Theoretical analysis on the stiffness of compression–torsion coupling metamaterials

Abstract

The compression–torsion coupling metamaterials constructed by cells based on chiral mechanism of inclined rods with weak transverse constraints, display superior compression–torsion properties among the metamaterials reported previously. Aiming at metamaterials of this type, a general representative cell is extracted to reveal the relationship between the load and the deformation with considering the compression–torsion coupling effect. The stiffness matrix of the chiral 3D cell is derived based on Euler beam theory and applying dummy-load method, which is expressed as functions of the geometry parameters of cell structures and the mechanical properties of base material. The analytical predictions show good agreement with the numerical simulations. Results show that there exist optimal inclined angles of the rods corresponding to the maximal shear stiffness and the maximal compression–torsion coupling stiffness, respectively, which are both determined by the ratio of circular loop diameter to inclined rod length. This work provides guidelines for the design and analysis of compression–torsion coupling metamaterials, and opens a new avenue for theoretically analyzing the deformation coupling problem.