Contribution of tension-torsion coupling effect on elastic properties of chiral and anti-chiral structures

Tension-induced rotation and rotation-induced tension are two types of tension-torsion coupling (TTC). The rotation deformation along with TTC effect is a major factor that can induce the planar porous structure to exhibit the auxetic behavior, but why do some structures have numerous rotations but do not exhibit the auxetic behavior? In this study, we propose an analytical framework to address this issue by quantitatively analyzing the independent effects of direct bending of ligaments and rotation of rigid rings on the mechanical properties of the chiral and antichiral honeycombs. The chirality and the angle between force and ligament mainly affect rotation of rigid rings and direct bending of ligaments, respectively. The analytical expressions of TTC coefficients, Poisson's ratio and Young's modulus of antichiral-4, antichiral-3 and chiral-3 honeycombs are derived. The effects of the eccentric distance, the rotation stiffness, the tension and bending stiffness of ligaments on the TTC coefficients, Poisson's ratio and Young's modulus are revealed via analytical expressions and numerical results. This work provides a guideline for tailoring Young's modulus and Poisson's ratio by tuning the TTC effect to alter the relative strength of direct and rotation-induced deformations in the porous structures from a theoretical point of view.