Dynamics of graphene origami-enabled auxetic metamaterial beams via various shear deformation theories

Although auxetic metamaterials exhibit unique and unusual mechanical properties, such as a negative Poisson's ratio, their mechanics remains poorly understood. In this study, we model a graded beam fabricated from graphene origami-enabled auxetic metamaterials and investigate its dynamics from the perspective of different shear deformation theories. The auxetic metamaterial beam is composed of multiple layers of graphene origami-enabled auxetic metamaterials, where the content of graphene origami varies through the layered thickness; both the auxetic property and other properties are varied in a graded manner, which are effectively be approximated via micromechanical models. The Euler-Bernoulli, third-order, and higher-order shear deformable refined beam theories are adopted to model the auxetic metamaterial beam as a continuous system. Following this, the governing motion equations are derived using the Hamiltonian principle and then are numerically solved using a weighted residual method. The obtained results provide a comprehensive understanding of how graphene origami content and its distribution pattern, graphene folding degree, and the utilisation of different shear deformation theories influence the dynamic behaviour of the beam.