A regularized XFEM framework for embedded cohesive interfaces

Benvenuti, Elena

doi:10.1016/j.cma.2008.05.012

Cited by 79 publications

(83 citation statements)

References 38 publications

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“…The second function is taken from Benvenuti [12]. This function also depends on two parameters and n. The lower the value of n, the steeper will be the function for the same width .…”

Section: Different Classes Of Regularized Step Functionsmentioning

confidence: 99%

“…They used a tangent hyperbolic type function for the enrichment. Benvenuti [12] also used a similar function for simulating the embedded cohesive interfaces. Waisman and Belytschko [13] proposed a parametric adaptive strategy for capturing high gradient solutions.…”

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confidence: 99%

“…In [10,11,12], the regularized Heaviside functions depend on physical considerations. Only one enrichment function is used in [11,13].…”

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confidence: 99%

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The XFEM for high‐gradient solutions in convection‐dominated problems

Abbas

Alizada

Fries

2009

Numerical Meth Engineering

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SUMMARYConvection-dominated problems typically involve solutions with high gradients near the domain boundaries (boundary layers) or inside the domain (shocks). The approximation of such solutions by means of the standard finite element method requires stabilization in order to avoid spurious oscillations. However, accurate results may still require a mesh refinement near the high gradients. Herein, we investigate the extended finite element method (XFEM) with a new enrichment scheme that enables highly accurate results without stabilization or mesh refinement. A set of regularized Heaviside functions is used for the enrichment in the vicinity of the high gradients. Different linear and non-linear problems in one and two dimensions are considered and show the ability of the proposed enrichment to capture arbitrary high gradients in the solutions.

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“…The second function is taken from Benvenuti [12]. This function also depends on two parameters and n. The lower the value of n, the steeper will be the function for the same width .…”

Section: Different Classes Of Regularized Step Functionsmentioning

confidence: 99%

mentioning

confidence: 99%

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The XFEM for high‐gradient solutions in convection‐dominated problems

Abbas

Alizada

Fries

2009

Numerical Meth Engineering

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“…The key concept underlying regularization of discontinuous and highly localized functions is simple: the Dirac delta function is replaced by a weight function whose support is governed by a length parameter ρ, while the standard Heaviside function is constructed by integration of such a weight function. For vanishing ρ, the Heaviside and delta functions are recovered [17]. Regularization obviously introduces approximations in the computation.…”

Section: Introductionmentioning

confidence: 99%

“…Regularized XFEM is also an effective alternative to nonlocal and cohesive crack-models [13][14][15][16]. The key concept underlying regularization of discontinuous and highly localized functions is simple: the Dirac delta function is replaced by a weight function whose support is governed by a length parameter ρ, while the standard Heaviside function is constructed by integration of such a weight function.…”

Section: Introductionmentioning

confidence: 99%

Finite Element Quadrature of Regularized Discontinuous and Singular Level Set Functions in 3D Problems

2012

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Regularized Heaviside and Dirac delta function are used in several fields of computational physics and mechanics. Hence the issue of the quadrature of integrals of discontinuous and singular functions arises. In order to avoid ad-hoc quadrature procedures, regularization of the discontinuous and the singular fields is often carried out. In particular, weight functions of the signed distance with respect to the discontinuity interface are exploited. Tornberg and Engquist (Journal of Scientific Computing, 2003, 19: 527-552) proved that the use of compact support weight function is not suitable because it leads to errors that do not vanish for decreasing mesh size. They proposed the adoption of non-compact support weight functions. In the present contribution, the relationship between the Fourier transform of the weight functions and the accuracy of the regularization procedure is exploited. The proposed regularized approach was implemented in the eXtended Finite Element Method. As a three-dimensional example, we study a slender solid characterized by an inclined interface across which the displacement is discontinuous. The accuracy is evaluated for varying position of the discontinuity interfaces with respect to the underlying mesh. A procedure for the choice of the regularization parameters is proposed.

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2014

Extended Finite Element Method

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A regularized XFEM framework for embedded cohesive interfaces

Cited by 79 publications

References 38 publications

The XFEM for high‐gradient solutions in convection‐dominated problems

The XFEM for high‐gradient solutions in convection‐dominated problems

Finite Element Quadrature of Regularized Discontinuous and Singular Level Set Functions in 3D Problems

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