Author:

Abstract:

Experimental techniques for nondestructive testing using nonlinear ultrasound stimulate the theoretical interest in wave propagation in materials containing crack-type defects (i.e. internal contacts). The presence of cracks invokes two major mechanisms of nonlinearity: an asymmetric reaction of the crack to normal compression/tension, and friction-induced hysteresis activated by shearing action. The generated nonlinear response of a sample highly depends on its geometry, for which a numerical description is most suitable. Our numerical tool consists of two components: a unit for solving the elasticity equations in the bulk volume and a unit that provides appropriate boundary conditions to be imposed at the internal boundaries in the material. The crack model has to provide load-displacement relationships for any value of the drive parameters. The traditional Coulomb friction law written for loads does not have this property, and therefore we use another concept that is, however, based on Coulomb’s friction law as well. The approach includes the account for roughness of the defect faces which results in the appearance of an additional contact regime of partial slip, when some parts of the contact zone slip and some do not. This situation is successfully dealt with by using the previously developed method of memory diagrams. In this method, the hysteretic load-displacement solution is constructed with the help of an internal system function (memory diagram) that contains all memory information. This displacement-driven solution can be easily extended to two other contact regimes (contact loss and total sliding) and is finally computed for any normal and tangential displacement histories. Memory diagrams have to be maintained at each discretization point on the crack surface and updated following the applied displacement fields. The load-displacement data provides input to the solid mechanics unit programmed in COMSOL®. We present an exemplar simulated configuration and discuss the results.