Mechanical Failure in Microstructural Heterogeneous Materials

Bordas, Stéphane Pierre Alain; Hoppe, Ronald H. W.; Petrova, Svetozara I.

doi:10.1007/978-3-540-70942-8_64

Cited by 5 publications

(8 citation statements)

References 15 publications

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“…For the case of LEFM, two sets of functions are used: a Heaviside jump function to capture the jump across the crack faces and asymptotic branch functions that span the two‐dimensional asymptotic crack tip fields (three‐dimensional methods have been proposed in 32 and applied to real‐life damage tolerance assessment 33, 34. The enriched approximation for LEFM takes the form 17, 35, 36 where a J and b

_{α}^{italicK}

are nodal degrees of freedom corresponding to the Heaviside function H and the near‐tip functions, { B α } 1⩽α⩽4 , given by where ( r , θ) are the crack tip polar coordinates. Nodes in set 𝒩 c are such that their support is split by the crack and nodes in set 𝒩 f belong to the elements that contain a crack tip.…”

Section: Basics Of the Extended Finite Element Methods (Xfem)mentioning

confidence: 99%

On the performance of strain smoothing for quadratic and enriched finite element approximations (XFEM/GFEM/PUFEM)

Bordas

Kerfriden

Augarde

et al. 2011

Numerical Meth Engineering

155

103

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To date, the SFEM has only been investigated for bilinear and Wachspress approximations and is limited to linear reproducing conditions. The goal of this paper is to extend the strain smoothing to higher order elements and to investigate numerically in which condition strain smoothing is beneficial to accuracy and convergence of enriched finite element approximations. We focus on three widely used enrichment schemes, namely: (a) weak discontinuities; (b) strong discontinuities; (c) near-tip linear elastic fracture mechanics functions. The main conclusion is that strain smoothing in enriched approximation is only beneficial when the enrichment functions are polynomial (cases (a) and (b)), but that non-polynomial enrichment of type (c) lead to inferior methods compared to the standard enriched FEM (e.g. XFEM).

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_{α}^{italicK}

Section: Basics Of the Extended Finite Element Methods (Xfem)mentioning

confidence: 99%

On the performance of strain smoothing for quadratic and enriched finite element approximations (XFEM/GFEM/PUFEM)

Bordas

Kerfriden

Augarde

et al. 2011

Numerical Meth Engineering

155

103

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“…It is often difficult to ascertain compatibility between the different formats, which makes communicating CAD data often long and tedious. Level set and Partition of Unity technologies in association with digital imaging is being further developed in various research groups [18][19][20][21][22]. Research endeavours seem to tend toward the use of digital images to produce pixel (2D) or voxel (3D) data, which in turns permits an implicit definition of the part of interest.…”

Section: Discussionmentioning

confidence: 99%

“…With this technique and the rapidly growing power of computers (Moore's law predicts its doubling every 18 months), it will become increasingly easy to solve multi-million degree of freedom problems, fully continuum models of complex components would be seamlessly constructed. In addition, Partition of Unity technology is being further developed to include the effect of complex internal microstructures [18], which would allow the use of those models for advanced materials such as composite materials.…”

Section: Discussionmentioning

confidence: 99%

A simulation-based design paradigm for complex cast components

Bordas

Conley

Moran

et al. 2006

Engineering with Computers

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This paper describes and exercises a new design paradigm for cast components. The methodology integrates foundry process simulation, non-destructive evaluation (NDE), stress analysis and damage tolerance simulations into the design process. Foundry process simulation is used to predict an array of porosity-related anomalies. The probability of detection of these anomalies is investigated with a radiographic inspection simulation tool (XRSIM). The likelihood that the predicted array of anomalies will lead to a failure is determined by a fatigue crack growth simulation based on the extended finite element method and therefore does not require meshing nor remeshing as the cracks grow. With this approach, the casting modeling provides initial anomaly information, the stress analysis provides a value for the critical size of an anomaly and the NDE assessment provides a detectability measure. The combination of these tools allows for accept/reject criteria to be determined at the early design stage and enables damage tolerant design philosophies. The methodology is applied to the design of a cast monolithic door used on the Boeing 757 aircraft.

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“…Though numerous studies on crack problems have been conducted during the past decades using various methods such as conventional FEM [1][2][3], boundary element method [4][5][6], meshless method [7][8][9][10], extended finite element method (XFEM) [11][12][13][14], and finite 'crack' element method [15], most of those studies have been limited to the case of homogeneous materials with a few exceptions [16][17][18][19][20]. 0021 Recently, it has attracted an amount of substantial attention to explore the effect of microstructures on the macroscopic failure behavior of heterogeneous materials or structures [21][22][23][24]. This has been made possible due to the availability of increasingly strong computing powers and the development of new numerical schemes.…”

Section: Introductionmentioning

confidence: 99%