Remeshing techniques for r-adaptive and combined h/r-adaptive analysis with application to 2D/3D crack propagation

Askes, Harm; Sluys, L.J.; Jong, B.B.C. de

doi:10.12989/sem.2001.12.5.475

Cited by 10 publications

(4 citation statements)

References 20 publications

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“…It is evident that this approach is appropriate for situations where the crack path is known a priori whereas for situations where the crack path has to be predicted this approach will obviously produce mesh dependent solutions. An alternative approach which seems to be the most common in industrial applications, is the remeshing technique, see, e.g., [16,17]. The first approach to truly simulate arbitrary discrete failure surfaces in finite element meshes was the embedded discontinuity technique, see, e.g., [18][19][20][21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

Towards the treatment of boundary conditions for global crack path tracking in three-dimensional brittle fracture

2009

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The aim of the present paper is a systematic elaboration of a three dimensional finite element analysis tool for discontinuous fracture in brittle solids. Brittle or quasi-brittle fracture usually occurs when a material reaches the limit of its strength and no plastic deformation has been observed prior to failure. In the present approach, this kind of failure is characterized by three sets of governing equations: (i) the elastic bulk problem and (ii) the cohesive interface problem regarding the solid deformation field and (iii) the crack tracking problem concerning the crack kinematics. This manuscript describes a unique modular tool set for the coupled set of nonlinear equations. We focus in particular on the boundary conditions for the crack tracking problem of this analysis tool. We critically discuss important implementation details: (i) the choice of crack onset boundary conditions for the additional global field, (ii) the numerical integration, (iii) the modeling of geometrically exact crack tips for cohesive fracture, and (iv) the post-processing procedure for the discontinuity visualization. The potential of the method to simulate brittle fracture is demonstrated by qualitative and quantitative comparisons with experiments from the literature as well as by common benchmark problems.

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Section: Introductionmentioning

confidence: 99%

Towards the treatment of boundary conditions for global crack path tracking in three-dimensional brittle fracture

2009

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“…The use of structured including skewed/non-symmetric meshes (Okada et al, 2005) is neither computationally efficient, nor guarantees the constant error in computed local fields. A concept of adaptivity and remeshing in capturing the stress fields in the vicinity of cracks is discussed by Askes et al (2000) and Bouchard et al, (2003). The application of h-adaptivity with stress-based indicator for 2D fracture problems is also presented by Kačianauskas et al (2002), Stupak and Kačianauskas (2003).…”

Section: Introductionmentioning

confidence: 99%

Three-dimensional Correction of the Stress Intensity Factor for Plate with a Notch

et al. 2005

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International Journal of Fracture (2005) 136:75-98Abstract. The 3D effects of the 2D mode I stress intensity factor for the plate with a V-shaped straight through-thickness notch are investigated by the finite element method and three-dimensional thicknessdependent correction of SIF is suggested. The correction relies on the assumed relationship between the SIF and the constraint factor (out-of-plane degree of freedom). The 3D finite element mesh generator combining the 2D in-plane adaptive unstructured mesh with the structured through-thickness mesh Is developed and applied for the analysis purposes. Three-dimensionality was examined by using two independent indicators, namely, stress-or strain-based constraint factors. The three-point bend and tensile center-cracked plates are investigated. The results demonstrated that the developed 3D corrections may be treated as upper bound estimates of the SIF for three-point bend plate,while directly obtained numerical values are considered as lower bound estimates. Analysis of the tensile center-cracked plate demonstrated a different nature of the 3D SIF profile, which cannot be simply explained as a transitional state between plain strain and plain stress. Therefore, the suggested 3D correction concept is of a particular character.

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“…Other than flipping, Hoppe et al implemented splitting and merging as an energy lowering process while maintaining the topological features of the original meshes [10]. Ma and Klug [14] introduced an artificial viscosity term to achieve r-adaptive remeshing [15] that kept the connectivity of the edges and the equilateral shape of the triangles but allowed area variation among individual triangles. Other related works include [16][17][18].…”

Section: Limitations Of Current Approachesmentioning

confidence: 99%

Remeshing flexible membranes under the control of free energy

Wang

Danuser

2022

PLoS Comput Biol

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Cell membranes are flexible and often undergo large-scale morphological changes during processes like mitosis, protrusion and retraction, or vesicle fusion. Mathematical modeling of cell membranes depends on a representation of the free-form surface by discrete meshes. During morphological changes, these meshes must be adjusted under the minimization of the total free energy. Current methodology for meshing is limited in one of two ways: 1) Free energy-dependent methods have no restriction on the mesh geometry. The resulting irregular meshes cause artifacts in follow-up models of morphodynamics. 2) Geometry-dependent methods maintain mesh quality but violate the physics of free energy minimization. To fill this gap, we regulate mesh geometries via a free-energy-determined remeshing process: adding and removing mesh elements upon morphological changes based on barrier crossings in a double-barrier potential between neighboring vertices in the meshes. We test the method’s robustness by reproducing the morphodynamics of red blood cells and vesicle fusions; and we demonstrate the method’s adaptability by simulating the formation of filopodia, lamellipodia and invaginations. Finally, we use the method to study a mechanical decoupling effect of two connected membrane tethers that has been recently observed experimentally, but has not been mechanistically explained in the context of a complete membrane surface. We propose a biophysical model that strengthens the decoupling effect and broadens the original interpretation of the experiment. The method is developed in C/Matlab and distributed via https://github.com/DanuserLab/biophysicsModels.

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Remeshing techniques for r-adaptive and combined h/r-adaptive analysis with application to 2D/3D crack propagation

Abstract: Abstract. Remeshing strategies are formulated for r-adaptive and h/r-adaptive

Cited by 10 publications

References 20 publications

Towards the treatment of boundary conditions for global crack path tracking in three-dimensional brittle fracture

Towards the treatment of boundary conditions for global crack path tracking in three-dimensional brittle fracture

Three-dimensional Correction of the Stress Intensity Factor for Plate with a Notch

Remeshing flexible membranes under the control of free energy

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