Particulate thermal interface materials (TIMs) are commonly used to transport heat from chip to heat sink. While high thermal conductance is achieved by large volume loadings of highly conducting particles in a compliant matrix, small volume loadings of stiff particles will ensure reduced thermal stresses in the brittle silicon device. Developing numerical models to estimate effective thermal and mechanical properties of TIM systems would help optimize TIM performance with respect to these conflicting requirements. Classical models, often based on single particle solutions or regular arrangement of particles, are insufficient as real-life TIM systems contain a distribution of particles at high volume fractions, where classical models are invalid. In our earlier work, a computationally efficient random network model (RNM) was developed to estimate the effective thermal conductivity of TIM systems (Kanuparthi et al., 2008, “An Efficient Network Model for Determining the Effective Thermal Conductivity of Particulate Thermal Interface Materials,” IEEE Trans. Compon. Packag. Technol., 31(3), pp. 611–621; Dan et al., 2009, “An Improved Network Model for Determining the Effective Thermal Conductivity of Particulate Thermal Interface Materials,” ASME Paper No. InterPACK2009-89116.) . This model is extended in this paper to estimate the effective elastic modulus of TIMs. Realistic microstructures are simulated and analyzed using the proposed method. Factors affecting the modulus (volume fraction and particle size distribution (PSD)) are also studied.

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Point projection is an important geometric need when boundaries described by parametric curves and surfaces are immersed in domains. In problems where an immersed parametric boundary evolves with time as in solidification or fracture analysis, the projection from a point in the domain to the boundary is necessary to determine the interaction of the moving boundary with the underlying domain approximation. Furthermore, during analysis, since the driving force behind interface evolution depends on locally computed curvatures and normals, it is ideal if the parametric entity is not approximated as piecewise-linear. To address this challenge, we present in this paper an algebraic procedure to project a point on to Non-uniform rational B-spline (NURBS) curves and surfaces. The developed technique utilizes the resultant theory to construct implicit forms of parametric Bézier patches, level sets of which are termed algebraic level sets (ALS). Boolean compositions of the algebraic level sets are carried out using the theory of R-functions. The algebraic level sets and their gradients at a given point on the domain are then used to project the point onto the immersed boundary. Beginning with a first-order algorithm, sequentially refined procedures culminating in a second-order projection algorithm are described for NURBS curves and surfaces. Examples are presented to illustrate the efficiency and robustness of the developed method. More importantly, the method is shown to be robust and able to generate valid solutions even for curves and surfaces with high local curvature or G 0 continuity—problems where the Newton–Raphson method fails due to discontinuity in the projected points or because the numerical iterations fail to converge to a solution, respectively.

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