Two dimensional mortar contact methods for large deformation frictional sliding.

*(English)*Zbl 1161.74497Summary: This paper presents a mortar-based formulation for the solution of two dimensional frictional contact problems involving finite deformation and large sliding. As is widely recognized, traditional node-to-surface contact formulations have several drawbacks in solution of deformable-to-deformable contact problems, including lack of general patch test passage, degradation of spatial convergence rates, and robustness issues associated with the faceted representation of contacting surfaces. The mortar finite element method, initially proposed as a technique to join dissimilarly meshed domains, has been shown to preserve optimal convergence rates in tied contact problems [see B. I. Wohlmuth, Discretization Methods and Iterative Solvers Based on Domain Decomposition, Springer-Verlag, Heidelberg (2001; Zbl 0966.65097) for a recent review], and is examined here as an alternative spatial discretization method for large sliding contact. In particular, a novel description for frictional sliding conditions in large deformation mortar formulations is proposed in this work. In recent years, the mortar element method has already been successfully implemented to solve frictional contact problems with linearized kinematics [T. A. Laursen and J. C. Simo, Int. J. Numer. Methods Eng. 36, No. 20, 3451–3485 (1993; Zbl 0833.73057)]. However, in the presence of large deformations and finite sliding, one must face difficulties associated with the definition and linearization of contact virtual work in the case where the mortar projection has a direct dependence on the tangential relative motion along the interface.

In this paper, such a formulation is presented, with particular emphasis on key aspects of the linearization procedure and on the robust description of the friction kinematics. Some novel techniques are proposed to treat the non-smoothness in the contact geometry and the searching required to define mortar segments. A number of numerical examples illustrate the performance and accuracy of the proposed formulation.

In this paper, such a formulation is presented, with particular emphasis on key aspects of the linearization procedure and on the robust description of the friction kinematics. Some novel techniques are proposed to treat the non-smoothness in the contact geometry and the searching required to define mortar segments. A number of numerical examples illustrate the performance and accuracy of the proposed formulation.

##### MSC:

74S05 | Finite element methods applied to problems in solid mechanics |

74M15 | Contact in solid mechanics |

74M10 | Friction in solid mechanics |

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\textit{B. Yang} et al., Int. J. Numer. Methods Eng. 62, No. 9, 1183--1225 (2005; Zbl 1161.74497)

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##### References:

[1] | , , . A new nonconforming approach to domain decomposition: The mortar element method. In Nonlinear Partial Differential Equations and Their Applications, , (eds). Pitman: London, Wiley: New York, 1992; 13-51. |

[2] | . Discretization Methods and Iterative Solvers Based on Domain Decomposition. Springer-Verlag: Heidelberg, 2001. · Zbl 0966.65097 |

[3] | Hallquist, Computer Methods in Applied Mechanics and Engineering 51 pp 107– (1985) |

[4] | Benson, Computer Methods in Applied Mechanics and Engineering 78 pp 141– (1990) |

[5] | Wriggers, Communications in Applied Numerical Methods 1 pp 199– (1985) |

[6] | Papadopoulos, Computer Methods in Applied Mechanics and Engineering 94 pp 373– (1992) |

[7] | . Computational Contact and Impact Mechanics. Springer: Berlin, 2002. |

[8] | Hild, Computer Methods in Applied Mechanics and Engineering 184 pp 99– (2000) |

[9] | Belgacem, Computer Methods in Applied Mechanics and Engineering 116 pp 59– (1994) |

[10] | Belhachmi, Computer Methods in Applied Mechanics and Engineering 116 pp 53– (1994) |

[11] | , , . Nonconforming mortar element methods: application to spatial discretization. In Domain Decomposition Methods, SIAM: Philadelphia, 1989; 392-418. |

[12] | Belgacem, Comptes Rendus De L’Academie Des Sciences 324 pp 123– (1997) |

[13] | Belgacem, Mathematical and Computer Modeling 28 pp 263– (1998) |

[14] | McDevitt, International Journal for Numerical Methods in Engineering 48 pp 1525– (2000) |

[15] | , . A dirchlet-neumann type algorithm for contact problems with friction. Technical Report, Universitat Augsburg, 2001. |

[16] | Wriggers, Computers and Structures 37 pp 319– (1990) |

[17] | Laursen, International Journal for Numerical Methods in Engineering 36 pp 3451– (1993) |

[18] | Puso, Computer Methods in Applied Mechanics and Engineering 129 pp 601– (2004) |

[19] | Simo, Computer Methods in Applied Mechanics and Engineering 50 pp 163– (1985) |

[20] | . Contact Mechanics. Cambridge University Press: Cambridge, 1985. · Zbl 0599.73108 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.