A mortar-based frictional contact formulation for large deformations using Lagrange multipliers

Tur, M.; Fuenmayor, F. J.; Wriggers, Peter

doi:10.1016/j.cma.2009.04.007

Cited by 112 publications

(123 citation statements)

References 18 publications

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“…Exact evaluation of the contact surface integrals would need a segmentation of the surface, as proposed for the mortar method in [56,40,39]. Instead of looking for exact integration, in this work we use the same strategy proposed in [18,50,22] and depicted in Figure 4. The approximate integration is performed evaluating the integrand at the quadrature points defined on the surface Γ (1) C regardless of whether the integrand belongs to one or other body.…”

Section: Lagrange Multiplier Interpolation: Penalty Methodsmentioning

confidence: 99%

“…We have chosen the definition given in a previous paper [50], to which we refer for details of linearizations. Also, we neglect the linearization of the Jacobian because it leads to a non-symmetric tangent matrix.…”

Section: Large Deformationsmentioning

confidence: 99%

“…We use the definition of the gap based on the ray tracing, so we follow the formulation proposed in [50] also used in [24] for 2D problems, but extended to 3D. We recall here the main steps of the derivation.…”

Section: Large Deformationsmentioning

confidence: 99%

“…We consider both standard finite elements and the so called immersed boundary elements in which an underlying Cartesian grid made of regular hexahedral elements is cut by the real geometry and integration is performed only in the internal part of the elements. In recent years segment-to-segment formulations like the mortar method [8] have been successfully applied to solving a wide variety of contact problems in 2D [35,27,55] and 3D [39,38], with linear and quadratic elements [28,53], in large and small deformations including Coulomb friction [40,41,17,18,42,50,20] and dynamic problems [24]. The theoretical basis of the mortar method is well known [15,28,32,30,31].…”

Section: Introductionmentioning

confidence: 99%

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A modified perturbed Lagrangian formulation for contact problems

et al. 2015

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The aim of this work is to propose a formulation to solve both small and large deformation contact problems using the finite element method. We consider both standard finite elements and the so-called immersed boundary elements. The method is derived from a stabilized Nitsche formulation. After introduction of a suitable Lagrange multiplier discretization the method can be simplified to obtain a modified perturbed Lagrangian formulation. The stabilizing term is iteratively computed using a smooth stress field. The method is simple to implement and the numerical results show that it is robust. The optimal convergence rate of the finite element solution can be achieved for linear elements.

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Section: Lagrange Multiplier Interpolation: Penalty Methodsmentioning

confidence: 99%

Section: Large Deformationsmentioning

confidence: 99%

Section: Large Deformationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A modified perturbed Lagrangian formulation for contact problems

et al. 2015

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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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Dual mortar methods for computational contact mechanics – overview and recent developments

Popp

Wall

2014

GAMM-Mitteilungen

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Mortar-based finite element discretization in computational contact mechanics has seen a great thrust of research activities over the last years. In this contribution, we review the most important features of the so-called dual mortar finite element approach for finite deformation contact and friction. Advantageous properties of the devised algorithms comprise superior robustness as compared with the traditional node-to-segment (NTS) approach, the absence of any unphysical user-defined parameters (e.g. penalty parameter), the integration of all types of nonlinearities into one single iteration loop and the possibility to condense the biorthogonal discrete Lagrange multipliers from the global system of equations. Beside this general overview, some recent developments are highlighted, such as improved consistency and robustness of dual mortar methods, investigations on efficient numerical integration schemes, an extension to second-order interpolation as well as the combined treatment of contact and elastoplasticity. Several numerical examples are presented to illustrate the high quality of results obtained with the proposed methods.

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A mortar-based frictional contact formulation for large deformations using Lagrange multipliers

Cited by 112 publications

References 18 publications

A modified perturbed Lagrangian formulation for contact problems

A modified perturbed Lagrangian formulation for contact problems

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

Dual mortar methods for computational contact mechanics – overview and recent developments

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