Multiscale Mechanics and Energy Absorption of Auxetic Structural Systems Constitutive Modeling, Stability, and Performance Metrics

Auxetic structures exhibit a negative effective Poisson’s ratio: under longitudinaltension, they expand laterally, whereas under longitudinal compression, they contract laterally. This response is primarily associated with architecture-dependent mechanisms, including cell-wall rotation, bending, hinging, and buckling, rather than with an unusual property of the constituent material alone. Such mechanisms can influence stiffness, indentation resistance, fracture behavior, and crushing response; however, auxeticity does not guarantee superior energy absorption in every design.Performance depends on topology, relative density, constituent behavior, loadingrate, boundary conditions, and the onset of failure or densification.This paper develops a theory-guided framework for analyzing auxetic structuralsystems. It combines small-strain homogenized elasticity, finite-strain kinematics,unit-cell energy methods, nonlinear constitutive response, stability assessment, and energy-absorption metrics. A re-entrant cell is used as a representative architecture, while the framework is intended to extend to other periodic cellular systems.Governing relations are presented for effective Poisson’s ratio, elastic admissibility, absorbed work, specific energy absorption, crush-force efficiency, and dynamic response. A validation protocol is proposed using full-field strain measurement,quasi-static compression, impact testing where appropriate, and finite-element analysis. The framework distinguishes established continuum-mechanics relations from model-dependent predictions and does not claim experimental findings that have not been measured.