Compression–Torsion Coupling in Chiral Metamaterials: A Micropolar Continuum Framework for Instantaneous Torque

Chiral metamaterials can convert axial compression into rotation or torsionthrough the geometry and handedness of their unit cells. This response cannot, ingeneral, be fully represented by classical Cauchy elasticity, which lacks independentmicrorotation and couple-stress fields. This paper develops a continuum frameworkfor coupling between compressive loading and instantaneous torque in chiral architected solids. The formulation begins with the balance laws and constitutivestructure of micropolar elasticity, then reduces the response of a specimen to atwo-mode axial–torsional system. For a conservative, linearly elastic specimen,the effective stiffness matrix is symmetric, and its off-diagonal coefficient governsreciprocal compression–torsion coupling. The resulting torque under imposed axialdisplacement and the induced twist under axial force are derived explicitly. The paperfurther distinguishes this equilibrium coupling from inertial torque, rate-dependentresponse, buckling, and nonconservative or odd-elastic behavior. Thermodynamicstability bounds, handedness reversal, experimental identification, and a multiscalehomogenization procedure are presented. The framework provides a testable basisfor designing and characterizing chiral metamaterials, while emphasizing that thecoefficients must be determined for the specific architecture and loading regime.