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Topological Design of Microstructures of Materials Containing Multiple Phases of Distinct Poisson’s Ratios

Kai Long1,*, Xiaoyu Yang1, Nouman Saeed1, Zhuo Chen1, Yi Min Xie2

1 State Key Laboratory for Alternate Electrical Power System with Renewable Energy Sources, North China Electric Power University, Beijing, 102206, China
2 Centre for Innovative Structures and Materials, School of Engineering, RMIT University, Melbourne, 3001, Australia

* Corresponding Author: Kai Long. Email:

Computer Modeling in Engineering & Sciences 2021, 126(1), 293-310.


A methodology for achieving the maximum bulk or shear modulus in an elastic composite composed of two isotropic phases with distinct Poisson’s ratios is proposed. A topology optimization algorithm is developed which is capable of nding microstructures with extreme properties very close to theoretical upper bounds. The effective mechanical properties of the designed composite are determined by a numerical homogenization technique. The sensitivities with respect to design variables are derived by simultaneously interpolating Young’s modulus and Poisson’s ratio using different parameters. The so-called solid isotropic material with penalization method is developed to establish the optimization formulation. Maximum bulk or shear modulus is considered as the objective function, and the volume fraction of constituent phases is taken as constraints. The method of moving asymptotes is applied to update the design variables. Several 3D numerical examples are presented to demonstrate the effectiveness of the proposed structural optimization method. The effects of key parameters such as Poisson’s ratios and volume fractions of constituent phase on the nal designs are investigated. A series of novel microstructures are obtained from the proposed approach. It is found that the optimized bulk and shear moduli of all the studied composites are very close to the Hashin-Shtrikman-Walpole bounds.


Cite This Article

Long, K., Yang, X., Saeed, N., Chen, Z., Xie, Y. M. (2021). Topological Design of Microstructures of Materials Containing Multiple Phases of Distinct Poisson’s Ratios. CMES-Computer Modeling in Engineering & Sciences, 126(1), 293–310.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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