Material structural design with isotropy constraint

The objective of this study is to design periodic microstructures of materials using the bidirectional evolutionary structural optimization (BESO) technique integrated with constraint on material constitutive tensor. Maximum bulk or shear modulus are selected as objectives of material design subject to isotropy constraints while volumetric constraint is treated as an evolutionary parameter. Extra constraints are defined in the statement of optimization problem and the approach utilizes a gradient-based method to impose isotropy. Numerical examples show the computational efficiency of the approach and some interesting microstructures are presented that maximize the bulk or shear modulus of material. In addition, the method is flexible in the sense that it has the capability to impose other types of constraint on material elasticity tensor