Transient elastodynamic antiplane crack analysis of anisotropic solids

Abstract

Transient elastodynamic analysis of an antiplane crack in anisotropic solids is presented. A time-domain traction boundary integral equation (BIE) method is applied for this purpose. The traction BIE is hypersingular and has the crack-opening-displacement as its fundamental unknown quantity. Unlike the usual time-domain BIE method the present formulation applies a convolution quadrature developed by Lubich (Lubich, C., 1988a,b. Convolution quadrature and discretized operational calculus. Numer. Math. 52, 129–145 (Part I), 413–425 (Part II)) which requires only the Laplace-domain instead of the time-domain Green’s functions. The spatial variation of the crack-opening-displacement is approximated by an infinite series of Chebyshev polynomials which take the local behavior of the crack-opening-displacement at crack-tips into account. By using a Galerkin method, the time-domain BIE is converted into a system of linear algebraic equations which can be solved step by step. Special attention is devoted to the computation of dynamic stress intensity factors of an antiplane crack in generally anisotropic solids. Numerical results for isotropic solids are presented and compared with the well-known analytical results of Thau and Lu (Thau, S.A., Lu, T.H., 1970. Diffraction of transient horizontal shear waves by a finite crack and a finite rigid ribbon. Int. J. Enggn. Sci. 8, 857–874), to check the accuracy and efficiency of the present time-domain BIE method. The effect of the material anisotropy on the dynamic stress intensity factors is analyzed via several numerical examples.