Non-linear mechanics of geometrically imperfect graphene origami-enabled auxetic metamaterial third-order beam structures

Abstract

This paper investigates the non-linear mechanics of geometrically imperfect multilayered graphene origami-enabled auxetic metamaterial beams. The metamaterial beam is layer-wise composed of graphene origami-enabled auxetic metamaterials; both the auxetic and other properties are estimated using micromechanical models. Using a higher-order shear deformation theory, the beam is modelled as a continuous structure, accounting for the axial and transverse displacements, as well as the rotations. Large deflections are approximated via the von-Kármán geometric non-linearity and the coupled deformation equations are derived using an energy-work method. These coupled non-linear deformation equations are solved numerically using a generalised differential quadrature method. A finite element software, ANSYS, is used for a simplified version of the system (i.e., non-multilayered, non-metamaterial, geometrically perfect) to demonstrate the reliability of our methodology; also, the bending behaviour of simplified versions of the system is validated against literature. This study provides detailed discussions on how geometric imperfections, boundary conditions, graphene origami content and its distribution patterns, and folding degree influence the non-linear bending of metamaterial beams.