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The physical and mechanical properties of cellular materials not only depend on the constituent materials but also on the microstructures. Here we show that, when the cellular materials are constructed by self-repeated representative volume elements, their effective elastic tensor can be obtained by a fast Fourier transform-based homogenization method. Numerical examples confirm that the bulk modulus of cellular material with the topology of triply periodic minimal surfaces such as Diamond, Gyroid, Neovius, and Schwarz P surfaces can approach to the upper Hashin-Shtrikman bound. However, the high values of their Young's modulus are obtained at the cost of low shear modulus and vice versa. Such conflicting behavior suggests that these two individual moduli may complement each other in a hybrid structure via combining different surfaces in cellular material. It is envisaged that our approach will enable the creation of ideal isotropic materials with large Young's modulus, shear modulus, and bulk modulus.
Chen et al. (Thu,) studied this question.