Analytical modeling and parametric study of equivalent stiffness for auxetic structures

Auxetic materials have a negative Poisson's ratio, which is different from most engineering materials. Auxetic materials are used in various fields such as medicine, sports science, sensors and actuators, etc. An auxetic structure is made of several cells in parallel and series. In this paper, the equivalent stiffness of an auxetic cell and structure are analytically extracted. The effect of the geometrical parameters, such as the angle and beam length of the auxetic cell, on auxetic cell and structure equivalent stiffness, are investigated. The extracted equations are verified using the simulation of the auxetic structure in the Abaqus software. In this study, numerical simulation is used in order to study the effect of the parameters of the auxetic cell on its equivalent mass. The results of this study show that changing the geometrical parameters of the auxetic cell, affect the vibration behavior of the auxetic structure. Also, the effect of geometrical parameters of the auxetic structure on the Poisson's ratio is investigated.