This paper presents a topology optimization method to design periodic unit cell in cellular materials with extreme properties using a moving iso-surface threshold method. The aim is to determine the optimal distribution of material within the periodic unit cell. The effective properties of cellular material are obtained by using a finite element-based homogenization method. The penalty function approach is introduced to construct the objective function for designing material with extreme properties under condition of square or isotropic symmetry. New characteristic response functions of moving iso-surface threshold are proposed for maximum shear or bulk modulus, maximum shear modulus or negative Poisson’s ratio under isotropic symmetry. Several examples are presented and the results are compared to those obtained with the solid isotropic material with penalization method to demonstrate the validity of the method. A series of new and interesting microstructures with extreme properties are found and presented.
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