Tensile Strength Analysis of Knotted Fibrous Ropes:A Structural Mechanics Approach

Sammanfattning

Knotted fibres structures are commonly used in safety-critical applications, where mechanical reliability is essential. It is well-known, particularly in climbing, that the presence of a knot reduces the tensile strength of a rope. However, the underlying mechanism governing this strength reduction is not completely understood. In particular, the role of the fibre structure in influencing the global mechanical response of a rope in a knotted configuration remains unclear, raising the question whether the design of the fibre structure can be optimised to achieve certain global properties of the rope. In this work, a FEM method using Co-rotational formulation for beam elements is developed to simulate the mechanical response for knotted structures both for fibre structures and for single fibres. The formulation captures large rigid-body motions through exact rotational kinematics, while elastic deformations are described in a local co-rotated configuration using a Timoshenko beam model. Contact detection is achieved using a closest-point projection algorithm and enforced by a contact penalty method, which enables both the model to capture both self-contact and fibre-fibre contact. The simulations were performed under quasi-static loading. Two types of experiments were performed on the knotted rope, firstly a combination of a threedimensional digital image correlation (DIC) with a tensile test, and secondly, only tensile test. The three-dimensional digital image correlation was done on the double figure-eight knot while only tensile tests were done on the figure eight-knot. For the DIC experiments the importance of a high-contrast speckle pattern was found to be essential to obtain accurate results. A comparison between the simulations and experiments for small loads were done for the figure-eight knot, showing good agreement. This demonstrates the possibility of using numerical simulations to model knotted fibre structures.