Assessment of static rope behavior with asymmetric damage distribution

• A mechanical model is proposed to estimate asymmetric damaged static rope response.
• A wide range of degree of asymmetry in damage distribution is considered.
• Comparisons with experimental data and numerical and analytical simulations validate the model.
• The range of applicability of damage degree is extended relative to previous models.
• The proposed model is a computationally cheap tool for estimating damaged rope response.

In this paper, a mechanical model is proposed to estimate the static response (stiffness, residual capacity, deformed configuration, strain/strain distribution within cross-section, and deformation capacity) of a rope asymmetrically damaged. In this study, damage corresponds to the complete rupture of one or more rope components in a particular rope cross-section location. In the proposed model, the damaged rope is assumed to behave as a nonlinear beam under biaxial bending and axial load with Bernoulli's kinematic hypothesis. Biaxial bending arises from the unbalanced radial contact forces within rope cross-section, which are related to the initial helical geometry configuration of the rope components, due to the asymmetric damage distribution. An efficient and robust iterative cross-sectional numerical algorithm is implemented to estimate the asymmetric damaged rope capacity curve, stress and strain distributions throughout rope cross-section and rope geometry deformation for a prescribed axial displacement of the rope. The results given by the proposed model are found to be in good agreement with available static tension tests on asymmetrically damaged small-scale (ropes diameter equal to 6 mm) polyester ropes and their corresponding 3D finite element (FE) simulations with lower computational cost. Additionally, compared to the solutions obtained by previous analytical models reported in the literature, the range of applicability associated to the degree of damage to rope cross-section (number of broken rope components) is extended.