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

Abstract

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.

A nonsmooth method for spatial frictional contact dynamics of flexible multibody systems with large deformation

“…As expected, the vertical oscillations of the cable greatly decrease as the coefficient of friction increases. The simulation results of the first 3 s are close to the result from the work by Aguirre and Avril 60 . Then, the tip falls down quicker than the simulation by Aguirre and Avril.…”

“…The simulation results of the first 3 s are close to the result from the work by Aguirre and Avril. 60 Then, the tip falls down quicker than the simulation by Aguirre and Avril. The reason is that the normal contact condition in Equation ( 8) denotes the inelastic impact and more energy is dissipated in the simulation.…”

“…The fourth example studied the contact dynamics between a cable and a fixed rigid cylinder and is taken from the work by Wang et al 56 and the work by Aguirre and Avril 60 . The initial configuration of the cable‐cylinder system is shown in Figure 17.…”

“…The fourth example studied the contact dynamics between a cable and a fixed rigid cylinder and is taken from the work by Wang et al 56 and the work by Aguirre and Avril. 60 The initial configuration of the cable-cylinder system is shown in 56 The CPU time for these simulations and average and maximum numbers of Newton's iterations are listed in Table 1. The analysis of the convergence with respect to the time step size is shown in Figure 19.…”

An acoustic Riemann solver for large strain computational contact dynamics

“…The most common techniques addressing this issue include penalty method, Lagrange multiplier method, or a combination of both. In the penalty method, 4 the impenetrability constraint is enforced as a penalty normal traction along the contact surface. The disadvantage of the penalty approach is that the enforcement of the impenetrability condition is only approximate and its effectiveness depends on the selection of the user‐defined penalty parameters.…”