Numerical analysis of a one-dimensional nonlinear wave scattering at a contact interface with damageable adhesion and unilateral contact

Abstract

The nonlinear scattering of a longitudinal harmonic plane wave, induced by a contact interface, is investigated numerically, using a model that combines damageable adhesion and unilateral contact. This novel approach captures the smooth transition between a perfectly bonded interface and a disbonded clapping interface, also referred to as a kissing bond. This is achieved through an RCCM (Raous, Cangémi, Cocu and Monerie) contact law, where exceedance of the elastic limit in tension triggers the generation of damage and a progressive reduction of the tensile interface stiffness until zero, i.e. equivalent to unilateral contact. This RCCM law is implemented in a 1D finite difference model where the contact interface is defined between a semi-infinite domain and a rigid wall. Since the nonlinear scattering is only dependent on the interface law, damping in the propagation medium is not considered. The reflected wave is post-processed to obtain the nonlinear signature of the interface through the evolution of the normalized DC, fundamental and second harmonic components, as a function of the normalized frequency and the interface load. This analysis provides useful insights for understanding the interface response and shows that the nonlinear signature contains information on the different parameters of the RCCM law, as well as on the damage state of the interface. These encouraging results provide insight and guidance for the non-destructive evaluation of contact interfaces and adhesive joints using non-linear acoustics.