High contrast biphasic mechanical metamaterials for the mitigation of elastic wave propagation

This paper reports investigations on two-dimensional phononic crystals composed of two distinct material phases. Focus is on the undamped free propagation of elastic harmonic waves in high-contrast linear elastic materials, whereby the effects of topology and contrast rate of component phases are studied. Solid-solid biphasic mechanical metamaterials are composed of alternating solid phases with significant difference in material properties. Stop bandwidths depend on the contrast between the material properties of the inclusions and the matrix, as well as on the geometry of the array of inclusions and the inclusion shape. The SAFE method provides an analytical framework to compute dispersion relations: a tentative solution representing plane waves is substituted in the equations of motion, then periodicity conditions are applied on the boundary of the repetitive cell, providing an eigenvalue problem. Parametric and topological design has demonstrated the potential to achieve ultra-wide bandgaps in solid-solid phononic crystals within the frequency range of human sensitivity.