3D corrected XFEM approach and extension to finite deformation theory

Löhnert, Stefan; Mueller-Hoeppe, Dana; Wriggers, Peter

doi:10.1002/nme.3045

Cited by 89 publications

(60 citation statements)

References 28 publications

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“…Explicit modeling of cracks requires the mesh update by introducing new boundaries as the crack propagates. To avoid remeshing, the extended finite element method (XFEM) enriches the standard shape functions with discontinuous fields based on a partition of unit concept [12]. However, the XFEM is very onerous to implement in three dimensions and presents integration, conditioning and data handling issues [13].…”

Section: State Of the Art On Computational Modeling Of Cracking In Cementioning

confidence: 99%

A phase-field approach to fracture coupled with diffusion

Lorenzis

2016

Computer Methods in Applied Mechanics and Engineering

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Section: State Of the Art On Computational Modeling Of Cracking In Cementioning

confidence: 99%

A phase-field approach to fracture coupled with diffusion

Lorenzis

2016

Computer Methods in Applied Mechanics and Engineering

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“…where ξ is the local coordinate of the superimposed element (Figure 3 In order to deal with blending problems between the standard and the enriched part of the approximation [39][40][41][42][43][44], the techniques developed in the works of Fries [40] and Ventura et al [43] are employed as in our previous works [26,27]. Those techniques involve the definition of a weight function ϕ (x) that assumes a value of 1 for the fully enriched elements and linearly fades to zero for the blending elements.…”

Section: Discretizationmentioning

confidence: 99%

3D Crack Detection Using an XFEM Variant and Global Optimization Algorithms

Agathos

Chatzi

Bordas

2016

Proceedings of the 9th International Conference on Fracture Mechanics of Concrete and Concrete Structures

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Abstract. In the present work, a scheme is presented for the detection of cracks in three dimensional (3D) structures. The scheme is based on the combination of a newly introduced variation of the extended finite element method (XFEM) and global optimization algorithms.As with existing crack detection schemes, optimization algorithms are employed to minimize the norm of the difference between measured response of the structure, typically strains in some specific points along the boundary, and the response predicted numerically by XFEM. During the optimization procedure the crack geometry is parametrized and the parameters serve as design variables. The whole procedure involves the solution of a very large number of forward problems, which constitute the main computational effort. Therefore, emphasis is given in the reduction of the computational cost associated with the solution of each individual forward problem since it can directly affect the total computational time.The employed XFEM variant can provide increased accuracy for the forward problems at a reduced computational toll, thus decreasing the overall analysis time associated with the crack detection scheme. This reduction is a result of the improved conditioning of the system matrices which leads to a decrease in the time needed to solve the corresponding systems which ranges from 40% up to a few orders of magnitude depending on the enrichment strategy used.Since during the optimization procedure cracks are randomly generated, cracks that lie beyond the boundaries of the structure can occur. In order to exclude those cracks, implicit functions are defined in order to localize the cracks within the structure. In some cases those functions are modified so as to exclude also cracks lying in further invalid locations within the search space.The potential of the proposed scheme is demonstrated through numerical examples involving the detection of cracks in 3D structures.

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“…A Detailed description of this method can be found in reference [5]. The algorithm for tracking the crack during it's evolution follows a concept similar to [6].…”

Section: Crack Propagation Algorithmmentioning

confidence: 99%

“…A remedy for this is the modeling of cracks with the eXtended Finite Element Method (XFEM) nearly independent of the mesh. Here the three dimensional extension of the corrected XFEM [5] is used in combination with the crack propagation algorithm proposed in [6] and [7]. In consequence of the aforementioned reason we use the non-local damage model to predict the nucleation an growth of voids and use a discrete crack representation with damage based propagation criterion for evolving fracture.…”

Section: Introductionmentioning

confidence: 99%