A finite element method for crack growth without remeshing

Moës, Nicolas; Dolbow, John E.; Belytschko, Ted

doi:10.1002/(sici)1097-0207(19990910)46:1<131::aid-nme726>3.3.co;2-a

Cited by 1,239 publications

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“…In the spirit of previous works on crack propagation in a single-phase medium [11,12,13,14] the interpolation of each component of the displacement field of the solid phase is enriched by discontinuous functions:…”

Section: Discretisationmentioning

confidence: 99%

“…To integrate the traction forces and leakage flux at a discontinuity, integration points located at the discontinuity are used. To achieve an accurate numerical integration, one needs sufficient integration points on each side of an element crossed by a discontinuity [11]. Details of the adopted integration scheme can be found in [12].…”

Section: Finite Element Implementationmentioning

confidence: 99%

“…The opening of this plane is governed by a traction-separation relation. In order to allow for the nucleation and the propagation of cracks in arbitrary directions, irrespective of the structure of the underlying finite element mesh, the model exploits the partitionof-unity property of finite element shape functions [10], see also [11,12,13,14]. At the fine scale the flow in the crack is modelled as a viscous fluid using Stokes' equations.…”

Section: Introductionmentioning

confidence: 99%

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A large deformation formulation for fluid flow in a progressively fracturing porous material

Irzal

Remmers

Huyghe

et al. 2013

Computer Methods in Applied Mechanics and Engineering

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ReuseThis article is distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs (CC BY-NC-ND) licence. This licence only allows you to download this work and share it with others as long as you credit the authors, but you can't change the article in any way or use it commercially. More information and the full terms of the licence here: https://creativecommons.org/licenses/ Takedown If you consider content in White Rose Research Online to be in breach of UK law, please notify us by emailing eprints@whiterose.ac.uk including the URL of the record and the reason for the withdrawal request.A large deformation formulation for fluid flow in a progressively fracturing porous material AbstractA general numerical model has been developed for fluid flow in a progressively fracturing porous medium subject to large deformations. The fluid flow away from the crack is modelled in a standard manner using Darcy's relation, while in the discontinuity Stokes' flow is assumed, taking into account the change of permeability due to progressive damage evolution inside the crack. The crack is described in a discrete manner by exploiting the partition-of-unity property of finite element shape functions. The nucleation and the opening of micro-cracks are modelled by a tractionseparation relation. A heuristic approach is adopted to model the orientation of the cracks at the interfaces in the deformed configuration. A two-field formulation is derived, with the solid and the fluid velocities as unknowns. The weak formulation is derived next, assuming a Total Lagrangian formulation. This naturally leads to a set of coupled equations for the continuous and for the discontinuous parts of the mixture. The resulting discrete equations are nonlinear due to the cohesive-crack model, the large-deformation kinematic relations, and the coupling terms between the fine scale and the coarse scale. The capabilities of the model are shown at the hand of some example problems.

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Section: Discretisationmentioning

confidence: 99%

Section: Finite Element Implementationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A large deformation formulation for fluid flow in a progressively fracturing porous material

Irzal

Remmers

Huyghe

et al. 2013

Computer Methods in Applied Mechanics and Engineering

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“…Recently, there has been significant progress in the direction of discrete crack growth modeling -the development of a partition of unity finite element method for crack modeling (coined as the extended finite element method or X-FEM) [17,18] has provided an accurate and robust numerical method that removes the need to mesh the crack surfaces in static or quasi-static crack growth simula-N. SUKUMAR and D.J. SROLOVITZ 365 tions.…”

Section: Introductionmentioning

confidence: 99%

Finite element-based model for crack propagation in polycrystalline materials

Sukumar

Srolovitz

2004

Mat. apl. comput.

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Abstract.In this paper, we use an extended form of the finite element method to study failure in polycrystalline microstructures. Quasi-static crack propagation is conducted using the extended finite element method (X-FEM) and microstructures are simulated using a kinetic Monte Carlo Potts algorithm. In the X-FEM, the framework of partition of unity is used to enrich the classical finite element approximation with a discontinuous function and the two-dimensional asymptotic crack-tip fields. This enables the domain to be modeled by finite elements without explicitly meshing the crack surfaces, and hence crack growth simulations can be carried out without the need for remeshing. First, the convergence of the method for crack problems is studied and its rate of convergence is established. Microstructural calculations are carried out on a regular lattice and a constrained Delaunay triangulation algorithm is used to mesh the microstructure. Fracture properties of the grain boundaries are assumed to be distinct from that of the grain interior, and the maximum energy release rate criterion is invoked to study the competition between intergranular and transgranular modes of crack growth.Mathematical subject classification: 74R10.

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“…Isogeometric analysis (IGA) represents a recently developed technology in computational mechanics that offers the possibility of integrating FEA into conventional NURBS-based CAD design tools (Hughes et al, 2005). On the other hand, the extended finite element method (XFEM) is a numerical technique which extends the classical FEM approach by enriching the solution space for solutions to differential equations with discontinuous functions (Moës et al, 1999). Based on the generalized FEM and the partition of unity method (PUM), the method was developed to ease difficulties in solving problems with localized features (e.g., discontinuities) that are not efficiently resolved by mesh refinement.…”

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confidence: 99%

Computational Structural Engineering: Past Achievements and Future Challenges

Plevris

Tsiatas

2018

Front. Built Environ.

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PAST ACHIEVEMENTS AND CURRENT TRENDSComputational methods are computer-based methods used to numerically solve mathematical models that describe physical phenomena. The purpose of computational modeling is to study the behavior of complex systems by means of computer simulations and it can be used to make predictions of the system's behavior under different conditions, often for cases in which intuitive analytical solutions are not available (Nature, 2018). Computational methods have emerged in engineering during the 1960s. Since then, structural engineers have been leaders in technological solutions to engineering analysis and design problems. The evolution of electronic computers together with the tremendous increase of computational power has triggered the continuous development of computational methods. Rapid advances in computer hardware have had a profound effect on various engineering disciplines. The applications are numerous and cover a broad field of engineering branches including civil, mechanical, naval, electrical, aerospace, material, biomolecular, among others. Computational structural engineering has evolved as an insightful blend combining both structural analysis and computer science.Among all computational methods, the Finite Element Method (FEM) and the Boundary Element Method (BEM) are the most prevalent ones. Both methods exhibit unique characteristics as well as advantages and disadvantages. The FEM, as a simulation tool, enables sophisticated methods of computational mechanics, computer technology and applied mathematics. It has been broadly adopted in scientific research and engineering applications and it can be considered as the most popular method used for structural analysis, tackling linear and nonlinear problems of systems with various geometries, material properties and loads (Reddy, 2005). In FEM, the solution domain is subdivided into a finite number of elements. Each element approximately reproduces the behavior of a small region of the body it represents, but continuity between the elements is only enforced in an overall minimum energy sense. The FEM is especially suitable for problems with complex geometries, but the whole-body discretization scheme that is utilized inevitably leads to a large number of finite elements and, thus, increased computational cost. Although Professor R. Clough coined the term "Finite Element Method" in his pioneer work dated back in 1960 (Clough, 1960), the answer to the question "who invented FEM in everyday use?" is possibly M. Jonathan (Jon) Turner at Boeing who generalized and perfected the Direct Stiffness Method, and convinced his company to commit resources to it, over the period 1952 -1964(Felippa, 2017. The FEM obtained its real impetus in the 1960s and 1970s by the developments of pioneers J. H. Argyris, R. W. Clough, H. C. Martin, O. C. Zienkiewicz and their co-workers who evolved the method and applied it to a wide range of structural problems and applications.In the years since its first use, FEM has grown and developed into a standard...

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A finite element method for crack growth without remeshing

Cited by 1,239 publications

References 8 publications

A large deformation formulation for fluid flow in a progressively fracturing porous material

A large deformation formulation for fluid flow in a progressively fracturing porous material

Finite element-based model for crack propagation in polycrystalline materials

Computational Structural Engineering: Past Achievements and Future Challenges

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