Mechanics of beams made from chiral metamaterials: Tuning deflections through normal-shear strain couplings

Abstract

In the current work, we demonstrate the potential of structures made of chiral artificial materials to balance bending loads through tensile loads, exploiting their inner normal to shear strain coupling. To that scope, we employ beam structures which we architecture with tetrachiral unit-cells. For the latter, we quantify their inherently coupled normal to shear strain behavior, making use of homogenization analysis techniques. We subsequently derive the equations that characterize the bending mechanics of beams with an inner bending to normal loading coupling, starting from first principles. Thereupon, we compute the normal forces required to equilibrate the effect of bending loads on beam structures, providing relevant closed-form parametric expressions. Using the derived analytical formulas, we carry out both numerical simulations and experiments for the case of cantilever beams. Results suggest that the coupling of normal and shear deformations can be used as a primal load-balancing mechanism, providing new possibilities in the control of the artificial structure's kinematics and overall mechanics.