Highlights • A fully implicit discrete model was developed to simulate the nonlinear dynamic contact of space net capture system. • The geometric nonlinearity was achieved by discrete differential geometry and the boundary nonlinearity was handled by incremental potential contact. • A parameter sweep was performed to show the configuration evolution of nets with different shooting locations.

Abstract An efficient computational method is proposed to combine the discrete differential geometry (DDG) method with the multi-dimensional incremental potential (IP) formulation to simulate the contact dynamics between a shooting net and a defunct satellite. The geometrically nonlinearity of the elastic net is described using the DDG method, which discretizes the flexible net into multiple nodes and connected edges. The internal elastic forces and the associated Jacobians are derived analytically. The multi-dimensional incremental potential formulation is used to achieve the intersection-free condition during the physical collision between deformable tether-net and rigid space debris. The smooth IP barrier functional constructed for contact simulation is differentiable, such that the nonlinear elastodynamic system can be robustly solved through a fully implicit time-marching scheme. Our numerical approach is first applied to simple examples, and demonstrating its effectiveness in dealing with non-penetration contacts of elements with different dimensions, such as ‘edge-to-edge’ and ‘edge-to-surface’. Next, the dynamic interaction between the deploying net and defunct satellite is analysed. A parameter sweep is performed with our robust and efficient simulator to show the configuration evolution of the net shot from different relative locations of the target object. Our numerical results can provide an optimal deployment strategy for tether-net capture systems during the active debris removal missions.