NONLINEAR ELASTIC PROPERTIES OF MICROINHOMOGENEOUS HIERARCHICALLY STRUCTURED MEDIA

This paper examines the manner in which the internal structure of a me dium can affect its nonlinear elastic properties. It is shown that, fo r the elasticity of a microinhomogeneous medium to possess a high leve l of nonlinearity, there must be a small proportion of a soft componen t present in the material. The way in which the hierarchical structure of the rigid sind soft elements can influence the parameters of the m edium is investigated. It is demonstrated that, if the rigid elements are arranged in a hierarchical structure, the internal levels present in the structure will not affect the further increase in the nonlinear ity of the medium. On the contrary, if the soft elements are arranged in a hierarchical structure, then the nonlinearity of the medium can i ncrease in a geometric progression. In real physical media, however th e range of variations in the elasticity of the components is limited t o 3 or 4 orders of magnitude. Therefore, the ultimate increase ill the nonlinearity coefficient compared to a homogeneous medium is likewise limited to the range slated.