INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING Int. J. Numer. Meth. Biomed. Engng. 2010; 26:1934–1946 Published online 22 June 2009 in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/cnm.1285 COMMUNICATIONS IN NUMERICAL METHODS IN ENGINEERING Elastodynamic analysis of multiple crack problem in 3-D bi-materials by a BEM V. Mykhas’kiv 1 , I. Zhbadynskyi 1 and Ch. Zhang 2, ∗, † 1 Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, Lviv 79060, Ukraine 2 Department of Civil Engineering, University of Siegen, Siegen D-57068, Germany SUMMARY The three-dimensional (3-D) problem of bi-materials or two ideally bonded elastic half-spaces with interacting sub-interface cracks subjected to time-harmonic loading is analyzed. The boundary value problem is reduced to a system of boundary integral equations (BIEs) in the frequency domain for the crack-opening-displacements (CODs) only. Boundary integrals over the finite crack-surfaces are obtained by introducing modified elastodynamic Green’s functions, which identically satisfy the contact conditions on the infinite interface. The singularity subtraction technique under consideration of the ‘square-root’ behavior of the CODs at the crack-front is applied for the regularization of the BIEs. By using a collocation scheme, the BIEs are converted into a system of linear algebraic equations. Numerical calculations are performed for a bi-material with two penny-shaped cracks located on both sides of the interface subjected to time-harmonic tensile loading of constant amplitude on the crack-surfaces. Numerical results for the mode-I dynamic stress intensity factor as a function of the wave number are presented and discussed for various material combinations and distances between the interface and the cracks. Copyright 2009 John Wiley & Sons, Ltd. Received 22 January 2009; Revised 22 April 2009; Accepted 1 May 2009 KEY WORDS: bi-materials; sub-interface interacting cracks; time-harmonic loading; dynamic stress inten- sity factors; boundary element method 1. INTRODUCTION Layered composite materials or laminates belong to the advanced high-performance engineering materials in novel and innovative technologies. Fracture analysis of such piecewise-homogeneous materials under dynamic loading involves the investigation of dynamic stress concentrations in the vicinity of cracks, which can be located on the interfaces or beside them. Most previous publications concerning dynamic fracture in multiphase materials have been focused on the dynamic response of interfacial cracks [1–6]. Indeed, cracks may also exist in the component materials. Two-dimensional (2-D) dynamic crack problems in layered materials have been investigate in References [7, 8], while axisymmetric dynamic analysis of layered materials with penny-shaped cracks located parallel to the interfaces has been performed in Reference [9]. In the three-dimensional (3-D) case, the time-harmonic interaction between a single penny-shaped crack and an interface due to reflected waves has been considered in [10], where the crack is perpendicular to the interface. In particular, a boundary integral equation (BIE) formulation without integration over the infinite interface has ∗ Correspondence to: Ch. Zhang, Department of Civil Engineering, University of Siegen, Siegen D-57068, Germany. † E-mail: c.zhang@uni-siegen.de Contract/grant sponsor: German Research Foundation; contract/grant number: ZH 15/12-1 Copyright 2009 John Wiley & Sons, Ltd.