Distance fields on unstructured grids: Stable interpolation, assumed gradients, collision detection and gap function

Wolff, Sebastian; Bucher, Christian

doi:10.1016/j.cma.2013.02.015

Cited by 8 publications

(1 citation statement)

References 39 publications

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“…The overall approach can be seen as a Lagrangian beam immersed within an Eulerian (rigid) solid. The use of level sets and/or Eulerian solids in computational contact, has been explored before for 3D solids in [27][28][29][30][31][32] but, to the best of the authors knowledge, this is the first application where it is combined with a Lagrangian beam.…”

Section: Introductionmentioning

confidence: 99%

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

Aguirre

Avril

2020

Computer Methods in Applied Mechanics and Engineering

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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.

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Section: Introductionmentioning

confidence: 99%

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

Aguirre

Avril

2020

Computer Methods in Applied Mechanics and Engineering

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Signed distance field framework for unified DEM modeling of granular media with arbitrary particle shapes

Lai

Zhao

et al. 2022

Comput Mech

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Continuous gap contact formulation based on the screened Poisson equation

2023

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We introduce a PDE-based node-to-element contact formulation as an alternative to classical, purely geometrical formulations. It is challenging to devise solutions to nonsmooth contact problem with continuous gap using finite element discretizations. We herein achieve this objective by constructing an approximate distance function (ADF) to the boundaries of solid objects, and in doing so, also obtain universal uniqueness of contact detection. Unilateral constraints are implemented using a mixed model combining the screened Poisson equation and a force element, which has the topology of a continuum element containing an additional incident node. An ADF is obtained by solving the screened Poisson equation with constant essential boundary conditions and a variable transformation. The ADF does not explicitly depend on the number of objects and a single solution of the partial differential equation for this field uniquely defines the contact conditions for all incident points in the mesh. Having an ADF field to any obstacle circumvents the multiple target surfaces and avoids the specific data structures present in traditional contact-impact algorithms. We also relax the interpretation of the Lagrange multipliers as contact forces, and the Courant–Beltrami function is used with a mixed formulation producing the required differentiable result. We demonstrate the advantages of the new approach in two- and three-dimensional problems that are solved using Newton iterations. Simultaneous constraints for each incident point are considered.

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Distance fields on unstructured grids: Stable interpolation, assumed gradients, collision detection and gap function

Cited by 8 publications

References 39 publications

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

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

Signed distance field framework for unified DEM modeling of granular media with arbitrary particle shapes

Continuous gap contact formulation based on the screened Poisson equation

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