i.e. complex Bloch vector as a function of frequency), and (ii) time-harmonic response of finite assemblies of unit cells. Differently from the rationale of homogenisation theories - where an approximating continuum is sought - superelements tend at further discretizing or "anti-homogenising" metamaterials.

International audience; Efficient absorbers are important to create a pleasant acoustic environment, or to meet certain technical specifications. Standard solutions make use of open-pore foams or thin resonating plates. The first option requires a thick layer to be efficient at low frequencies, reducing the available space. Plate absorbers, on the other hand, can be thin constructions, but they have a very narrow absorption band. Wideband high absorption levels at low frequencies can be achieved by careful design of the porosity and pore connectivity of a foam. If the matrix material is sufficiently rigid, the acoustic absorption can be predicted in two steps. First, a finite element model of a representative volume element (RVE) yields a set of non-acoustic parameters: flow resistivity, thermal and viscous length, tortuosity, and thermal permeability. In the second step, these values lead to equivalent homogenized fluid properties, as formalized in the Johnson-Champoux-Allard- Lafarge (JCAL) model. Gypsum foams are rigid, closed-cell materials with a narrow, controllable, pore size and wall thickness distribution. The inherent acoustic absorption is weak due to the closed cells. We investigated how a rectangular array of sub-millimeter perforations of the foam results in a high acoustic absorption coefficient. JCAL model predictions based on a Kelvin cell RVE are validated by impedance tube measurements for a variety of perforation diameters. The results show that a suitable combination of pore geometry and perforation pattern leads to a perfect absorption peak below 1 kHz for foam layers as thin as several centimeters. An optimal design of the perforated foams, e.g. using random perforation patterns or graded pore sizes, can lead to the engineering of a desired absorption curve.