Investigation of size effect of micro auxetic structures by finite element method

Auxetic structures are structures that show negative Poisson's ratio unlike the conventional structures. This means that when auxetics are stretched laterally, they expand longitudinally. This unique behavior of auxetics brings some advantages over conventional materials such as indentation resistance, fracture toughness, shear resistance, high energy absorption, good acoustic performance etc. A structure can show negative Poisson's ratio either due to its natural molecular form such as arsenic, black phosphorus or due to its artificial structural shapes such as re-entrant, chiral. Both types of auxetic structures are investigated for a long time by researchers at macro scale. Advances in manufacturing technology of small scales structures direct the researchers to micro/nano scale auxetic studies as well, especially for the last few decades. It has been proven that as the structures become smaller, size effects occur. Size effects cannot be captured by classical continuum theories. To be able to capture size effects, researchers developed higher order continuum theories over the years. In this study, small scale auxetics are investigated utilizing finite element methodology. For this purpose, based on a Modified Couple Stress Theory, a higher order continuum theory, stiffness and mass matrices of Timoshenko Beam is derived. To verify the current work at macro scale, tensile testing experiments are performed and similar works in the literature at macro scale are utilized. Then, different aspects of re-entrant auxetic structures are studied in micro scale: Poisson's ratio, deformation mechanisms, elastic modulus, fundamental frequencies and entropy generation rate. It is shown that most of the current literature that use analytical and numerical methods fail to accurately estimate the behavior of small scale auxetics. Only the studies that perform micro/nano experiments or utilize advance simulation tools can capture the size effects. Even if they capture the size effects, the methodologies they use are commercially and/or computationally expensive methods. Moreover, they are not explicitly showing the difference between large and small scale auxetic behavior including the size effects. On the other hand, the current work utilizes basic finite element principles and can be easily modified to see the difference between large and small scales, including size effects.