Abstract
Our research emphasizes on developing new methods to simulate the effective conductivities of the composites possessive of contact resistance. We concern composites with inclusions dispersed randomly in the matrix. The inclusions can be spherical particles, or infinitely long fibers. They are named particulate-reinforced composite and long-fiber-reinforced composites, respectively.There is an abundant knowledge about how to obtain the effective conductivities of composites. The critical Biot number,, gives “neutral effect.” That is, we can neglect interface properties while we treat composites’ effective conductivities. We focus on construction of a simulation model, that can be used to calculate the effective conductivities of the composites with any size or any irregular type inclusions dispersed randomly in the matrix.We image that thermal molecules do random walks among inclusions and matrix. Kim and Torquato (1990,1991) brought up the ideas whether the test thermal molecules will walk across the interface or not and how much time it will spend on crossing the interface or coming back. They obtained the effective conductivity of two phase composites. However, they considered single-sized inclusions, and a perfect contact with the matrix. (Temperature fields are continuous across the matrix-inclusion, so are the normal heat fluxes). They didn’t work on problems involving poly-dispersed inclusions with contact resistance at the matrix-inclusion interface. (Temperature fields are not continuous, but the normal heat fluxes are continuous.) However, it is common that contact resistance exists between matrix and inclusions. When the Biot number is infinite, contact resistance will disappear. Then, the matrix contacts the inclusions perfectly. Therefore, the contact resistance problem is a limiting case of the contact resistance problems.The new method is a breakthrough in the area of composites’ effective conductivities. We obtained satisfactory results of the effective conductivities of the fibers and particles arranged regularly in the matrix. Moreover, the effective conductivities of the particulate-reinforced and the fiber-reinforced composites with inclusions randomly distributed are also computed. And we confirm that Biot number is an important parameter again. When Bi is less than the critical Biot number, the combined effect of interface and inclusion is enhancing to the matrix. When Bi is greater than the critical Biot number, the combined effect of interface and inclusion is enhancing to the matrix. We also verify that the inclusions generated are dispersed randomly enough.