A sandwich material having both structural strength and significant acoustic attenuation. In one embodiment, a sandwich is composed of an architected core secured between two facesheets, with a compliant layer forming the connection between the core and the facesheets. The compliant core has a low modulus, resulting in a low speed for elastic shear waves in the sandwich, at low static loads. At high static loads the compliant material stiffens and allows the sandwich to exhibit significant structural strength.