Damage-based fracture with electro-magnetic coupling

Areias, P.; Silva, Hugo; Goethem, Nicolas Van; Bezzeghoud, Mourad

doi:10.1007/s00466-012-0742-6

Cited by 6 publications

(7 citation statements)

References 27 publications

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“…The simple algorithm of edge rotation for computational fracture of shells provides an advantageous alternative to the tip‐remeshing algorithm proposed by the authors (cf. ). Compared with XFEM , several advantages can be observed, specifically the simplicity of coding and generality of the results.…”

Section: Discussionmentioning

confidence: 97%

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Finite strain fracture of plates and shells with configurational forces and edge rotations

Areias

Rabczuk

2013

Numerical Meth Engineering

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231

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SUMMARYWe propose a simple and efficient algorithm for FEM‐based computational fracture of plates and shells with both brittle and ductile materials on the basis of edge rotation and load control. Rotation axes are the crack front nodes, and each crack front edge in surface discretizations affects the position of only one or two nodes. Modified positions of the entities maximize the modified mesh quality complying with the predicted crack path (which depends on the specific propagation theory in use). Compared with extended FEM or with classical tip remeshing, the proposed solution has algorithmic and generality advantages. The propagation algorithm is simpler than the aforementioned alternatives, and the approach is independent of the underlying element used for discretization. For history‐dependent materials, there are still some transfer of relevant quantities between elements. However, diffusion of results is more limited than with tip or full remeshing. To illustrate the advantages of our approach, three prototype models are used: tip energy dissipation linear elastic fracture mechanics (LEFM), cohesive‐zone approaches, and ductile fracture. Both the Sutton crack path criterion and the path estimated by the Eshelby tensor are employed. Traditional fracture benchmarks, including one with plastic hinges, and newly proposed verification tests are solved. These were found to be very good in terms of crack path and load ∕ deflection accuracy. Copyright © 2013 John Wiley & Sons, Ltd.

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Section: Discussionmentioning

confidence: 97%

“…In addition to these elements, our flexible code (see, e.g. ) introduces the hinges as they are required. Contour plots are shown for the two meshes in Figure .…”

Section: Computational Fracture Examplesmentioning

confidence: 99%

Finite strain fracture of plates and shells with configurational forces and edge rotations

Areias

Rabczuk

2013

Numerical Meth Engineering

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231

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“…Total and partial remeshing approaches [25,32,10,18], versions of local displacement [47,46,41,57,44] (and strain [50,2,58]) enrichments, clique overlaps [38], edges repositioning or edge-based fracture with R-adaptivity [45]; Element erosion [63], smeared procedures [49], viscousregularized techniques [37], gradient and non-local continua [60,54]; Phase-field models based on decoupled optimization (equilibrium/crack evolution) with sensitivity analysis [27].…”

Section: Introductionmentioning

confidence: 99%

An Efficient Technique for Surface Strain Recovery from Photogrammetric Data using Meshless Interpolation

Godinho

Dias-da-Costa

Valença

et al. 2013

Strain

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a b s t r a c tIn the context of plane fracture problems, we introduce an algorithm based on our previously proposed rotation of edges but now including the injection of continuum softening elements directly in the process region. This is an extension of the classical smeared (or regularized) approach to fracture and can be seen as an intermediate proposition between purely cohesive formulations and the smeared modeling. Characteristic lengths in softening are explicitly included as width of injected elements. For materials with process regions with macroscopic width, the proposed method is less cumbersome than the cohesive zone model. This approach is combined with smoothing of the complementarity condition of the constitutive law and the consistent updated Lagrangian method recently proposed, which simplifies the internal variable transfer. Propagation-wise, we use edge rotation around crack front nodes in surface discretizations and each rotated edge is duplicated. Modified edge positions correspond to the crack path (predicted with the Ma-Sutton method). Regularized continuum softening elements are then introduced in the purposively widened gap. The proposed solution has algorithmic and generality benefits with respect to enrichment techniques such as XFEM. The propagation algorithm is simpler and the approach is independent of the underlying element used for discretization. To illustrate the advantages of our approach, yield functions providing particular cohesive behavior are used in testing. Traditional fracture benchmarks and newly proposed verification tests are solved. Results are found to be good in terms of load/deflection behavior.

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“…[9,16,11,10,14]). Crack paths are more regular, NewtonRaphson convergence is better and less mesh distortion occurs.…”

Section: Discussionmentioning

confidence: 99%

“…• Full and localized rezoning and remeshing approaches [21,30,9,14], variants of local displacement [46,45,38,42] (or strain [49,2]) enrichments, clique overlaps [37], edges repositioning or edge-based fracture with R-adaptivity [44];…”

Section: Introductionmentioning

confidence: 99%

Element-wise fracture algorithm based on rotation of edges

Areias

Rabczuk

Dias-da-Costa

2013

Engineering Fracture Mechanics

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218

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Please cite this article as: Areias, P., Rabczuk, T., Dias-da-Costa, D., Element-wise fracture algorithm based on rotation of edges, Engineering Fracture Mechanics (2013), doi: http://dx.doi.org/10.1016/j.engfracmech. 2013.06.006 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.Element-wise fracture algorithm based on rotation of edges AbstractWe propose an alternative, simpler algorithm for FEM-based computational fracture in brittle, quasibrittle and ductile materials based on edge rotations. Rotation axes are the crack front edges (respectively nodes in surface discretizations) and each rotated edge affects the position of only one or two nodes. Modified positions of the entities minimize the difference between the predicted crack path (which depends on the specific propagation theory in use) and the edge or face orientation. The construction of all many-to-many relations between geometrical entities in a finite element code motivates operations on existing entities retaining most of the relations, in contrast with remeshing (even tip remeshing) and enrichment which alter the structure of the relations and introduce additional entities to the relation graph (in the case of XFEM, enriched elements which can be significantly different than classical FEM elements and still pose challenges for ductile fracture or large amplitude sliding). In this sense, the proposed solution has algorithmic and generality advantages. The propagation algorithm is simpler than the aforementioned alternatives and the approach is independent of the underlying element used for discretization. For history-dependent materials, there are still some transfer of relevant quantities between meshes. However, diffusion of results is more limited than with tip or full remeshing. To illustrate the advantages of our approach, two prototype models are used: tip energy dissipation (LEFM) and cohesive-zone approaches. The Sutton crack path criterion is employed. Traditional fracture benchmarks and newly proposed verification tests are solved. These were found to be very good in terms of crack path and load/deflection accuracy. Nomenclature

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Damage-based fracture with electro-magnetic coupling

Cited by 6 publications

References 27 publications

Finite strain fracture of plates and shells with configurational forces and edge rotations

Finite strain fracture of plates and shells with configurational forces and edge rotations

An Efficient Technique for Surface Strain Recovery from Photogrammetric Data using Meshless Interpolation

Element-wise fracture algorithm based on rotation of edges

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