A contact description for continuum beams with deformable arbitrary cross-section

This work introduces a surface-to-surface contact description in the context of beam-to-beam contact. The introduced contact description is formulated in the frame work of the absolute nodal coordinate formulation. Leveraging the solid element-like features of the absolute nodal coordinate beam formulation and utilizing an interpolation scheme to parameterize the cross-section geometry, the computationally expensive discretization in beam's thickness directions can be avoided. The developed formulation is general to account for internal and external contact scenarios. Numerical examples illustrate the robustness and applicability of the introduced formulation in contact problems comprising beams with arbitrary cross-sectional geometry and material nonlinearities. The numerical results indicate the effectiveness of the proposed contact solution to problems entailing various contact configurations, such as the presence of coupled large deformation modes within contact, contact between beams with sharp-edges, and a scenario where an arbitrary curve-to-curve contact takes place across beams’ surfaces. Accuracy of the contact integrals and the stability of the proposed formulation are also examined, respectively using the contact path and inf–sup tests.