Mathematical Modeling
Vol. 4 (2020), Issue 1, pg(s) 10-12

THEORETICAL FOUNDATIONS AND SPECIFICITY OF MATHEMATICAL MODELLING

Nagata patch interpolation for finite volume mechanical contact simulations

  • 1 Faculty of Mechanical Engineering and Naval Architecture, Zagreb, Croatia
  • 2 University College Dublin, School of Mechanical and Materials Engineering, Belfield, Ireland
  • 3 NV Bekaert SA, Belgium

Abstract

This paper describes a finite volume contact algorithm with surface smoothing using the Nagata patch interpolation. Nagata interpolation is derived from existing discretisation, using the mesh points positions and their calculated normal vectors. The contact between a deformable and a rigid body is analysed, whereas the rigid body is described with Nagata patch interpolation. Such approach allows a more accurate evaluation of the resulting contact stresses and forces

Keywords

References

  1. P. Wriggers, Computational Contact Mechanics. Springer, 2nd edition, (2006).
  2. P. Cardiff, Ž. Tuković, P. DeJaeger, M. Clancy, A. Ivanković, A Lagrangian cell-centred finite volume method for metal forming simulation, International Journal for Numerical Methods in Engineering, 109(13), 1777-1803, (2017) .
  3. Ž. Tuković, A. Karač, P. Cardiff, H. Jasak and A. Ivanković, OpenFOAM finite volume solver for fluid-solid interaction. Transactions of FAMENA, 42(3), pp.1-31, 2018.
  4. H. Jasak, H. Weller, Finite Volume Methodology for Contact Problems of Linear Elastic Solids, Proceedings of 3rd International Conference of Croatian Society of Mechanics, Cavtat/Dubrovnik, 253-260, (2000).
  5. P. Cardiff, A. Karač, A. Ivanković. Development of a finite volume contact solver based on the penalty method, Computational Materials Science, 283-284, (2012).
  6. V. Škurić, P. De Jaeger and H. Jasak, Lubricated elastoplastic contact model for metal forming processes in OpenFOAM. Computers & Fluids, 172, pp.226-240, (2018).
  7. D. M. Neto, M. C. Oliveira, and L. F. Menezes, Surface smoothing procedures in computational contact mechanics, Archives of Computational Methods in Engineering 24.1, 37-87, (2017).
  8. M. Hachani and L. Fourment, 3D contact smoothing method based on Quasi-C1 interpolation, Trends in computational contact mechanics, 58, 23-40, (2011).
  9. T. Hama, T. Nagata, C. Teodosiu, A. Makinouchi and H. Takuda, Finite-element simulation of springback in sheet metal forming using local interpolation for tool surfaces. International Journal of Mechanical Sciences, 50(2), 175-192, (2008).
  10. T. Nagata, Simple local interpolation of surfaces using normal vectors, Computer Aided Geometric Design, 22, 327-347, (2005).
  11. D. M. Neto, M. C. Oliveira, L. F. Menezes and J. L. Alves, Applying Nagata patches to smooth discretized surfaces used in 3D frictional contact problems, Computer Methods in Applied Mechanics and Engineering, 271, 296-320, (2014).
  12. D. M. Neto, M. C. Oliveira, L. F. Menezes and J. L. Alves, A contact smoothing method for arbitrary surface meshes using Nagata patches, Computer Methods in Applied Mechanics and Engineering 299, 283-315, (2016).
  13. L. Krstulović-Opara, P. Wriggers, and J. Korelc, AC 1- continuous formulation for 3D finite deformation frictional contact, Computational Mechanics, 29.1, 27-42, (2002).

Article full text

Download PDF