SUMMARYA general, efficient and robust boundary element method (BEM) formulation for the numerical solution of three-dimensional linear elastic problems in transversely isotropic solids is developed in the present work. The BEM formulation is based on the closed-form real-variable expressions of the fundamental solution in displacements U ik and in tractions T ik , originated by a unit point force, valid for any combination of material properties and for any orientation of the radius vector between the source and field points. A compact expression of this kind for U ik was introduced by Ting and Lee (Q. J. Mech. Appl. Math. 1997; 50:407-426) in terms of the Stroh eigenvalues on the oblique plane normal to the radius vector. Working from this expression of U ik , and after a revision of their final formula, a new approach (based on the application of the rotational symmetry of the material) for deducing the derivative kernel U ik, j and the corresponding stress kernel i jk and traction kernel T ik has been developed in the present work. These expressions of U ik , U ik, j , i jk and T ik do not suffer from the difficulties of some previous expressions, obtained by other authors in different ways, with complex-valued functions appearing for some combinations of material parameters and/or with division by zero for the radius vector at the rotational-symmetry axis. The expressions of U ik , U ik, j , i jk and T ik have been presented in a form suitable for an efficient computational implementation. The correctness of these expressions and of their implementation in a three-dimensional collocational BEM code has been tested numerically by solving problems with known analytical solutions for different classes of transversely isotropic materials.

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A general numerical tool for the analysis of three-dimensional bimaterial interface cracks is presented in this paper. The proposed tool is based on a multidomain formulation of the Boundary Element Method (BEM), with the crack located at the interface of the domain. Mixed mode stress intensity factors are computed along the three-dimensional crack fronts using the Energy Domain Integral (EDI) methodology and decoupled via the Interaction Integral. The capability of the procedure is demonstrated by solving a number of examples. The last of these examples consists in a thick centre cracked panel for which the behaviour of the J-integral and the mixed-mode stress intensity factors along the crack front is studied as a function of the material mismatch.

A parallel domain decomposition boundary integral algorithm for three-dimensional exponentially graded elasticity has been developed. As this subdomain algorithm allows the grading direction to vary in the structure, geometries arising from practical functionally graded material applications can be handled. Moreover, the boundary integral algorithm scales well with the number of processors, also helping to alleviate the high computational cost of evaluating the Green’s functions. For axisymmetric plane strain states in a radially graded material, the numerical results for cylindrical geometries are in excellent agreement with the analytical solution deduced herein.