Mortar Methods for Single- and Multi-Field Applications in Computational Mechanics

Popp, Alexander; Gee, Michael W.; Wall, Wolfgang A.

doi:10.1007/978-3-642-32454-3_12

Cited by 5 publications

(7 citation statements)

References 20 publications

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“…The dual mortar approach is crucial to accomplish the large‐scale numerical analysis of realistic engineering projects within an acceptable computational timeframe . The method has become increasingly popular, with new contributions focusing on many active directions, including multiphysics contacts, such as thermal mechanical, fluid structure, and others. However, the application of the dual mortar approach to porous media contacts has not yet been reported.…”

Section: Introductionmentioning

confidence: 99%

A dual mortar contact method for porous media and its application to clay‐core rockfill dams

Wang

Zhou

Zhang

et al. 2019

Num Anal Meth Geomechanics

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Summary The clay‐core rockfill dam is a multibody contact system in which the hydromechanical response of the clay core plays a crucial role. This complex problem is highly challenging to model numerically. We present a numerical approach that considers the multibody contact, consolidation, and strong geometric and material nonlinearities for the modeling of clay‐core rockfill dams. Within the framework of the dual mortar finite element method, the presented approach considers the contact bodies as independent porous media continuums. The nonlinear contact conditions are derived based on the effective contact traction on contact interfaces and pore pressure continuity. The weak forms are obtained by introducing Lagrange multipliers as additional unknowns, which are then condensed through an extended general transformation. The presented method is first validated with a patch test considering the contact between two porous media. Then, a three‐dimensional analysis of the Rumei clay‐core rockfill dam is performed. The main numerical analysis concerns are the two observation galleries planned for construction inside the clay core. The galleries consist of dozens of tunnel‐like concrete blocks, giving rise to complex concrete‐concrete and concrete‐clay contacts. The discontinuous separation and sliding between concrete blocks are investigated. For the concrete‐concrete contact, both hard and soft joint approaches are evaluated and compared. The pore pressure results of the concrete structures are also analyzed.

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Section: Introductionmentioning

confidence: 99%

A dual mortar contact method for porous media and its application to clay‐core rockfill dams

Wang

Zhou

Zhang

et al. 2019

Num Anal Meth Geomechanics

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“…sliding bodies over a surface or rolling and rebounding of different discretized entities. Other somehow related applications are connected with fluid structure interaction [ 7 ] and multiphysics [ 14 , 41 ] analysis where different discretizations are taken into account due to the distinct physical nature of interacting components.…”

Section: Introductionmentioning

confidence: 99%

The domain interface method: a general-purpose non-intrusive technique for non-conforming domain decomposition problems

et al. 2015

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A domain decomposition technique is proposed which is capable of properly connecting arbitrary non-conforming interfaces. The strategy essentially consists in considering a fictitious zero-width interface between the non-matching meshes which is discretized using a Delaunay triangulation. Continuity is satisfied across domains through normal and tangential stresses provided by the discretized interface and inserted in the formulation in the form of Lagrange multipliers. The final structure of the global system of equations resembles the dual assembly of substructures where the Lagrange multipliers are employed to nullify the gap between domains. A new approach to handle floating subdomains is outlined which can be implemented without significantly altering the structure of standard industrial finite element codes. The effectiveness of the developed algorithm is demonstrated through a patch test example and a number of tests that highlight the accuracy of the methodology and independence of the results with respect to the framework parameters. Considering its high degree of flexibility and non-intrusive character, the proposed domain decomposition framework is regarded as an attractive alternative to other established techniques such as the mortar approach.

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“…The most complex and time-evolving situations for non-conforming interfaces can be definitely found in the field of contact mechanics [16,28,31,41] which has boosted the appearance of a considerable number of strategies to handle non-matching grids. It is also necessary to resort to these type of algorithms when the nature of the physics involved in each of the studied domains is remarkably different, e.g.…”

Section: Introductionmentioning

confidence: 99%

“…In such scenarios, the performance of mortar methods might be less optimal as argued in [8,18]. More advanced mortar techniques [30][31][32]40] consider a more convenient Lagrange multiplier space or even a third auxiliary surface with an optimal node distribution in order to minimize the gap between domains (cf. Fig.…”

Section: Introductionmentioning

confidence: 99%

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The domain interface method in non-conforming domain decomposition multifield problems

et al. 2016

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The Domain Interface Method (DIM) is extended in this contribution for the case of mixed fields as encountered in multiphysics problems. The essence of the nonconforming domain decomposition technique consists in a discretization of a fictitious zero-thickness interface as in the original methodology and continuity of the solution fields across the domains is satisfied by incorporating the corresponding Lagrange Multipliers. The multifield DIM inherits the advantages of its irreducible version in the sense that the connections between non-matching meshes, with possible geometrically non-conforming interfaces, is accounted by the automatic Delaunay interface discretization without considering master and slave surfaces or intermediate surface projections as done in many established techniques, e.g. mortar methods. The multifield enhancement identifies the Lagrange multiplier field and incorporates its contribution in the weak variational form accounting for the corresponding consistent stabilization term based on a Nitsche method. This type of constraint enforcement circumvents the appearance of instabilities when the Ladyzhenskaya-Babuška-Brezzi (LBB) condition is not fulfilled by the chosen discretization. The domain decomposition framework is assessed in a large deformation setting for mixed displacement/pressure formulations and coupled thermomechanical problems. The continuity of the mixed field is studied in well selected benchmark problems for both mixed formulations and the objectivity of the response is compared to reference monolithic solutions. Results suggest that the presented strategy shows sufficient potential to be a valuable tool in situations where the evolving physics at particular domains require the use of different spatial discretizations or field interpolations.

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Mortar Methods for Single- and Multi-Field Applications in Computational Mechanics

Cited by 5 publications

References 20 publications

A dual mortar contact method for porous media and its application to clay‐core rockfill dams

A dual mortar contact method for porous media and its application to clay‐core rockfill dams

The domain interface method: a general-purpose non-intrusive technique for non-conforming domain decomposition problems

The domain interface method in non-conforming domain decomposition multifield problems

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