An implicit 3D corotational formulation for frictional contact dynamics of beams against rigid surfaces using discrete signed distance fields

Miquel Aguirre (1) , Stéphane Avril (1)

1 SAINBIOSE - Santé Ingénierie Biologie Saint-Etienne

The interaction of beam-like structures against surfaces is a challenging problem with applications in engineering (wheel-rail contact, pipeline-soil interaction, ropes sliding on the seabed) and in medical applications such as surgical planning and training (catheter navigation, aneurysm coiling, stent deployment). This contact problem is traditionally solved using Total Lagrangian beam formulations, which interact against Lagrangian triangulated surfaces. Overall, the computational speed is affected, due to the nonlinearities of the beam formulation and, as well as due to the expensive search algorithms, required to find the close point projection. In the search towards an efficient beam to surface contact algorithm, this paper explores the combined use of 1) a corotational beam formulation, where the motion of the beam element is decomposed in rigid body and pure deformational parts and 2) an implicit description of the surface by means of discrete signed distance fields (SDF), which can be seen as a Lagrangian beam immersed within an Eulerian (rigid) solid. To do so, a previously reported implicit corotational formulation for beam dynamics is modified to account for frictional contact, by means of a penalty term. The new contributions are fully linearized to update the tangent operator and the system is integrated in time by means of the HHT-α method. Overall, a consistent implicit contact dynamics formulation is provided. A SDF, defined in a voxel-type grid, is used to represent implicitly the surface geometry. The SDF values and derivatives are computed at the Lagrangian point of integration of the beam by means of an efficient tensor product of compact, high order, 1D Kernels, as widely used in immersed Fluid-Structure Interaction techniques. A wide variety of validation tests are presented which prove the accuracy and robustness of the proposed algorithm.

Mots clés: Contact; 3D Corotational beams; Nonlinear dynamics; Finite Elements; Eulerian Solids; Signed Distance Fields

Domaines: Mécanique [physics.med-ph]; Biomécanique [physics.med-ph]

Miquel Aguirre, Stéphane Avril. An implicit 3D corotational formulation for frictional contact dynamics of beams against rigid surfaces using discrete signed distance fields. Computer Methods in Applied Mechanics and Engineering, 2020, 371, pp.113275. ⟨10.1016/j.cma.2020.113275⟩. ⟨hal-03139761⟩