A mortar segment-to-segment contact method for large deformation solid mechanics

Puso, Michael A.; Laursen, Tod A.

doi:10.1016/j.cma.2003.10.010

Cited by 310 publications

(351 citation statements)

References 11 publications

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“…Continuously averaged non-mortar side normal vectors ( Figure 1b) Yang presented in his paper [3] (see also [4], [5], [6]) a new method on defining the normal vectors. Those methods have in common that there is an averaged unit normal defined on start and end nodes of the contact edges (mostly non-mortar side edges).…”

Section: Discontinuous Mortar Side Normal Vectors (Figure 1a)mentioning

confidence: 99%

Structural contact problems for large deformations ‐ Comparison of steady and non steady normal field

Hammer

2011

Proc Appl Math and Mech

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We will present a comparison between two formulations of the normal vector field for contact algorithms based on the mortar method. First the non steady normal field is discussed. The non steadiness is a result of the C 0 continuity of the boundary discretization. This is the common result if one discretize the domain with classical finite element methods. Second we will present results for a special normal field distribution. We average the nodal normal vector of two ascending edges and interpolate this nodal normal throughout the edges. We have implemented both methods and present comparisons based on numerical experiments. .Discontinuous mortar side normal vectors ( Figure 1a) The proposed mortar side normal was presented in [1] and also in other publications. As the normal vector is normal to its adjacent edge on the mortar side it is obvious that the direction of the normal vector jumps on start and end nodes of a mortar edge.Continuously averaged non-mortar side normal vectors (Figure 1b 2 Problems related to C 0 only surfaces in contact mechanics Oscillation of projection For the nearest point projection we have to determine the corresponding edge for a given projection point. This edge might change during the Newton-Raphson procedure from one iteration to the next. This situation is shown in figure 2b. If the "best" projection edge changes back again in the next iteration the projection starts to oscillate and no convergence can be reached. This problem is not influenced by averaging.

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Section: Discontinuous Mortar Side Normal Vectors (Figure 1a)mentioning

confidence: 99%

Structural contact problems for large deformations ‐ Comparison of steady and non steady normal field

Hammer

2011

Proc Appl Math and Mech

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“…Following Puso and Laursen [7,Section 2], the potential function of the normal contact constraints pertaining to the mortar method can be derived from an integral form of the contact complementarity condition. Accordingly, (1) , t)·(u (1),h (X (1) , t)−u (2),h (X (2) , t)) d =:…”

Section: Mortar Contact Constraintsmentioning

confidence: 99%

“…Moreover, a constant unit outward normal m e has been employed for each e ∈¯ (1) . This is slightly different from the use of a nodally averaged normal in Puso and Laursen [7]. We further remark that, for the semi-discrete system under consideration, the virtual work expression (12) can be written as…”

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confidence: 99%

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A mortar method for energy‐momentum conserving schemes in frictionless dynamic contact problems

Hesch

Betsch

2008

Numerical Meth Engineering

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SUMMARYIn the present work the mortar method is applied to planar large deformation contact problems without friction. In particular, the proposed form of the mortar contact constraints is invariant under translations and rotations. These invariance properties lay the foundation for the design of energy-momentum timestepping schemes for contact-impact problems. The iterative solution procedure is embedded into an active set algorithm. Lagrange multipliers are used to enforce the mortar contact constraints. The solution of generalized saddle point systems is circumvented by applying the discrete null space method. Numerical examples demonstrate the robustness and enhanced numerical stability of the newly developed energymomentum scheme.

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“…Recently, various combinations of the Mortar method have been developed in e.g. [4], [5], [6] allowing to overcome overstiff behavior especially in the case where contact tractions are computed point-wise at integration points. In addition, good results for the patch-test have been shown also in [3] exploiting the, so-called, segment-to-segment approach, coinciding with the Mortar method with penalty descriptions of the contact traction.…”

Section: Introductionmentioning

confidence: 99%

Symmetrization of Various Friction Models Based on an Augmented Lagrangian Approach

Konyukhov¹,

Schweizerhof²

IUTAM Symposium on Computational Methods in Contact Mechanics

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A mortar segment-to-segment contact method for large deformation solid mechanics

Cited by 310 publications

References 11 publications

Structural contact problems for large deformations ‐ Comparison of steady and non steady normal field

Structural contact problems for large deformations ‐ Comparison of steady and non steady normal field

A mortar method for energy‐momentum conserving schemes in frictionless dynamic contact problems

Symmetrization of Various Friction Models Based on an Augmented Lagrangian Approach

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