Shape optimization of bowtie-shaped auxetic structures using beam theory

Auxetic structures with a negative Poisson's ratio (NPR) are known for their novel mechanical properties. Recent studies have shown that these properties can be tailored using numerical simulations based on the finite element method where plane or solid elements are applied, combined with optimization techniques. However, an optimization procedure based on beam theory, which is expected to be more computationally efficient than the prevalent plane or solid element formulations, has not been developed thus far. In this paper, we propose a nonlinear beam theory-based model discretized by the Ritz method for the optimum design of bowtie-shaped auxetic structures. For a systematic design process, effective stiffness, NPR, maximum stress, and volume are defined as the main performance indices. Two design parameters, namely, the initial shape of the centerline and the thickness profile represented by B-spline curves, are used to maximize the performance of the system. Our study confirmed that auxetic structures can be tailored to yield a minimum value of the NPR, stress, and volume without the loss of effective stiffness. 3D-printed prototypes were tested to verify the accuracy of the proposed model and the optimality of the design.