A novel analytical solution for determining the shear behavior of the lattice structure based on the Primitive unit cell considering the shear and bending effect

Abstract

The lattice structure of Schwarz Primitive triply periodic minimal surfaces (P-TPMS) has recently attracted significant attention. This attention arises from its unique topological configuration and superior mechanical properties. This paper studied the effect of changing geometric parameters and the effect of the number of unit cells on the shear modulus of the P-TPMS structure. An analytical model considering the shear and bending effects was derived for the first time, which can efficiently and accurately determine the shear modulus of the P-TPMS lattice structure. Shear modulus was obtained for relative densities in the range of 0.24–0.76. The relative density was calculated by considering the geometric parameter of the surface size (k). The analytical expression was verified by carrying out finite element simulations. Based on the results of this investigation, the shear modulus of the Primitive unit cell changes significantly with different surface size values. Specifically, at k = 0.35, the normalized shear modulus value is 24 times greater than at k = 0.65. This characteristic of the Primitive unit cell extends the range of choices for designers. The completed Ashby diagram suggests that lattice structures based on Primitive unit cells could be one of the most appropriate choices for achieving high shear modulus compared to other structures.

Keywords:

• Shear modulus
• analytical solution
• primitive triply periodic minimal surfaces
• parametric study
• finite element analysis

Disclosure statement

No potential conflict of interest was reported by the authors.