Poisson’s ratio control in auxetic metamaterials under large tensile strains

Abstract

Auxetic materials exhibit the remarkable property of negative Poisson’s ratios, enabling exceptional mechanical performance, such as enhanced indentation resistance and energy absorption. However, controlling the Poisson’s ratio under large tensile strains remains challenging due to the geometric nonlinearity inherent in slender auxetic architectures. This nonlinearity is critical for applications like shape-morphing systems, where auxetic metamaterials must maintain a desired Poisson’s ratio under extreme deformations. This work introduces a novel data-driven framework for designing auxetic unit cells with programmable Poisson’s ratio responses across large deformations. We develop a parametric finite element model for anti-chiral auxetic unit cell and the resulting metamaterial sheet. Through extensive parametric studies, we elucidate that maintaining the rotational mechanism via the compatible deformation of the vertical and horizontal beam components is critical for a constant Poisson’s ratio. A machine learning surrogate model is trained to predict the Poisson’s ratio as a function of geometric parameters of auxetic building block within a 25% nominal tension strain range. Applying this surrogate model, an inverse design framework is formulated to optimise the unit cell geometry for achieving a desired Poisson’s ratio target within the supposed tensional regime. 3D-printed specimens with optimised geometries are then manufactured and experimentally tested via uniaxial tension. The excellent agreement between experimental results and predictions validates the effectiveness of the proposed methodology. This data-driven optimisation method offers a computationally efficient and robust tool for the inverse design of auxetic materials with precisely controlled Poisson’s ratio behaviour under large deformations. By addressing the challenge of geometric nonlinearity, our methodology paves the way for advanced applications in soft robotics, morphing structures, and other engineering fields requiring tunable mechanical properties. • Parametric FE model explores auxetic behaviour under large deformation. • Surrogate model & generic algorithm enable efficient inverse design of auxetics. • Bending-dominated deformation in component elements governs constant Poissons ratio under large deformation. • Numerical results validated via uniaxial tensile testing of 3D printed auxetic sheets.