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A dynamic implicit 3D material point-to-rigid body contact approach for large deformation analysis

Robert E. Bird, Giuliano Pretti, William M. Coombs, Charles E. Augarde, Yaseen U. Sharif, Michael J. Brown, Gareth Carter, Catriona Macdonald, Kirstin Johnson

Abstract

Accurate and robust modelling of large deformation three dimensional contact interaction is an important area of engineering, but it is also challenging from a computational mechanics perspective. This is particularly the case when there is significant interpenetration and evolution of the contact surfaces, such as the case of a relatively rigid body interacting with a highly deformable body. The numerical challenges come from several non-linear sources: large deformation mechanics, history dependent material behaviour and slip/stick frictional contact. In this paper the Material Point Method (MPM) is adopted to represent the deformable material, combined with a discretised rigid body which provides an accurate representation of the contact surface. The three dimensional interaction between the bodies is detected though the use of domains associated with each material point. This provides a general and consistent representation of the extent of the deformable body without introducing boundary representation in the material point method. The dynamic governing equations allows the trajectory of the rigid body to evolve based on the interaction with the deformable body and the governing equations are solved within an efficient implicit framework. The performance of the method is demonstrated on a number of benchmark problems with analytical solutions. The method is also applied to the specific case of soil-structure interaction, using geotechnical centrifuge experimental data that confirms the veracity of the proposed approach.

A dynamic implicit 3D material point-to-rigid body contact approach for large deformation analysis

Abstract

Accurate and robust modelling of large deformation three dimensional contact interaction is an important area of engineering, but it is also challenging from a computational mechanics perspective. This is particularly the case when there is significant interpenetration and evolution of the contact surfaces, such as the case of a relatively rigid body interacting with a highly deformable body. The numerical challenges come from several non-linear sources: large deformation mechanics, history dependent material behaviour and slip/stick frictional contact. In this paper the Material Point Method (MPM) is adopted to represent the deformable material, combined with a discretised rigid body which provides an accurate representation of the contact surface. The three dimensional interaction between the bodies is detected though the use of domains associated with each material point. This provides a general and consistent representation of the extent of the deformable body without introducing boundary representation in the material point method. The dynamic governing equations allows the trajectory of the rigid body to evolve based on the interaction with the deformable body and the governing equations are solved within an efficient implicit framework. The performance of the method is demonstrated on a number of benchmark problems with analytical solutions. The method is also applied to the specific case of soil-structure interaction, using geotechnical centrifuge experimental data that confirms the veracity of the proposed approach.

Paper Structure

This paper contains 32 sections, 74 equations, 19 figures, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Material point method
  3. Continuum formulation
  4. Material point and background grid spatial discretisation
  5. Basis functions
  6. Discretisation in time
  7. Stabilisation
  8. Rigid body
  9. Coordinate systems
  10. Kinematics
  11. Contact
  12. Contact introduction
  13. Gap function
  14. Normal contact
  15. Tangential contact
  16. ...and 17 more sections

Figures (19)

  • Figure 1: Material point method steps (adapted from coombs2020aample).
  • Figure 2: The rigid body global and local coordinate systems.
  • Figure 3: Rigid body: truss frame description.
  • Figure 4: CPP: A contact vertex (red dot) of a GIMP domain, shown in grey, in contact with a rigid body triangle, blue. The gap function is also shown by the yellow arrow.
  • Figure 5: Closest point projection: (a) is the 3D view of a GIMP in contact with a concave edge of the rigid body, (b) is the corresponding slice view through the domain with green regions showing where the CPP is onto triangles, and red regions the CPP onto points/lines of the rigid body.
  • ...and 14 more figures