Embedded crack model: I. Basic formulation

Jirásek, Milan; Zimmermann, Thomas

doi:10.1002/1097-0207(20010228)50:6<1269::aid-nme11>3.0.co;2-u

Cited by 130 publications

(68 citation statements)

References 25 publications

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“…These degrees of freedom give rise to both: i) a translation and ii) a rotation. The first case was taken into account in the former embedded formulations, namely in the works presented in Simo et al [10], Lofti and Shing [11], Armero and Callari [12], Oliver [14,15], Jirásek and Zimmermann [17,18], Borja [20], Wells and Sluys [21], Alfaiate et al [22], where a constant jump was adopted. Thus, the present formulation can also be considered as a generalization of the former embedded discontinuity models, in which the rigid body rotation is additionally considered.…”

Section: Discretizationmentioning

confidence: 99%

“…In the former case, the discontinuities are modelled as finite width bands and the displacement field remains continuous [7], whereas in the second case, the kinematics of a true discontinuous displacement field is approximated. Many examples of the strong discontinuity approach can be found in literature [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22], which are compared and discussed in [23]. Moreover, towards a unified view of both weak and strong discontinuities, Oliver et al [24,25] introduced a continuum strong discontinuity approach (CSDA), in which a strong discontinuity is consistently obtained from a weak discontinuity when the crack band width tends to zero.…”

Section: Introductionmentioning

confidence: 99%

“…In all these works, constant displacement jumps are adopted within each parent finite element, the parent element is a constant strain triangle, a local formulation at element level is introduced and a non-symmetric variational formulation is built. As a consequence, the jumps are not continuous across element boundaries and stress locking may occur, depending on the relative position of the discontinuity with respect to the element edges [23,17,26]. Oliver et al [24,25], developed an algorithm aiming to eliminate stress locking.…”

Section: Introductionmentioning

confidence: 99%

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A discrete strong discontinuity approach

Dias-da-Costa

Alfaiate²,

Sluys

et al. 2009

Engineering Fracture Mechanics

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a b s t r a c tIn this paper, strong discontinuities are embedded in finite elements to describe fracture in quasi-brittle materials. A new formulation is presented in which global nodes are introduced along the crack path. The displacement jumps are transferred to the element nodes as a rigid body motion. This approach is compared to the discrete approach, in which interface elements are inserted to model discontinuities. The adopted embedded discontinuities and the interface elements share similar kinematics as well as the same numerical integration schemes. Thus, the present formulation is obtained within the framework of a discrete approach and this is why it is called the discrete strong discontinuity approach (DSDA). Numerical tests are considered, namely a shear band, a mode-I and a mixed-mode fracture examples and a failure test of a RC beam externally reinforced with a steel sheet. Results are compared with those obtained from analyses using interface elements and with experimental results. Finally, conclusions are drawn with respect to mesh independence and robustness of the method.

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Section: Discretizationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A discrete strong discontinuity approach

Dias-da-Costa

Alfaiate²,

Sluys

et al. 2009

Engineering Fracture Mechanics

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“…This is a general technique of EFEM. The standard FEM is applied for the continuous strain and the discontinuous strain is transformed from the crack opening width (e) by means of scalable effective length of the element ( eff l ), which is the projection of the element on the normal to the crack direction [16,19]. That is,…”

Section: Additional Assumptions For the Current Modelmentioning

confidence: 99%

An embedded FE model for modelling reinforced concrete slabs in fire

Huang

2008

Engineering Structures

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It is evident from a series of tests on simply supported reinforced concrete slabs that the failure of the slabs at large deflections is due to the formation of individual large cracks. This failure mode was also observed in the Cardington full-scale fire tests. Previous research indicates that the global behaviour of concrete slabs subject to large deflections can be well predicted by the smeared cracking model; however, the model cannot quantitatively predict the openings of individual cracks within the slabs at large deflection. For the discrete approach it is usually assumed that the cracks are formed along element edges, therefore continuous re-meshing is required during the analysis.Consequently, the results are mesh-dependent and the computing cost is high. In recent years, mesh independent finite element procedures, such as embedded (EFEM) and extended (XFEM) approaches, were widely used for modelling of the crack initiation and growth in structural members. However, most of the meshless models developed are either based on in-plane loading conditions or confined to thin shells with assumed full-depth cracks, which form apparent displacement jumps within an element.For a reinforced concrete slab, out-of -plane load causes coupled stretching and bending of the slab, cracks are usually initiated at discrete positions and then propagated, until at last some individual full-depth cracks are formed. Pure stretching or assumed full-depth cracking is inadequate for modelling this kind of failure. Therefore, in this research, a non-linear layered procedure with embedded weak discontinuity is developed to quantitatively model the progressive tensile failure of reinforced concrete slabs subjected to large deflections. The current model inherits the advantage of smeared approach, and at the same time, introduces the opening width of crack explicitly by taking the advantage of the better description of the kinematic characteristics of EFEM approach. A series of validations have been conducted against test data at both ambient and elevated temperatures, and as well as to identify the occurrence and severity of crack failure in reinforced concrete slabs subjected to extreme loading conditions, such as fire.

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“…Currently, there are many different approaches available in the literature, which can simulate material separation. Most approaches are based on nodal [1][2][3][4] or element enrichment techniques [5][6][7][8][9][10][11], or even on remeshing strategies [12][13][14]. These approaches were typically validated using benchmark tests with few cracks and by comparing overall displacements.…”

Section: Introductionmentioning

confidence: 99%