Abstract

Nonlinear ultrasonic techniques are of great importance to detect incipient structural damages in structural health monitoring (SHM) and nondestructive testing (NDT). High-power ultrasound could lead to clapping behaviors or slipping behaviors of an interface, this procedure can generate some distinctive nonlinear features, which is known as contact acoustic nonlinearity (CAN). In this work, the spectral finite element method (SFEM) combined with a bi-potential contact theory is presented to simulate CAN. A complete contact law describing three possible scenarios on the contact areas combines Signorini conditions and Coulomb friction rules, and the contact force is solved by a local iterative method called Uzawa algorithm. Furthermore, a first order algorithm is adopted to time integration of the discretized equation of wave motion. Two numerical examples are carried out to illustrate the accuracy and efficiency of the proposed method. The first numerical case studies on nonlinear interaction between Lamb waves and micro-cracks with various lengths and widths. Distinctive higher harmonic generation and DC response are captured in this case, a nonlinear damage index is considered to describe the degree of the nonlinear effect induced by the micro-crack. The second numerical example focuses on the nonlinear interaction of shear horizontal (SH) wave with a frictional contact interface of two identical isotropic elastic bodies. The relationship between energy dissipation of the sticking-sliding interface and higher-order odd harmonics is investigated. In addition, the effects of friction coefficient, incident wave amplitude and static normal pre-load are also studied. This work may provide some physical insight of CAN and guide for closed cracks or imperfectly bonded interfaces detection.

Keywords: Nonlinear ultrasonics; Contact acoustic nonlinearity; SFEM; Bi-potential theory