A unified treatment of nonclassical nonlinear effects in the propagation of ultrasound in heterogeneous media
Recent experiments on rocks and other materials, such as soil, cement, concrete and damaged elastic materials, have led to the discovery of nonlinear hysteretic effects in their elastic behaviour. These observations suggest the existence of a nonlinear mesoscopic elasticity universality class, to which all the aforementioned materials belong. The purpose of the present contribution is to search for the basic mathematical roots for nonclassical nonlinearity, in order to explain its universality, classify it and correlate it with the underlying meso- or microscopic interaction mechanisms. In our discussions we explicitely consider two quite different kinds of specimens: a two-bonded-elements structure and a thin multigrained bar. It is remarkable that, although the former includes only one interface and the latter very many interstices, the same "interaction box" formalism can be applied to both. Another important result of the proposed formalism is that the spectral contents of an arbitrary system for any input amplitude may be predicted, under certain assumptions, from the result of a single experiment at a higher amplitude.