Comparative study of time and frequency domain approaches in contact problem for the I-mode crack under harmonic loading

Abstract

In this paper two approaches, time-domain (TD) and frequency domain (FD) have been applied for the solution of the dynamic unilateral contact problem. We investigate crack in two-dimensional (2-D) plane, homogeneous, isotropic and linear elastic solids under action of the longitudinal P-wave with considering unilateral contact of the crack edges. For the problem solution a special iterative algorithm of the Udzava's type and boundary element methods (BEM) in the time-domain (TD) and frequency domain (FD) are used. For evaluation of the hypersingular integrals involved in BIEs a special regularization process that converts these integrals to regular ones is applied. Simple regular formulas for their calculation are presented. Numerical results for the crack opening, contact forces and dynamic stress intensity factor (SIF) for the case of a finite I-mode crack in an infinite 2-D domain which is subjected to a harmonic loading with considering crack edges unilateral contact interaction are presented and discussed.