Design of an Isotropic Metamaterial With Constant Stiffness and Zero Poisson's Ratio Over Large Deformations

A great deal of engineering effort is focused on changing mechanical material properties by creating microstructural architectures instead of modifying chemical composition. This results in meta-materials, which can exhibit properties not found in natural materials and can be tuned to the needs of the user. To change Poisson's ratio and Young's modulus, many current designs exploit mechanisms and hinges to obtain the desired behavior. However, this can lead to nonlinear material properties and anisotropy, especially for large strains. In this work, we propose a new material design that makes use of curved leaf springs in a planar lattice. First, analytical ideal springs are employed to establish sufficient conditions for linear elasticity, isotropy, and a zero Poisson's ratio. Additionally, Young's modulus is directly related to the spring stiffness. Second, a design method from the literature is employed to obtain a spring, closely matching the desired properties. Next, numerical simulations of larger lattices show that the expectations hold, and a feasible material design is presented with an in-plane Young's modulus error of only 2% and Poisson's ratio of $2.78×10−3$⁠. These properties are isotropic and linear up to compressive and tensile strains of 0.12. The manufacturability and validity of the numerical model is shown by a prototype.