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Negative Poisson’s ratio NPR material attracts a lot of attentions for its unique mechanical properties. However, achieving NPR is at the expense of reducing Young’s modulus. It has been observed that the composite stiffness can be enhanced when blending positive Poisson’s ratio PPR material into NPR material. Based on the respective interpolation of Young’s modulus and Poisson’s ratio, two concurrent topology optimization problems with different types of constraints, called Problem A and B, are respectively discussed to explore the Poisson’s ratio effect in porous microstructure. In Problem A, the volume constraints are respectively imposed on macro and micro structures; in Problem B, besides setting an upper bound on the total available base materials, the micro thermal insulation capability is considered as well. Besides considering the influence of micro thermal insulation capability on the optimized results in Problem B, the similar and dissimilar influences of Poisson’s ratios, volume fractions in Problem A and B are also investigated through several 2D and 3D numerical examples. It is observed that the concurrent structural stiffness resulting from the mixture of PPR and NPR base materials can exceed the concurrent structural stiffness composed of any individual base material.

Two-scale topology optimization of macrostructure and porous microstructure composed of multiphase materials with distinct Poisson’s ratios