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SUMMARYA new variable-order singular boundary element for two-dimensional stress analysis is developed. This element is an extension of the basic three-node quadratic boundary element with the shape functions enriched with variable-order singular displacement and traction ÿelds which are obtained from an asymptotic singularity analysis. Both the variable order of the singularity and the polar proÿle of the singular ÿelds are incorporated into the singular element to enhance its accuracy. The enriched shape functions are also formulated such that the stress intensity factors appear as nodal unknowns at the singular node thereby enabling direct calculation instead of through indirect extrapolation or contour-integral methods. Numerical examples involving crack, notch and corner problems in homogeneous materials and bimaterial systems show the singular element's great versatility and accuracy in solving a wide range of problems with various orders of singularities. The stress intensity factors which are obtained agree very well with those reported in the literature.

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SUMMARYIn this paper, we propose a new fast algorithm for solving large problems using the boundary element method (BEM). Like the fast multipole method (FMM), the speed-up in the solution of the BEM arises from the rapid evaluations of the dense matrix-vector products required in iterative solution methods. This fast algorithm, which we refer to as fast Fourier transform on multipoles (FFTM), uses the fast Fourier transform (FFT) to rapidly evaluate the discrete convolutions in potential calculations via multipole expansions. It is demonstrated that FFTM is an accurate method, and is generally more accurate than FMM for a given order of multipole expansion (up to the second order). It is also shown that the algorithm has approximately linear growth in the computational complexity, implying that FFTM is as efficient as FMM.

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Delamination of interfaces in integrated circuit (IC) packages gives rise to electrical and mechanical failures such as popcorn cracking. Hence it is important to be able to analyze the mechanics of delamination from small interfacial defects which may exist at interfaces due to contamination or random factors. This paper describes the mechanics of interfacial delamination and the application of the boundary element method to analyze delamination propagation at interfaces. Now, a crack tip at an interface between two materials has an order of singularity which is a function of the material properties. For an accurate analysis, a special variable-order singular boundary element has been developed and used. The effect of defect size and location along the pad-encapsulant interface on interfacial delamination has been studied. It was found that the energy release rate or stress intensity factor increases with defect size as well as proximity to the pad corner. This implies that when a small delamination near a pad corner delaminates the crack tip nearer the pad corner will propagate first. The analysis has also shown that this delamination, once started, will continue until the crack tip reaches the pad corner. If the variation of interface toughness as a function of mode mixity is known, the delamination propagation behavior can be determined. Depending on the shape of the curve describing the variation of interface toughness with mode mixity, the delamination growth can either be stable, catastrophic, or initially unstable followed by stable growth.

A methodology for predicting sites and modes ofthermomechanical failure in IC and MEMS packages is developed. Singular stress fields around several stress concentration locations in a typical plastic-encapsulated IC package are calculated using special variable-order singular boundary elements and the singular value decomposition method. The strain energy density distributions around all the stress concentration locations are then obtained from the singular stress fields and compared. The most likely failure site as the temperature ofthe package is raised is then determined as well as the likely modes of failure, ie interfacial delamination or cracking ofmold compound.