Design of maximum permeability material structures

This paper extends recent advances in the topology optimization of fluid flows to the design of periodic, porous material microstructures. Operating in a characteristic base cell of the material, the goal is to determine the layout of solid and fluid phases that will yield maximum permeability and prescribed flow symmetries in the bulk material. Darcy's law governs flow through the macroscopic material while Stokes equations govern flow through the microscopic channels. Permeability is computed via numerical homogenization of the base cell using finite elements. Solutions to the proposed inverse homogenization design problem feature simply connected pore spaces that closely resemble minimal surfaces, such as the triply periodic Schwartz P minimal surface for 3 - d isotropic, maximum permeability materials.