A mortar segment-to-segment frictional contact method for large deformations

Puso, Michael A.; Laursen, Tod A.

doi:10.1016/j.cma.2004.06.001

Cited by 209 publications

(229 citation statements)

References 15 publications

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“…But even if all slave elements are fully covered by the master surface, an integration based on a segmentation process as illustrated in [36,54,55] is more accurate than an element based integration usually performed on slave elements [41,56], see also [57] for a comparison in terms of accuracy and efficiency. Recently, element based integration for isogeometric mortar methods has been analyzed in [58], where also an alternative non-symmetric integration rule for the mortar integrals is used to reduce the integration error.…”

Section: Accurate Contact Integration For Igamentioning

confidence: 99%

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Isogeometric dual mortar methods for computational contact mechanics

Seitz

Farah

Kremheller

et al. 2016

Computer Methods in Applied Mechanics and Engineering

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In recent years, isogeometric analysis (IGA) has received great attention in many fields of computational mechanics research. Especially for computational contact mechanics, an exact and smooth surface representation is highly desirable. As a consequence, many well-known finite e lement m ethods a nd a lgorithms f or c ontact m echanics h ave b een t ransferred t o I GA. I n t he present contribution, the so-called dual mortar method is investigated for both contact mechanics and classical domain decomposition using NURBS basis functions. In contrast to standard mortar methods, the use of dual basis functions for the Lagrange multiplier based on the mathematical concept of biorthogonality enables an easy elimination of the additional Lagrange multiplier degrees of freedom from the global system. This condensed system is smaller in size, and no longer of saddle point type but positive definite. A very simple and commonly used element-wise construction of the dual basis functions is directly transferred to the IGA case. The resulting Lagrange multiplier interpolation satisfies discrete inf-sup stability and biorthogonality, however, the reproduction order is limited to one. In the domain decomposition case, this results in a limitation of the spatial convergence order to O(h 3 /2 ) in the energy norm, whereas for unilateral contact, due to the lower regularity of the solution, optimal convergence rates are still met. Numerical examples are presented that illustrate these theoretical considerations on convergence rates and compare the newly developed isogeometric dual mortar contact formulation with its standard mortar counterpart as well as classical finite elements based on first and second order Lagrange polynomials.

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Section: Accurate Contact Integration For Igamentioning

confidence: 99%

“…Here, we propose a very simple but efficient extension of the segmentation procedure described in [24,36,54,55] for standard first order finite elements to IGA similar to [14], that merely consists of pre-and post-processing our already existing segmentation algorithm as depicted in Fig. 3.…”

Section: Accurate Contact Integration For Igamentioning

confidence: 99%

Isogeometric dual mortar methods for computational contact mechanics

Seitz

Farah

Kremheller

et al. 2016

Computer Methods in Applied Mechanics and Engineering

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“…This next example demonstrates the applicability of hierarchical refinement to Mortar based frictional contact, using a setup similar to the ironing problem in Puso and Laursen [37]. Fig.…”

Section: Ironingmentioning

confidence: 99%

Hierarchical NURBS and a higher-order phase-field approach to fracture for finite-deformation contact problems

Hesch

Franke

Dittmann

et al. 2016

Computer Methods in Applied Mechanics and Engineering

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Highlights• We present a hierarchical refinement scheme for isogeometric analysis.• A frictional Mortar contact algorithm for hierarchical refined NURBS is introduced.• A higher-order phase-field approach to brittle fracture is applied to the concept of HNURBS and combined with frictional contact problems. AbstractIn this paper we investigate variationally consistent Mortar contact algorithms applied to a phase-field approach to brittle fracture. Phase-field approaches allow for an efficient simulation of complex fracture problems, as they arise in contact and impact situations. To improve accuracy and convergence, a fourth-order phase-field model is considered, requiring C 1 continuity throughout the domain. An isogeometrical framework is used for the spatial discretisation subject to hierarchical refinements to resolve local features. This reduces the computational effort tremendously, as will be shown in a series of representative examples.

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“…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%

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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A mortar segment-to-segment frictional contact method for large deformations

Abstract: Work performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract W-7405-Eng-48.

Cited by 209 publications

References 15 publications

Isogeometric dual mortar methods for computational contact mechanics

Isogeometric dual mortar methods for computational contact mechanics

Hierarchical NURBS and a higher-order phase-field approach to fracture for finite-deformation contact problems

A modified perturbed Lagrangian formulation for contact problems

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