A one-dimensional model for mechanical coupling metamaterials using couple stress theory

A new model for a one-dimensional (1D) metamaterial model is formulated based on the couple stress theory. Different point groups of crystal will affect the mechanical couplings in the 1D metamaterial model. We find that when the material belongs to D₂ point group, an unusual set of equations is decoupled from governing equations: axial force–torsion–warping (FTW) metamaterial model, which describes an unusual mechanical coupling that cannot occur in traditional materials. The deformation behaviors of the current model under a different axial force are analyzed by using the FTW metamaterial model. The numerical results show that the middle part of the current model has maximum torsional deformation when subjected to sine-type axial force. Since the end of the current model is fixed, the current model does not have compressional deformation globally. Moreover, when the current model is subjected to cosine-type axial force, the FTW coupling is successfully achieved. Then, we study a rod-like metamaterial model under an axial end force. The results show that the compressional deformation occurs at the free end, with a counterclockwise torsion. The current work provides guidance for the structural design and theoretical analysis of the rod-like metamaterial when using the couple stress theory.