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

Abstract

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.

Structural topology optimization with positive and negative Poisson’s ratio materials

“…Furthermore, this model was extended to establish a computational framework to optimize composite microstructures and concurrent structures in consideration of the hybrid of PPR and NPR materials (Long et al, 2016;Long et al, 2017a;Long et al, 2017b). With void in micro-scale, Jia et al (Jia et al, 2018) proposed two concurrent models to discuss the Poisson's ratio effect.…”

“…Until now, studies based on topology optimization (Long et al, 2016;Long et al, 2017aLong et al, , 2017bJia et al, 2018) are primarily focused on improving the stiffness of NPR materials in micro-scale through mixing with the PPR materials. Recently, the auxetic cellular structure design demonstrates the potential in large-scale structural systems (Cabras and Brun, 2016;Subramani et al, 2016;Magalhaes et al, 2016).…”

“…E (2) . Elemental Young's modulus and Poisson's ratio are penalized by the SIMP interpolation (Strek et al, 2014;Long et al, 2016;Jia et al, 2018):…”

“…The proper values of the above two parameters are determined by convergence and optimized topologies through numerical examples. It is recommended that p = 4 and q = 1 (Jia et al, 2018).…”