Data-Driven calibration and experimental observations of the main hypothesis employed in the definition of the wTCM finite element under compression

Abstract

Auxetic metamaterials, characterized by a negative Poisson’s ratio, exhibit distinctive deformation mechanisms that make them attractive for applications requiring enhanced energy absorption and stiffness control. In this work, a quasi-static compression test is performed on a 3D-printed coupon based on the General Auxetic Metamaterial (GAM) cell to experimentally characterize its global response and dominant deformation mechanisms. The experimental results are used to inform and support the calibration of a data-driven multiscale finite element methodology based on the wedge Topologically Consistent Metamaterial (wTCM) element. The approach establishes an energetic equivalence between the discrete strut architecture and an equivalent continuum representation, allowing geometric nonlinearities and effective stiffness degradation to be captured through pre-calibrated strut-level response curves. A detailed explicit finite element model is employed as a geometric reference to isolate geometric nonlinear effects, and the numerical responses obtained with the wTCM formulation are compared against both the experimental results and the explicit simulations. With appropriate calibration, the wTCM approach is shown to capture the relevant nonlinear structural response — including auxetic kinematics and strain localization — while retaining a reduced computational complexity.