Computationally generated cross-property bounds for stiffness and fluid permeability using topology optimization

We compute Pareto fronts that estimate the upper bounds of the bulk modulus and fluid permeability cross-property space for periodic porous materials over a range of porosities. The fronts are generated numerically using topology optimization, which is a systematic, free-form design algorithm for optimizing material layouts. The presented microstructures demonstrate the trade-off between the bulk modulus and fluid permeability achievable with a multifunctional porous material and will be useful for designers of materials for which both stiffness and permeability are important. Our results suggest that the range of achievable stiffness and permeability properties is significantly restricted when considering elastic isotropy, as compared to cubic elastic symmetry. The estimated bounds are of practical importance given the lack of microstructure-independent theoretical cross-property bounds.