An alternative formulation for quasi-static frictional and cohesive contact problems

  • Authors:

  • P. Areias;A. Pinto Da Costa;T. Rabczuk;F. J. Queirós De Melo;D. Dias-Da-Costa;Mourad Bezzeghoud

  • Affiliations:

  • Physics Department, University of Évora, Évora, Portugal 7002-554 and ICIST, Lisbon, Portugal;ICIST, Lisbon, Portugal and Departamento de Engenharia Civil, Arquitetura e Georecursos, Instituto Superior Técnico, University of Lisbon, Lisbon, Portugal 1049-001;Institute of Structural Mechanics, Bauhaus-University Weimar, Weimar, Germany 99423;Departamento de Engenharia Mecânica, University of Aveiro, Aveiro, Portugal 3810-193;School of Civil Engineering, The University of Sydney, Sydney, Australia 2006 and INESC Coimbra, Department of Civil Engineering, University of Coimbra, Coimbra, Portugal 3030-788;Physics Department, University of Évora, Évora, Portugal 7002-554 and CGE, Centro de Geofísica de Évora, Évora, Portugal

  • Venue:
  • Computational Mechanics
  • Year:
  • 2014

Quantified Score

Hi-index 0.00

Visualization

Abstract

It is known by Engineering practitioners that quasi-static contact problems with friction and cohesive laws often present convergence difficulties in Newton iteration. These are commonly attributed to the non-smoothness of the equilibrium system. However, non-uniqueness of solutions is often an obstacle for convergence. We discuss these conditions in detail and present a general algorithm for 3D which is shown to have quadratic convergence in the Newton---Raphson iteration even for parts of the domain where multiple solutions exist. Chen---Mangasarian replacement functions remove the non-smoothness corresponding to both the stick-slip and normal complementarity conditions. Contrasting with Augmented Lagrangian methods, second-order updating is performed for all degrees-of-freedom. Stick condition is automatically selected by the algorithm for regions with multiple solutions. The resulting Jacobian determinant is independent of the friction coefficient, at the expense of an increased number of nodal degrees-of-freedom. Aspects such as a dedicated pivoting for constrained problems are also of crucial importance for a successful solution finding. The resulting 3D mixed formulation, with 7 degrees-of-freedom in each node (displacement components, friction multiplier, friction force components and normal force) is tested with representative numerical examples (both contact with friction and cohesive force), which show remarkable robustness and generality.