Summary A new numerical scheme, termed the seamless‐domain method (SDM), is applied in a multiscale technique. The SDM requires only points and does not require a stiffness equation, mesh, grid, cell, or element. The SDM consists of two steps. The first step is a microscopic analysis of the local (small) simulation domain to obtain interpolation functions for discretizing governing equations. This allows an SDM solution to represent a heterogeneous material with microscopic constituents without homogenization. The second step is a macroscopic analysis of a seamless global (entire) domain that has no mesh and only coarse‐grained points. The special functions obtained in the first step are used in interpolating the continuous dependent‐variable distribution in the seamless global domain whose gradient is also continuous everywhere. The SDM would give a quite accurate solution for domains with strong boundary effects, anisotropic and heterogeneous materials, and isotropic homogeneous fields. Numerical examples of steady‐state heat conduction fields are presented. For heterogeneous material, the SDM using only 117 points provided solutions as accurate as those of the traditional finite element method using 21,665 nodes. Analysis of an isotropic material verified the cost effectiveness of the SDM as in the analysis of heterogeneous material. Copyright © 2015 John Wiley & Sons, Ltd. John Wiley & Sons, Ltd.

Polymers containing ceramics filler are used in various fields that require good thermal conductivity and electric insulation. For material design, prediction of the thermal conductivity is thus critical. There are several prediction methods to determine the thermal conductivity of filler-dispersed composites, such as the Hatta-Taya and Bruggeman models. However, these models do not consider the effect of interaction between fillers; thus, the actual thermal conductivity is larger than the predicted thermal conductivity. In this research, the thermal conductivity of polymers containing ceramic filler was numerically simulated, and the results were compared with the values predicted using the Hatta-Taya model to investigate the effect of filler orientation angle and aspect ratio. The trend of the thermal conductivity change was similar to that observed for the Hatta-Taya model, however, the simulated thermal conductivities were 30% larger than those determined using the Hatta-Taya model for a filler thermal conductivity and volume content of 40 W/(mK) and 25%, respectively. The simulated thermal conductivity results prominently deviated from the Hatta-Taya model values when the filler content ratio was large, the filler aspect ratio was small, or the filler orientation was along the heat-transfer direction.

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