A quasistatic ALE cable formulation for multibody systems applications

This paper presents an arbitrary Lagrangian–Eulerian (ALE) formulation for a quasistatic cable finite element. The objective is to propose a theoretical framework for the derivation of the ALE equilibrium equations of the cable starting from a continuous formulation and the principle of virtual work. The model aims to be simple, as only axial strains are considered. The advantages of using an ALE formulation are also shown through several numerical examples. In the case of a distributed loading, the ALE setting yields an energy-optimal mesh. In some cases, the problem can be nonconvex and a regularization of the equations is proposed to ensure the convergence of the Newton solver to one of the solutions. A cable–pulley system is also investigated without and with friction. In the latter case, the results are validated with an analytical formula for the evolution of the tension force in the cable. Finally, a multibody model of a soft finger is proposed in which the coupling of a system of rigid bodies with the cable model is enforced through kinematic constraints.