X-FEM Analysis of dynamic crack growth under transient loading in thick shells

Elguedj, Thomas; Jan, Yannick; Combescure, Alain; Leblé, Bruno; Barras, Guillaume

doi:10.1016/j.ijimpeng.2018.08.013

Cited by 8 publications

(3 citation statements)

References 58 publications

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“…The use of both the algorithm and the library can also be extended to simulations where the objects' shapes and locations vary dynamically, such as, for instance, an object that breaks into fragments or computer graphics in general [95][96][97][98]. Thus, the effectiveness of the presented algorithm and the simplicity of the use of the library and its ease of implementation into any computational framework make them well-suited means for a broad variety of potential applications, since numerical integration of polynomial functions with jump discontinuities is a frequent problem in various fields [16,55,56,[99][100][101][102][103][104][105][106][107][108][109][110][111]. However, it has to be noted that the use of equivalent polynomials leads to a higher computational effort during quadrature than splitting the integration domain since the integrand function doubles its degree [13,19].…”

Section: Discussionmentioning

confidence: 99%

Integration of Polynomials Times Double Step Function in Quadrilateral Domains for XFEM Analysis

et al. 2023

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The numerical integration of discontinuous functions is an abiding problem addressed by various authors. This subject gained even more attention in the context of the extended finite element method (XFEM), in which the exact integration of discontinuous functions is crucial to obtaining reliable results. In this scope, equivalent polynomials represent an effective method to circumvent the problem while exploiting the standard Gauss quadrature rule to exactly integrate polynomials times step function. Certain scenarios, however, might require the integration of polynomials times two step functions (i.e., problems in which branching cracks, kinking cracks or crack junctions within a single finite element occur). In this context, the use of equivalent polynomials has been investigated by the authors, and an algorithm to exactly integrate arbitrary polynomials times two Heaviside step functions in quadrilateral domains has been developed and is presented in this paper. Moreover, the algorithm has also been implemented into a software library (DD_EQP) to prove its precision and effectiveness and also the proposed method’s ease of implementation into any existing computational software or framework. The presented algorithm is the first step towards the numerical integration of an arbitrary number of discontinuities in quadrilateral domains. Both the algorithm and the library have a wide application range, in addition to fracture mechanics, from mathematical computing of complex geometric regions, to computer graphics and computational mechanics.

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Section: Discussionmentioning

confidence: 99%

Integration of Polynomials Times Double Step Function in Quadrilateral Domains for XFEM Analysis

et al. 2023

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“…The paper [ 20 ] deals with the simulation of fracture initiation under impact loading on a shell made of a composite composed of metallic elements using X-FEM. The fracture is described as a simple 1D mesh located on the centroidal surface and is independent of the finite element mesh.…”

Section: Current Status Of the Issuementioning

confidence: 99%

Comparison of Structural Analysis of Thin-Walled Structures Accomplished by Isogeometric Analysis and the Finite Element Method

et al. 2022

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Isogeometric analysis (IGA) represents a relatively new method of problem-solving in engineering practice. A huge advantage of this method over the finite element method (FEM), is the reduction of the simulation execution time. Non-uniform rational B-splines (NURBS) allow the use of higher-order basis functions, thus increasing the accuracy of the solution. This paper deals with the comparison of structural analysis of thin-walled structural elements using isogeometric analysis and the finite element method. The investigated objects are modelled using a single patch in MATLAB. The basic functions are created from NURBS, which were previously used in the creation of an accurate geometric model. The paper contains a comparison of the results obtained by the above-mentioned methods. All computations are performed in the elastic domain.

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“…For this reason in this work it is considered that there is a region that Mode I and Mode II mechanisms are interacting leading to a Mode mixicity law. The adopted mixicity law in this work is inspired by the work of Haboussa et al[68], also employed by Elguedj et al[72].Here the transition zone between Mode I and Mode II type localization is delimited by the local stress triaxiality values T sh (denoting shear) and T ten (denoting tension). These values will be evaluated in Section 4.3.1.…”

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confidence: 99%

Progressive failure of ductile metals: Description via a three-dimensional coupled CZM–XFEM based approach

Nikolakopoulos

Crété

Longère

2021

Engineering Fracture Mechanics

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X-FEM Analysis of dynamic crack growth under transient loading in thick shells

Cited by 8 publications

References 58 publications

Integration of Polynomials Times Double Step Function in Quadrilateral Domains for XFEM Analysis

Integration of Polynomials Times Double Step Function in Quadrilateral Domains for XFEM Analysis

Comparison of Structural Analysis of Thin-Walled Structures Accomplished by Isogeometric Analysis and the Finite Element Method

Progressive failure of ductile metals: Description via a three-dimensional coupled CZM–XFEM based approach

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