Effect of Wrapping Force on the Effective Elastic Behavior of Packed Cylinders

Abstract

When cylinders are packed and wrapped by the bands around the surface, the effective elastic behavior in the cross section of the assembly, which is of significance to its stability and integrity, can be controlled by the wrapping force in the band. The wrapping force is transferred to the cylinders through the Hertz contact between each pair of neighboring cylinders, which is validated by the experiments. The Singum model is introduced to study the mechanical behaviors of the packed cylinders with two-dimensional (2D) packing lattices, in which an inner cylinder is simulated by a continuum particle of Singum and the inter-cylinder force is governed by the Hertz contact model so as to derive the effective stress-strain relationship. The wrapping force will produce configurational forces given a displacement variation, which significantly changes the effective stiffness of the packed cylinders. The hexagonal packing exhibits isotropic elasticity whereas the square packing is anisotropic. The efficacy of our model is demonstrated by comparing the closed form elasticity against the numerical simulation and the previous models. The explicit form of elasticity can be used for packing design and quality control of cable construction and installation.