Numerical simulation of deployable cable nets for the active removal of orbital debris

Active debris removal (ADR) will be part of any future strategy for sustainable space activities in low Earth orbits. The development of effective and adaptable capture devices is one of the main difficulties faced by ADR mission developers, together with the high costs expected. Tethered cable nets are a promising concept for the capture of derelict non-cooperative vehicles, but their modelling, analysis, and design is a non-trivial task. In fact, the net is a kinematically indeterminate, flexible structure undergoing both large displacements and finite strains. Cables have different responses to tensile and compressive forces. The tumbling target constitutes a rheonomic constraint for the net. During the capture phase, multiple unilateral contacts are expected between net and target. We developed a finite element model for the cable net, adopting the nodal positions as the main unknowns in line with the position-based finite element formulation (PFEF). Large displacements and finite deformations are considered through the Green-Lagrange strain tensor. Cable elements are assumed to react only in tension according to a relaxed hyper-elastic constitutive law. Global damping is introduced into the model according to Rayleigh’s hypothesis. Contact with the target is considered applying the method of Lagrange multipliers and by introducing slack variables to treat the inequality constraint equations. The governing equations for the nonlinear dynamical problem are solved numerically by means of the Newmark method. The case of a steady obstacle of spherical shape is presented. The proposed approach turns out to be computationally effective to simulate both the deployment of the net and the capture of the debris.