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Design of lattice materials with isotropic stiffness through combination of two complementary cubic lattice configurations

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Abstract

Lattice materials possess excellent mechanical properties such as light weight, high specific stiffness and high energy absorption capacity. However, the commonly used lattice materials inspired by Bravais lattice often give rise to property anisotropy that is not desirable for engineering application such as bone implants. For this sake, a design methodology for isotropic stiffness is proposed in this paper. Firstly, an efficient theoretical method for calculating the elastic matrices of lattice materials was presented. The method is based on Euler–Bernoulli beam theory and the assumption of affine deformation of cell vertices applicable to cubic truss-lattice materials. The theoretical approach was validated by comparing with the finite element simulations. Utilizing the validated theoretical method, and by properly combining the lattice configurations with complementary stiffness along different directions, an elastic isotropic lattice material can be obtained. A few examples are presented to demonstrate the effectiveness and adaptability of the proposed design strategy by permutating the combinations of different classic lattices. The method proposed in this paper can provide a new approach in the design of lattice materials with excellent anisotropy control.

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Acknowledgements

This work was supported by the opening project of State Key Laboratory of Explosion Science and Technology (Beijing Institute of Technology) (KFJJ22-08M), State Key Laboratory of Mechanics and Control of Mechanical Structures with (MCMS-E-0221G02), National Natural Science Foundation of China (11972261), and Shanghai Supercomputer Center.

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  1. School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai, 200092, China

    Puhao Li, Fan Yang, Yijie Bian, Siyuan Zhang & Lihua Wang

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  1. Puhao Li
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Correspondence to Fan Yang or Lihua Wang.

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Li, P., Yang, F., Bian, Y. et al. Design of lattice materials with isotropic stiffness through combination of two complementary cubic lattice configurations. Acta Mech 234, 1843–1856 (2023). https://doi.org/10.1007/s00707-023-03480-y

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