Multi-layer auxetic surfaces with compliant mechanisms

Despite its unique deployment mechanisms known as a negative Poisson's ratio, most existing studies on deployable auxetic structures have overlooked how to solve the dilemma between deployability and stability. In this study, we propose a method to improve both properties by introducing surface overlaying and joints with compliant mechanisms. We first derive open angles to achieve the target shape using conformal mapping. This derivation considers the combined effect of thickness and curvature, which contributes to a better surface approximation of multi-layer auxetic surfaces. Through the unique kerf joint system designed for the auxetic surfaces, we explain the importance of adjusting joint flexibility and stiffness in achieving the target shape. The simulation and physical experiment results of a unit cell show that double-layer auxetic surfaces effectively constrain in-plane torsional motion and efficiently transmit loads through in-plane forces like continuum shell structures. We further create a shell structure made of medium-density fiberboard with the proposed method and demonstrate its deployability and stability.