Interface handling for three‐dimensional higher‐order XFEM‐computations in fluid–structure interaction

Mayer, U.; Gerstenberger, Axel; Wall, Wolfgang A.

doi:10.1002/nme.2600

Cited by 44 publications

(39 citation statements)

References 33 publications

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“…The principle idea of XFEM is shown in Figure 11, simplified for a crack in one dimension. Though XFEM has originally been developed for fracture, it has been extended to numerous applications including two-phase flow [122,123], fluid-structure interaction [124,125], biomechanics [126], inverse problems [127,128], multifield problems [129][130][131][132], among others. XFEM has been incorporated meanwhile into commercial software (XFEM) and has become one of the most popular methods for fracture.…”

Section: Extended Finite Element Methods (Xfem)mentioning

confidence: 99%

Computational Methods for Fracture in Brittle and Quasi-Brittle Solids: State-of-the-Art Review and Future Perspectives

Rabczuk

2013

ISRN Applied Mathematics

162

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An overview of computational methods to model fracture in brittle and quasi-brittle materials is given. The overview focuses on continuum models for fracture. First, numerical difficulties related to modelling fracture for quasi-brittle materials will be discussed. Different techniques to eliminate or circumvent those difficulties will be described subsequently. In that context, regularization techniques such as nonlocal models, gradient enhanced models, viscous models, cohesive zone models, and smeared crack models will be discussed. The main focus of this paper will be on computational methods for discrete fracture (discrete cracks). Element erosion technques, inter-element separation methods, the embedded finite element method (EFEM), the extended finite element method (XFEM), meshfree methods (MMs), boundary elements (BEMs), isogeometric analysis, and the variational approach to fracture will be reviewed elucidating advantages and drawbacks of each approach. As tracking the crack path is of major concern in computational methods that preserve crack path continuity, one section will discuss different crack tracking techniques. Finally, cracking criteria will be reviewed before the paper ends with future research perspectives.

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Section: Extended Finite Element Methods (Xfem)mentioning

confidence: 99%

Computational Methods for Fracture in Brittle and Quasi-Brittle Solids: State-of-the-Art Review and Future Perspectives

Rabczuk

2013

ISRN Applied Mathematics

162

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“…Thus, no global level-set functions or analytic functions are required. Subsequently, we apply a subdivision into tetrahedrons for domain integrals and triangles for boundary integrals [29] to accurately integrate the weak form in intersected elements. This integration cell technique is applicable to low-and high-order FEs and high-order interface approximations.…”

Section: Xfem Formulation For Background Fluidmentioning

confidence: 99%

“…The interface is localized by the surface mesh of the embedded fluid patch. With the help of parallel search trees [29], first all intersected elements are determined. The relative position to the interface, which is required to evaluate the Heaviside function Equation (42), is obtained via the normal vector of the surface patch elements.…”

Section: Xfem Formulation For Background Fluidmentioning

confidence: 99%

An XFEM‐based embedding mesh technique for incompressible viscous flows

Shahmiri

Gerstenberger

Wall

2010

Numerical Methods in Fluids

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SUMMARYThis paper presents a finite element (FE) embedding mesh technique to efficiently embed arbitrary fluid mesh patches into Cartesian or unstructured background fluid grids. Our motivating application for such a technique is to efficiently resolve flow features like boundary layers around structures, which is achieved by attaching fluid boundary layer meshes around these structure surfaces. The proposed technique can be classified as a non-overlapping domain decomposition method. The particular feature is that the embedded patch cuts a void region into the background grid independently of background element edges. Since the embedded fluid domain ends in the middle of background elements, extended FE techniques are used to model a sharp separation between active and inactive regions on the background grid. The active background region is coupled to the boundary layer mesh using a mixed/hybrid Lagrange multiplier technique as proposed in Gerstenberger and Wall (Int. J. Numer. Meth. Engng. 2010; 82:537-563). The coupling formulation works without stabilization for the Lagrange multiplier unknowns and the Lagrange multiplier can be completely condensed on the element level. Within this paper, the approach is derived for incompressible, viscous flows. Three-dimensional examples using linear and quadratic shape functions demonstrate the correctness and the versatility of the proposed approach.

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“…In our approach, we use linear sub-elements (finer mesh) incorporated into a boundary element E B to control a priori the faithfulness of the boundary representation. This approach was also used with boundaries represented by an analytical level set in 2D [40] and explicit 3D polygonal mesh in [43,44]. Following ideas similar to the Heaviside step function approach of [9,36], we will define the indicator functions K I[B and N B to simplify the description of the domain X h and its boundary C h , respectively, as follows:…”

Section: Numerical Integrationmentioning

confidence: 99%

“…Explicit surface representations independent of the mesh for 3D crack growth with hp-GFEM and interfaces in fluid-structure interaction with higher-order XFEM have been presented in the works of Pereira et al [43] and Mayer et al [44], respectively.…”

Section: Introductionmentioning

confidence: 99%

Finite element analysis on implicitly defined domains: An accurate representation based on arbitrary parametric surfaces

Moumnassi

Belouettar²,

Béchet

et al. 2011

Computer Methods in Applied Mechanics and Engineering

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a b s t r a c tIn this paper, we present some novel results and ideas for robust and accurate implicit representation of geometric surfaces in finite element analysis. The novel contributions of this paper are threefold: (1) describe and validate a method to represent arbitrary parametric surfaces implicitly; (2) represent arbitrary solids implicitly, including sharp features using level sets and boolean operations; (3) impose arbitrary Dirichlet and Neumann boundary conditions on the resulting implicitly defined boundaries. The methods proposed do not require local refinement of the finite element mesh in regions of high curvature, ensure the independence of the domain's volume on the mesh, do not rely on boundary regularization, and are well suited to methods based on fixed grids such as the extended finite element method (XFEM). Numerical examples are presented to demonstrate the robustness and effectiveness of the proposed approach and show that it is possible to achieve optimal convergence rates using a fully implicit representation of object boundaries. This approach is one step in the desired direction of tying numerical simulations to computer aided design (CAD), similarly to the isogeometric analysis paradigm.

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Interface handling for three‐dimensional higher‐order XFEM‐computations in fluid–structure interaction

Cited by 44 publications

References 33 publications

Computational Methods for Fracture in Brittle and Quasi-Brittle Solids: State-of-the-Art Review and Future Perspectives

Computational Methods for Fracture in Brittle and Quasi-Brittle Solids: State-of-the-Art Review and Future Perspectives

An XFEM‐based embedding mesh technique for incompressible viscous flows

Finite element analysis on implicitly defined domains: An accurate representation based on arbitrary parametric surfaces

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