Représentation quasicontinue d’un crystal phononique unidimensionnel en un métamatériau acoustique

International audienceOptimizing structures through the selection or design of multifunctional (meta-)materials as well as miniaturizing engineering devices require a good analytical understanding of the collective, anti- continuous, or filtering dynamic properties of the involved complex systems with microstructures. They also need to choose or propose continuous modelings that are more pertinent and realistic than those currently used. This work focuses on the basic physics and acoustic bandgap properties of Phononic crystals in order to extract their main mechanical features from homogeneous and enhanced continuum viewpoints. We notably revisit the Born’s diatomic chain model in order to clarify certain aspects of its temporal and spectral properties and proposes an equivalent multi-scale quasicontinuum (that is nonlocal in both space and time, and multi-fields) and homogenized one (that is local in space and nonlocal in time, and monofield) which may help to bridge the gap between standard continuum model and granular (or atomic) physics used as acoustic-wave filters. Keywords: phononic crystals, acoustic metamaterials, multifield continualization and homogenization