Wave propagation in a one-dimensional bar with rate-independent hysteresis

A single frequency ultrasonic wave propagation in nonlinear materials generates higher harmonics. The generation of higher harmonics depends on the type of material nonlinearity considered, like odd and even harmonics in quadratically nonlinear materials, and only odd harmonics in cubically nonlinear material. The objective of this study is to present numerical study of one dimensional wave propagation in rate-independent hysteretic media by considering one dimensional chain of spring masses. Preisach-Mayergoyz (1994) and Hodgdon hysteretic models (1988) are commonly used in the theoretical and numerical study of nonlinear wave propagation studies. Here we implement the famous scalar Bouc-Wen model (1976) and a recently developed two-state hysteresis model by Biswas and Chatterjee (2015) to consider hysteresis in the large spring mass system. Number of spring masses are decided based on the spatial resolution needed for the nonlinear wave propagation to capture higher harmonics. The study presents interesting comparison between the wave propagation through an aluminum bar damaged under low cycle fatigue modeled as two different rate-independent hysteretic models. Both models show higher harmonics in responses. However, being a scalar model, the Bouc-Wen model cannot capture small minor loops due to partial reversals, whereas the two-state model captures the minor loops well.