Mechanics of beams made from chiral metamaterials: Tuning deflections through normal-shear strain couplings. (April 2020) - Karathanasopoulos, N.
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. Graphical abstract: Unlabelled Image Highlights: The mechanics of chiral beams with inner normal-shear strain couplings is elaborated, starting from first principles. Normal deformations create bending deflections which are proportional to the material's shear-normal compliance coefficient. The use of inner strain couplings as an equilibration mechanism is numerically and experimentally tested for the first time. The bending deflections' equilibrating force is inversely proportional to the material's shear-normal coupling coefficient.