A finite element approximation of the Griffith?s model in fracture mechanics

Negri, Matteo

doi:10.1007/s00211-003-0456-y

Cited by 48 publications

(58 citation statements)

References 17 publications

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“…Such a scheme does not easily accommodate cohesive finite element methods or discontinuous Galerkin methods. Note that this is partially addressed by a careful estimate of the anisotropy induced by the mesh in (Negri, 1999), (Negri, 2003) or still through the use of adaptive finite element methods (Bourdin and Chambolle, 2000).…”

Section: Numerics and Griffithmentioning

confidence: 99%

“…Indeed, a numerical method that relies solely on (8.14) will lead to evolutions whose total energy E(t) is not an absolutely continuous (or even continuous) function (see Figure 11 in (Negri, 2003) or Figure 3(b) in ). This is incompatible with the convergence of the timediscretized to the time continuous evolution, culminating in Theorem 5.5.…”

Section: The Backtracking Algorithmmentioning

confidence: 99%

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The Variational Approach to Fracture

2008

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Section: Numerics and Griffithmentioning

confidence: 99%

Section: The Backtracking Algorithmmentioning

confidence: 99%

The Variational Approach to Fracture

2008

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“…Otherwise, the element is eroded. They showed that in contrast to many other element erosion approaches [66,67,73,74], the eigenerosion approach converges to Griffith fracture with increasing mesh refinement.…”

Section: Element Erosionmentioning

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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“…Several methods have been proposed, based on discontinuous (see [GP03]) or adaptive (see [BC00,Neg03]) finite elements. The class of methods on which we concentrate here relies on approximating the Francfort-Marigo energy, in the sense of Γ -convergence, by means of elliptic functionals.…”

Section: Approximation By Means Of Elliptic Functionalsmentioning

confidence: 99%

Numerical implementation of the variational formulation for quasi-static brittle fracture

Bourdin¹

2007

Interfaces Free Bound.

336

277

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This paper presents the analysis and implementation of the variational formulation of quasi-static brittle fracture mechanics proposed by G. A. Francfort and J.-J. Marigo in 1998. We briefly present the model itself, and its variational approximation in the sense of Γ -convergence. We propose a numerical algorithm based on Alternate Minimizations and prove its convergence under restrictive assumptions. We establish a new necessary condition for optimality for the entire time evolution from which we derive the Backtracking algorithm. We give some elements of analysis of the Backtracking algorithm on a simple problem. We present realistic numerical simulations of a traction experiment on a fiber-reinforced matrix, and of the propagation of cracks in a perforated sample under mode-I loading.

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A finite element approximation of the Griffith?s model in fracture mechanics

Cited by 48 publications

References 17 publications

The Variational Approach to Fracture

The Variational Approach to Fracture

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

Numerical implementation of the variational formulation for quasi-static brittle fracture

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