Optimal design of material microstructure for convective heat transfer in a solid-fluid mixture

Microstructural design for multi-functional composites of solid, fluid and heat transfer properties is newly presented in this work. Two major methods are utilized: topology optimization and the homogenization of porous media. In topology optimization, the geometry-control methods are extensively investigated using three types of design examples in solid mechanics. From the observations of the design results, it is concluded that the density filtering method yields acceptable design results in all design examples. For a clear segregation of material phases, the level-set based topology optimization is also examined. The level-set evolution via Hamilton-Jacobi equation may suffer from satisfying multiple constraints and the regularization for stable evolution plays an important role. Instead of Hamilton-Jacobi equation, the level-set evolution via the method of moving asymptotes is proposed to deal with multiple constraints. The constraints are smoothly satisfied by the proposed method of the level-set evolution via the MMA method. Numerical studies show that the move limit should be appropriately chosen for stable evolution of the level-set function in the proposed method.The topology design concept is applied to the optimal distribution of the solid or fluid volume in the fluid-flowing domain by employing the Brinkman-type governing equation. The inappropriate choices of the interpolation parameters for inverse permeability cause numerical instabilities such as design dependency and oscillation of the state variables. The existing interpolation schemes of material properties are investigated and interpolation of the inverse Darcy number is proposed. In the proposed method, the design dependency can be controlled by suppressing oscillation of velocity and pressure.The proposed and extensively investigated methodologies in topology optimization are applied to the microstructural design of multi-functional composites. To evaluate the fluid permeability and the effective heat dispersivity of microstructure, the homogenization of Stokes flow and convection-diffusion transport are presented. The objective formulation using the matrix norm and the inverse tensor is proposed. The existing results of negative Poisson's ratio design are successfully reproduced by the proposed objective formulations. The true orthotropic materials in elasticity are accomplished. In order to design multiple effective properties, several objective functions are adaptively scaled by the infimum of design sensitivity vectors and the objective values. As a design example for the multifunctional composite, the bone scaffold design is extended by employing the fluid permeability and the heat dispersivity. Consequently, the orthotropic multi-functional composites of solid, fluid, and heat transfer properties are newly accomplished in this work.