<p>Interaction of a single frequency ultrasonic wave with early-stage damages in metals, rocks, and ceramics generates higher harmonics. The early-stage damages include dislocation substructures, slip bands, imperfect grain boundaries, micro-cracks, inclusions, pores, disbonds, delamination’s, micro-voids, etc. The hysteretic behavior of such microscopic features can be predicted at the macroscopic level by considering hysteretic material models. Theoretical and numerical studies on wave propagation in symmetric hysteretic material models like Preisach–Mayergoyz (P-M), Hodgdon, &nbsp;Power Law, and Bouc-Wen hysteresis show that when a single frequency ultrasonic wave is passed through such hysteretic material only odd harmonics are generated. The theoretical and computational studies are carried out by various researchers like McCall, Guyer, Van Den Abeele, Johnson, Meurer, Nazarov, Radostin, Zhan, Ghodake, and others (1994-2021). Almost all the hysteretic models considered till now are non-pinched with an exception of Nazarov’s theoretical study (2001) on asymmetric pinched hysteretic model and rate-dependent with an exception of Ghodake’s computational study (2020, 2021). In this study, nonlinear wave propagation in a one-dimensional symmetric pinched rate-independent hysteretic material and the generation of higher harmonics is discussed. A one-dimensional space is discretized as a long chain of spring-mass elements. The hysteretic elements are added in parallel with the linear spring-mass elements. These hysteretic elements are modeled using a rate-independent pinched hysteresis model proposed by Biswas (2016), which is an improvement to Reid and Muravskii’s models. The system of equations of spring-mass elements is solved numerically. Results show that propagation of a single frequency wave through pinched rate-independent hysteretic material generates only odd harmonics. Very nice evolving symmetric pinched hysteretic loops are observed for a Gaussian input pulse. Wave mixing due to sending a single Gaussian pulse with two-input frequencies from one end of the spatial domain (one-way two-wave mixing) is demonstrated. Due to one-way two-wave mixing, sum and difference frequencies are observed along with the odd harmonics of the input frequencies. Here also symmetric pinched hysteretic curves are observed corresponding to input frequencies and their higher harmonics. Instead of small minor loops as seen in Bouc-Wen, Two-States (Ghodake 2020), and Asymmetric Bouc-Wen (Ghodake 2021) models, small symmetric pinched loops are observed because of wave mixing.</p>

One Dimensional Nonlinear Wave Propagation in a Rate Independent Pinched Hysteretic Material

Paper Proceedings: https://asmedigitalcollection.asme.org/qnde/QNDE2021/volume/85529

ASME 2021 48th Annual Review of Progress in Quantitative Nondestructive Evaluation (QNDE2021)

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