Compression Deformation Prediction of Chiral Metamaterials: A Compression–Shear Coupling Model

A category of metamaterials consisting of chiral cytosolic elements assembled periodically, in which the introduction of a rotatable annular structure gives metamaterials the ability to deform in compression–shear, has been a focus of research in recent years. In this paper, a compression–shear coupling model is developed to predict the compressive deformation behaviour of chiral metamaterials. This behaviour will be analysed by coupling the rotation of the annular node and the bending characteristics of ligament beam, which are obtained as a function of the length of ligament beam and the angle of rotation at the end of the beam. The shape function of the ligament beam under large deformation is obtained based on the elliptic integral theory; the function characterises the potential relationship between key parameters such as displacement and rotation angle at any point on the ligament beam. By simulating the deformation of cells under uniaxial compression, the reasonableness of the large deformation model of the ligament beam is verified. On this basis, a chiral cell-compression mechanical model considering the ductile deformation of the annular node is established. The compression–shear deformation of two-dimensional planar chiral metamaterials and three-dimensional cylindrical-shell chiral metamaterials was predicted; the offset displacements and torsion angles agreed with the experimental and finite element simulation results with an error of less than 10%. The developed compression–shear coupling model provides a theoretical basis for the design of chiral metamaterials, which meet the need for the precise control of shapes and properties.