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

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.

Automated summary

This paper proposes a theoretical method for calculating the elastic matrices of lattice materials and presents a design strategy for obtaining elastic isotropic lattice materials by combining lattice configurations with complementary stiffness along different directions. The effectiveness and adaptability of the proposed design strategy are demonstrated through examples of different classic lattices. The method proposed in this paper provides a new approach in the design of lattice materials with excellent anisotropy control.