Design of microstructure for porous material with maximum bulk modulus

This paper presents a new approach to designing periodic microstructures of cellular materials. The method is based on the bidirectional evolutionary structural optimization (BESO) technique. The optimization problem is formulated as finding a micro-structural topology with the maximum bulk under a prescribed volume constraint. Using the homogenization theory and finite element analysis within a periodic base cell (PBC). elemental sensitivity numbers are established for gradually removing and adding elements in PBC. Numerical examples demonstrate the effectiveness of the proposed method for achieving convergent microstructures of cellular materials with maximum bulk. Some interesting topological patterns have been found for guiding the cellular material design.