Spline-based smooth beam-to-beam contact model

The contact between bodies is a complex phenomenon that involves mechanical interaction, frictional sliding and heat transfer, among others. A common (and convenient) approach for the mechanical interaction in a finite element framework is to directly use the geometry of the elements to formulate the contact. The main drawback lies in the sharp corners that occur when straight finite elements are connected leading eventually to contact singularities. To circumvent this issue, particularly in the context of beam-to-beam contact, the present work proposes a pointwise contact formulation based on smooth C-1 continuous spline contact elements. The proposed spline-based formulation, which can be directly attached to any quadratic beam finite element formulation, guarantees a smooth description for the whole set of elements, where contact takes place. A specific nonlinear normal contact interaction law and a rheological model for friction, both with elastic and viscous damping contributions, are developed increasing robustness in practical applications. To demonstrate this robustness, specific examples are considered including comparisons with a similar surface-to-surface formulation and an alternative smooth contact scheme, smooth contact with finite elements having sharp corners, modeling of a knot tightening with self-contact, and a simulation involving multiple pointwise contacts.