ON THE QUASI-ANALYTIC TREATMENT OF HYSTERETIC NONLINEAR RESPONSE IN ELASTIC-WAVE PROPAGATION

Microscopic features and their hysteretic behavior can be used to pred ict the macroscopic response of materials in dynamic experiments. Prei sach modeling of hysteresis provides a refined procedure to obtain the stress-strain relation under arbitrary conditions, depending on the p ressure history of the material. For hysteretic materials, the modulus is discontinuous at each stress-strain reversal which leads to diffic ulties in obtaining an analytic solution to the wave equation. Numeric al implementation of the integral Preisach formulation is complicated as well. Under certain conditions an analytic expression of the modulu s can be deduced from the Preisach model and an elementary description of elastic wave propagation in the presence of hysteresis can be obta ined. This approach results in a second-order partial differential equ ation with discontinuous coefficients. Classical nonlinear representat ions used in acoustics can be found as limiting cases, The differentia l equation is solved in the frequency domain by application of Green's function theory and perturbation methods, Limitations of this quasi-a nalytic approach are discussed in detail. Model examples are provided illustrating the influence of hysteresis on wave propagation and are c ompared to simulations derived from classical nonlinear theory. Specia l attention is given to the role of hysteresis in nonlinear attenuatio n. In addition guidance is provided for inverting a set of experimenta l data that fall within the validity region of this theory, This work will lead to a new type of NDT characterization of materials using the ir nonlinear response. (C) 1997 Acoustical Society of America.