Static chiral Willis continuum mechanics for three-dimensional chiral mechanical metamaterials

Abstract

Recent static experiments on twist effects in chiral three-dimensional\nmechanical metamaterials have been discussed in the context of micropolar\nEringen continuum mechanics, which is a generalization of Cauchy elasticity.\nFor cubic symmetry, Eringen elasticity comprises nine additional parameters\nwith respect to Cauchy elasticity, of which three directly influence chiral\neffects. Here, we discuss the behavior of the static case of an alternative\ngeneralization of Cauchy elasticity, the Milton-Briane-Willis equations. We\nshow that in the homogeneous static cubic case only one additional parameter\nwith respect to Cauchy elasticity results, which directly influences chiral\neffects. We show that the Milton-Briane-Willis equations qualitatively describe\nthe experimentally observed chiral twist effects, too. We connect the behavior\nto a characteristic length scale.\n