Design of Sinusoidal Auxetic Structures for High Shear Flexure

Abstract

This paper presents the analytical model to predict the effective in-plane shear modulus G12* for auxetic honeycomb mesostructure with sinusoidal re-entrant wall. Also, a comparative study is conducted on the ability of the sinusoidal mesostructure over auxetic mesostructure for high shear flexure. In an effort to design components with high shear flexure, the re-entrant wall of the auxetic honeycomb is replaced with a sinusoidal wall. Existing analytical models that predict the effective in-plane elastic properties for auxetic honeycomb mesostructure are limited to straight re-entrant wall. In order to predict the effective in plane shear modulus, G12*, for conceptual design study, an analytical model is needed. The principle of energy methods is used to determine the effective in-plane shear modulus and is verified with the solution in ABAQUS. The analytical model is in agreement with the computational model with a 10% maximum error over a wide range of cell wall thickness and shear strain. The two structures are designed to possess the same equivalent shear modulus and the degree of shear flexure is measured computationally in terms of yield shear strain. The sinusoidal structure introduces nonlinearity with increase in cell wall thickness and shear strain. This nonlinearity causes the sinusoidal auxetic mesostructure to have low shear flexure at a high shear modulus which is higher than about 10MPa. However, it is marginally better than auxetic mesostructure at a low shear modulus which is 10MPa and less.