Three-dimensional re-entrant auxetic lattice cores for additively manufactured multirotor arms: a finite-element assessment

Auxetic lattices are usually proposed for energy absorption and impact protection, and their use as the main load-carrying structure of small aerial vehicles has received little attention. This study assesses a three-dimensional re-entrant lattice as the core of a printed sandwich arm for a 1.7 kg quadrotor. The arm is made of short-carbon-fibre polyamide 6, has 0.8 mm face sheets and a two-layer core with 2 mm struts, and weighs 26.3 g. The static response to flight, lateral-impact and landing loads, and the natural frequencies, were computed with quadratic tetrahedral models of the complete geometry. The arm was compared with an arm of equal mass having a conventional hexagonal core with the same cell strut lengths, and with a solid printed arm, a carbon-fibre laminate arm and a moulded glass-fibre polyamide arm. Under through-thickness compression the re-entrant lattice has a Poisson's ratio of −0.53, compared with +0.48 for the conventional lattice. In the first design, sharp junctions between the struts and the face sheets produced mesh-dependent stress peaks; conical fillets and continuous face sheets lowered the peak stresses by 59–71 %. The final arm has a stiffness of 55.0 N/mm at the motor, 9.3 times that of the solid printed arm, and a first natural frequency of 171 Hz. Its factor of safety under the landing load is 1.65 on in-plane strength, but would fall below unity if the peak stress acted across the printed layers. With the conventional core of equal mass the arm is 8 % stiffer and its peak stresses are 44–56 % lower, and the conventional core also resists local indentation better. In this application the stiffness comes from sandwich action, and an auxetic core would have to be justified by its behaviour under impact.