Dissipation in Microinhomogeneous Solids: Inherent Amplitude-Dependent losses of a Non-Hysteretical and Non-Frictional Type

A nonlinear, non-hysteretical and non-frictional mechanism of amplitude-dependent losses typical of microinhomogeneous media is proposed. This mechanism requires neither qausistatic hysteresis at the defects, nor friction-type losses such as slip at the defect's interface or another nonlinear viscosity. It is shown that inherent amplitude-dependent macroscopic attenuation in microinhomogeneous solids also occurs due to combined action of two factors, (i) purely linear (viscous-like or thermal) losses at the defects and (ii) elastic nonlinearity which is typical of such defects as cracks, intergrain contacts, etc. In particular, the defect nonlinearity of a hysteretical type also influences the resultant macroscopic amplititude-dependent attenuation via this mechanism. However, this contribution of the hysteretic nonlinearity is not related to the non-zero square of the hysteresis "stress-strain" loop, and is not associated with convential hysteretical losses. Therefore, in a hysteretical material, these essentially different mechanisms may exhibit themselves either simultaneously or separately depending on the particular type of the nonlinear effect. For example, the role of both conventional hysteretical and the mentioned non-hysteretical nonlinear losses is comparable in case of self-action of a tonal wave, but the non-hysteretical mechanism may dominate in the special case of interaction of two different waves. The case of a solid containing isotropically oriented highly compliant microinhomogeneities is analysed as an important instructive example. Complementary nonlinearity-produced variations in the elastic moduli and in the decrements are evaluated for the longitudinal, the Young (rod) and the transversal elastic waves. Inter-relationships of the microstructure of a solid, its elastic and dissipative properties are pointed out and the relevance of the model implications to published and own experimental observations is discussed. The obtained results allow for prediction of the amplitude-dependent absorption and of the complementary change in elastic parameters for microinhomogeneous materials without detailed knowing viscoelastic properties of the defects. The model is applicable to a wide class of materials, such as rocks, concretes and other microinhomogeneous solids.