Mortar based frictional contact formulation for higher order interpolations using the moving friction cone

Fischer, K.; Wriggers, Peter

doi:10.1016/j.cma.2005.09.025

Cited by 122 publications

(141 citation statements)

References 14 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%

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%

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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“…Therefore, all mortar integrals are evaluated through integration on the slave surface NURBS elements by evaluating the contact variables at the closest point projection of the integration point to the master surface. The order of integration is chosen to be sufficiently high in order to minimize the error in the evaluation of the integrals, following Fischer and Wriggers [13,14].…”

Section: Mortar-based Finite Element Discretizationmentioning

confidence: 99%

Three-dimensional mortar-based frictional contact treatment in isogeometric analysis with NURBS

Temizer

Wriggers

Hughes

2012

Computer Methods in Applied Mechanics and Engineering

157

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a b s t r a c tA three-dimensional mortar-based frictional contact treatment in isogeometric analysis with NURBS is presented in the finite deformation regime. Within a setting where the NURBS discretization of the contact surface is inherited directly from the NURBS discretization of the volume, the contact integrals are evaluated through a mortar approach where the geometrical and frictional contact constraints are treated through a projection to control point quantities. The formulation delivers a non-negative pressure distribution and minimally oscillatory local contact interactions with respect to alternative Lagrange discretizations independent of the discretization order. These enable the achievement of improved smoothness in global contact forces and moments through higher-order geometrical descriptions. It is concluded that the presented mortar-based approach serves as a common basis for treating isogeometric contact problems with varying orders of discretization throughout the contact surface and the volume.

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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 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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Mortar based frictional contact formulation for higher order interpolations using the moving friction cone

Cited by 122 publications

References 14 publications

Isogeometric dual mortar methods for computational contact mechanics

Isogeometric dual mortar methods for computational contact mechanics

Three-dimensional mortar-based frictional contact treatment in isogeometric analysis with NURBS

A modified perturbed Lagrangian formulation for contact problems

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