Isogeometric mortar methods

Brivadis, Ericka; Buffa, Annalisa; Wohlmuth, Barbara; Wunderlich, Linus

doi:10.1016/j.cma.2014.09.012

Cited by 175 publications

(215 citation statements)

References 44 publications

(62 reference statements)

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“…This is in contrast with the more usual situation of the coupling of IGA patches which is achieved along C 0 interfaces (see, e.g., [11,25,26,29,30]). …”

Section: Governing Equationscontrasting

confidence: 41%

“…For a better understanding of the new method, we first recall in the variational setting two strategies that have been classically used in IGA: the mortar coupling (see, e.g., [25,26]) and the Nitsche coupling (see, e.g., [26,11,27,29,28]). To avoid confusion with the newly developed method, we denote these established strategies by the "classical mortar coupling" and the "classical Nitsche coupling", respectively.…”

Section: The Proposed Coupling Methodsmentioning

confidence: 99%

“…To begin with, Dornisch and Klinkel [23] and Hesch and Betsch [24] used a Lagrange multiplier field to add the work performed by coupling tractions along the interface to the weak form. In the framework of NURBS Lagrange multiplier methods, one may also cite the work of Brivadis et al [25] where several choices of Lagrange multiplier spaces are investigated theoretically and numerically. Then, a comparative numerical study in Apostolatos et al [26] showed the efficiency of a Nitsche-based technique for NURBS.…”

Section: Introductionmentioning

confidence: 99%

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Development of a new, more regular, mortar method for the coupling of NURBS subdomains within a NURBS patch: Application to a non-intrusive local enrichment of NURBS patches

Bouclier

Passieux

Salaün

2017

Computer Methods in Applied Mechanics and Engineering

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of a new, more regular, mortar method for the coupling of NURBS subdomains within a NURBS patch: Application to a non-intrusive local enrichment of NURBS patches. (2017) Highlights• We develop a new mortar method for NURBS that keeps the benefit of using more regular functions.• We propose to match the tractions in addition to the displacements at the coupling interface.• We apply the methodology to perform the non-intrusive local enrichment of NURBS patches.• We demonstrate the performance of the method on a range of two-dimensional linear elastic numerical examples. AbstractIn this work, we develop a mortar method for the coupling of non-conforming NURBS subdomains within a NURBS patch that keeps the benefit of using more regular functions. The idea is to use two Lagrange multipliers to match, across the coupling interface, the tractions coming from the discrete displacements in addition to the discrete displacements. It results in a strategy that is suitable with the continuity of the physical solution: when the physical solution is sufficiently smooth, the strategy enables to represent a C 1 behavior; but, when only a C 0 displacement is expected, no additional errors are introduced since only the traction force is continuous and not the whole derivative fields. Lower stress jumps at the coupling interface can then be observed which allows for a better transition of the information. As an application, a non-intrusive algorithm is also built to solve the proposed coupling method, which enables simple and flexible local enrichments of NURBS patches without losing the interest of using more regular functions. A range of numerical examples in two-dimensional linear elasticity are carried out along with comparisons with other published NURBS coupling techniques to demonstrate the performance of the proposed coupling and its interest when combined to a non-intrusive strategy.

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“…This is in contrast with the more usual situation of the coupling of IGA patches which is achieved along C 0 interfaces (see, e.g., [11,25,26,29,30]). …”

Section: Governing Equationscontrasting

confidence: 41%

Section: The Proposed Coupling Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Development of a new, more regular, mortar method for the coupling of NURBS subdomains within a NURBS patch: Application to a non-intrusive local enrichment of NURBS patches

Bouclier

Passieux

Salaün

2017

Computer Methods in Applied Mechanics and Engineering

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“…In order for a unique solution to be guaranteed, an LBB-type(LadyzenskajaBabuška-Brezzi) condition (see [53]) for the discrete problem has to be satisfied which for a general formulation is not straight forward. However, for simpler problems it can be shown that special choices of the Lagrange multipliers discretizations fulfil an LBBcondition (see [54]). …”

Section: Lagrange Multiplier Methodsmentioning

confidence: 99%

Realization of CAD-integrated shell simulation based on isogeometric B-Rep analysis

Teschemacher

Bauer

Oberbichler

et al. 2018

Adv. Model. and Simul. in Eng. Sci.

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An entire design-through-analysis workflow solution for isogeometric B-Rep analysis (IBRA), including both the interface to existing CADs and the analysis procedure, is presented. Possible approaches are elaborated for the full scope of structural analysis solvers ranging from low to high isogeometric simulation fidelity. This is based on a systematic investigation of solver designs suitable for IBRA. A theoretically ideal IBRA solver has all CAD capabilities and information accessible at any point, however, realistic scenarios typically do not allow this level of information. Even a classical FE solver can be included in the CAD-integrated workflow, which is achieved by a newly proposed meshless approach. This simple solution eases the implementation of the solver backend. The interface to the CAD is modularized by defining a database, which provides IO capabilities on the base of a standardized data exchange format. Such database is designed to store not only geometrical quantities but also all the numerical information needed to realize the computations. This feature allows its use also in codes which do not provide full isogeometric geometrical handling capabilities. The rough geometry information for computation is enhanced with the boundary topology information which implies trimming and coupling of NURBS-based entities. This direct use of multi-patch trimmed CAD geometries follows the principle of embedding objects into a background parametrization. Consequently, redefinition and meshing of geometry is avoided. Several examples from illustrative cases to industrial problems are provided to demonstrate the application of the proposed approach and to explain in detail the proposed exchange formats.

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“…This variant is efficient to implement and satisfies the necessary convergence order for the quadratic primal space we use to fulfil the C 1 requirement of the coupled problem at hand, see Brivadis et al [33] for detailed investigations on this topic. In particular, we utilise a set of nodesω (1) = [q 1 , .…”

Section: Semi Discrete Formulation Of the Coupled Problemmentioning

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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Isogeometric mortar methods

Cited by 175 publications

References 44 publications

Development of a new, more regular, mortar method for the coupling of NURBS subdomains within a NURBS patch: Application to a non-intrusive local enrichment of NURBS patches

Development of a new, more regular, mortar method for the coupling of NURBS subdomains within a NURBS patch: Application to a non-intrusive local enrichment of NURBS patches

Realization of CAD-integrated shell simulation based on isogeometric B-Rep analysis

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

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