A Nonlinear Viscoelastic Contact Interphase Modeled as a Cosserat Rod-Like String

A nonlinear viscoelastic contact interphase is modeled using a Cosserat rod-like string. This Cosserat model is a rod with a deformable cross-section, but with no constitutive resistance to bending. The model allows for axial extension, tangential shear deformation and normal extension of the cross-section which are determined by finite deformations of the interphase. Moreover, the constitutive response of this string model can be determined directly by three-dimensional constitutive equations for a hyperelastic component and a Maxwell elastic-viscoplastic component that together produce viscoelastic response of the interphase. The example of vibrations of a rigid outer ring connected to a fixed inner disk by a nonlinear viscoelastic interphase is used to show that the Cosserat string model of the interface predicts torque and force applied to the outer ring which include nonlinear coupling that is not present in simple uncoupled models of Maxwell components for torque and force applied to the outer ring by the interphase.