Adhesion and nonlinear scattering by rough surfaces in contact: Beyond the phenomenology of the Preisach-Mayergoyz framework

Phenomenological models reproducing the elasticity and acoustic properties of geomaterials and materials with damage have been successfully developed. These models yield macroscopic stress-strain constitutive equations featuring hysteresis with end-point memory, and predict the efficient generation of higher harmonics accompanying the propagation of monochromatic waves. The assumption common to these models is that the material's microstructure is characterized by nonlinear compliant components of an unspecified nature which can exist in two states: open or closed. The density of the compliant units is defined on a mathematical continuum (the Preisach-Mayergoyz space) whose elements identify the dynamic behavior of the components. In this work, adhesion is shown to introduce hysteresis with end-point memory in the macroscopic behavior of an interface between two rough surfaces in contact, and, upon scattering, to generate higher harmonics bearing a striking similarity to those observed in wave propagation phenomena in media with distributed damage and in geomaterials. It appears, therefore, that two rough surfaces interacting via adhesion forces offer a meaningful example of macroscopic interface or bond with dynamics resembling that of the fictitious elements of the Preisach-Mayergoyz space, and acoustic nonlinear properties similar to those of rocks and damaged materials. (C) 2004 Acoustical Society of America.