A corotational finite element to model bending vibrations of metallic strands

A new formulation to model the mechanical response of metallic strands undergoing a combination of axial load and planar bending is developed. Each wire of the strand is modeled as an elastic curved thin rod. A kinematic model is then introduced to relate the generalized strain variables of the strand to those of the wires. The stress-strain state of the wires is evaluated starting from the analysis of the internal contact conditions. Friction is modeled through the classic Amontons-Coulomb law and the elastic tangential compliance of contact patches is accounted for. A non-holonomic material constitutive law in terms of the cross sectional generalized stresses and strains of the Euler-Bernoulli beam theory is obtained and implemented within a corotational beam element explicitly conceived for nonlinear static and dynamic analyses of flexible structures. Numerical applications are presented to highlight the role of the tangential compliance mechanism on the hysteretic bending behavior of a typical steel strand.