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An Auxetic Material With Negative Coefficient of Thermal Expansion and High Stiffness

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Abstract

Thermal stress has a negative effect on structural safety in many engineering fields, so it is particularly important to eliminate this negative effect as much as possible. This problem can be solved by designing the microstructure of the materials to make the coefficient of thermal expansion (CTE) close to 0, while negative thermal expansion (NTE) materials can become an important part of zero thermal expansion materials. Negative Poisson's ratio (NPR) materials have been favored by researchers because of their bright application prospects in many fields such as medical treatment and engineering. The research of lightweight mechanical metamaterials with both NTE and NPR effects is of great significance for the development of smart sensors with mechanical and temperature sensitivities, and the realization of multi-functional integration of structure. Inspired by the structure of natrolite, a material which can adjust the CTE and Poisson's ratio (PR) in a large range at the same time is designed in this paper. The analytical formulas of the equivalent CTE, PR and Young's modulus are derived and verified by finite element simulation. Meanwhile, the concept of stiffness index is introduced and analyzed by theoretical and finite element methods. Furthermore, the shear modulus of the material is analyzed by finite element method. The results show that the analytical formulas are valid for the material and the material can not only realize NTE and NPR effects at the same time, but also exhibits high stiffness in the principal axis and other directions. In addition, 3D material extended by the proposed 2D material is proposed and verified by finite element method whose parameter analysis have also been carried out, which can achieve NTE and NPR effects in three directions.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (grant number: 11672338), Guangdong Basic and Applied Basic Research Foundation (grant number: 2020A1515010836), the Science and Technology Program of Guangzhou, China (grant number: 201904010332), and Guangdong Education Department (grant number: 2018KTSCX124).

Funding

This work was supported by the National Natural Science Foundation of China (grant number: 11672338), Guangdong Basic and Applied Basic Research Foundation (grant number: 2020A1515010836), the Science and Technology Program of Guangzhou, China (grant number: 201904010332), and Guangdong Education Department (grant number: 2018KTSCX124).

Author information

Author notes

  1. Jingxiang Huang and Weihua Li contributed equally to this work and should be considered co-first authors

Authors and Affiliations

  1. Department of Applied Mechanics and Engineering, Sun Yat-Sen University, Guangzhou, 510275, PR China

    Jingxiang Huang, Mingming Chen & Minghui Fu

  2. College of Electromechanical Engineering, Guangdong Polytechnic Normal University, Guangzhou, 510665, PR China

    Weihua Li

Authors
  1. Jingxiang Huang
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Contributions

All authors contributed to the study conception and design. The analysis were performed by Huang Jingxiang, Li Weihua, Chen Mingming and Fu Minghui. The first draft of the manuscript was written by Huang Jingxiang and Li Weihua and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

Corresponding author

Correspondence to Minghui Fu.

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Appendix

Appendix

The equivalent PR of the proposed material can be expressed as \(\overline{\nu }=-\frac{Q}{R}\), in which

$$\left\{\begin{array}{c}\begin{array}{c}Q=4{P}^{2}Cos{\theta }_{1}\left(N\mathrm{Cos}{\theta }_{1}+M\mathrm{Cos}2{\theta }_{1}\right)\left(1-\mathrm{Sin}2{\theta }_{1}\right)+\sqrt{2}P\left(\mathrm{Cos}{\theta }_{1}-\mathrm{Sin}{\theta }_{1}\right)\left(\left(4{M}^{2}+\right.\right.\\ \left.\left.3{N}^{2}\right)\mathrm{Cos}{\theta }_{1}+{N}^{2}\mathrm{Cos}3{\theta }_{1}+4{M}^{2}\mathrm{Sin}{\theta }_{1}-4N{\mathrm{Cos}}^{2}{\theta }_{1}\left(-2M+N\mathrm{Sin}{\theta }_{1}\right)\right)-8M{N}^{2}Sin{\theta }_{1}{\mathrm{Sin}}^{2}2{\theta }_{1}\end{array}\\ \begin{array}{c}R=4{M}^{2}\left(\sqrt{2}P+4N{\mathrm{Sin}}^{2}{\theta }_{1}\right)+NP\left(\sqrt{2}N+P\right){\left(1+\mathrm{Cos}2{\theta }_{1}-\mathrm{Sin}2{\theta }_{1}\right)}^{2}-\\ \left.4M\mathrm{Cos}{\theta }_{1}\left(-4{N}^{2}{\mathrm{Sin}}^{2}{\theta }_{1}+\right.{P}^{2}\left(-1+\mathrm{Sin}2{\theta }_{1}\right)+\sqrt{2}NP\left(-3+\mathrm{Cos}2{\theta }_{1}+\mathrm{Sin}2{\theta }_{1}\right)\right)\end{array}\\ M={E}_{1}{t}_{1}\\ \begin{array}{c}N={E}_{2}{t}_{2}\\ P={E}_{3}{t}_{3}\end{array}\end{array}\right.$$
(12)

The equivalent Young’s modulus of the proposed material along y direction can be expressed as

figure a

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Huang, J., Li, W., Chen, M. et al. An Auxetic Material With Negative Coefficient of Thermal Expansion and High Stiffness. Appl Compos Mater 29, 777–802 (2022). https://doi.org/10.1007/s10443-021-09983-y

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