In this thesis, procedures are developed to simulate packed microstructures of particles so as to identify the optimal trade-off between thermal and mechanical behavior.
Experimental and numerical simulations of microstructures that have been generated
as reported in the literature were found to have volume fractions of around 60%. However, as commercially available thermal greases have volume fractions in the range of
60 − 80%, there is a need to develop an efficient algorithm to generate microstructures numerically. The particle packing is initially posed as a nonlinear programming
problem and rigorous optimization search algorithms are systematically applied to
generate particle systems that are compactly packed, but without particle overlap.
Since the packing problem is computationally expensive, the algorithms are systematically evaluated to improve computational efficiency as measured by the number of particles in the system, as well as the time to generate the microstructure. The
evaluated algorithms include the inefficient penalty function methods, best-in-class
sequential programming method, matrix-less conjugate gradient method as well as
the augmented Lagrangian method. In addition, heuristic algorithms are also evaluated to achieve computationally efficient packing. The evaluated heuristic algorithms
are mainly based on the Drop-Fall-Shake method, but modified to more effectively
simulate the mixing process in commercial planetary mixers. With the developed
procedures, Representative Volume Elements (RVE) with volume fraction as high as
74% were achieved.

After the microstructurs were generated, the effective thermal conductivity and
effective elastic modulus were estimated using a ‘Random Network Model (RNM)’
that was previously developed. The RNM solves the near-percolation heat conduction
problem with hundreds of thousands of particles in minutes compared to hours or days
that a full-field simulation requires. The approximations inherent in the RNM are
valid if the particulate composite has widely different matrix and particle properties,
which is true in the case of thermal greases. In the present thesis, the previously
developed RNM was modified to account for the fact that the generated RVEs contain
sides with cut particles.