We are developing a computational procedure for the analysis and design of 2D kirigami surfaces with auxetic patterns that can be deployed into arbitrary 3D shapes. We aim to precisely control not only the deployed shape but also the nonlinear stiffness in the deployed configuration through rationally designed bistability of comprising unit cells. In this way, various surfaces with the same target shape but different target stiffness values can be realized by 3D printing or laser cutting of 2D planar surfaces with designed auxetic patterns.

The unique negative Poisson behavior of the auxetic structure affects the static properties of the structure. Our group has aimed at applying auxeticity to the conventional structure to control the static characteristics. We are studying stiffness control of tubular structure by perforating a rotating rigid auxetic pattern. When the auxetic tube is applied by bending, a unit cell on the surface of the tube is tensioned or compressed, generating auxetic deformation, however, in the case of torsion, the unit cell deforms in non-auxetic deformation mode similar to a continuum. By harnessing the mode-dependent deformation of the auxetic pattern, we realized independent control of bending and torsional stiffness in a tubular structure.

As applying auxetic patterns into 2D or 3D curved structures, dynamic properties of structure also can be adjusted to specific purposes. Our team studies elastic wave propagation and vibration characteristics of the auxetic structure. We set effective properties which determine characteristics of a structure (ex: elastic stiffness tensor, eigen-frequency, Poisson's ratio, etc) to exhibit properties non-existing in nature, and suggest particular auxetic patterns to achieve effective properties. Based on FE simulation, elastic wave propagation and vibration characteristics are analyzed for various parameters of auxetic pattern and verified experimentally.

We develop mechanical meta-sheets whose Poisson’s ratio (PR) and coefficient of thermal expansion (CTE) can be independently modulated by using rotating rectangular auxetic units consisting of alternated bi-material beams. During mechanical compression or tension, a rigidly rotating mechanism is activated to control the PR, whereas, under thermal load, the CTE of the meta-sheet is dictated by a bending-induced rotating mechanism. Leveraging these independent deformation mechanisms, we have experimentally and numerically validated the independent design of both PR and CTE (including anisotropy) across negative and positive ranges. Additionally, we apply these meta-sheets as skins of a sandwich panel for thermo-mechanical shape morphing.