Novel Isotropic Anti-Tri-Missing Rib Auxetics with Prescribed In-Plane Mechanical Properties Over Large Deformations

Abstract

Analogy with the standard anti-tri-chiral auxetic structure, a novel anti-tri-missing rib structure is proposed in this work. Finite element (FE) analyses (on one unit-cell) were carried out first to investigate the auxeticity and the underlying deformation mechanisms of the proposed structure with linear elastic base material. FE results show that the structure exhibits constant NPR over a relatively large strain range at few specific orientations. However, its auxetic behavior is inconspicuous and the in-plane isotropy only holds over limited strain range owing to the deficient rotational mechanism. An enhanced design with increased interior angle of the ligament and triangle reinforcement within the rotational central core was then proposed to improve the auxeticity and its in-plane isotropy. A theoretical formulation of the elastic modulus and Poisson’s ratio for the enhanced design was further developed based on Castigliano’s theorem. Tunable elastic modulus in the linear elastic regime and controllable isotropic constant NPRs over large strain ranges were thus achieved for the enhanced design without significantly compromising the overall stiffness. The targeted NPR performances were also verified with nonlinear base materials. Uniaxial tensile experiments and finite size simulations for lattice structures comprising an array of enhanced anti-tri-missing rib unit cells were finally performed to validate the FE and theoretical results obtained from unit-cell analyses.