An embedded strong discontinuity model for cracking of plain concrete

Feist, Christian; Hofstetter, Günter

doi:10.1016/j.cma.2005.01.028

Cited by 57 publications

(31 citation statements)

References 34 publications

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“…Oliver [17], Feist et al [18] and Linder et al [19] all present a similar shape function to the one applied here, however, in these works the stress continuity across the crack is stated in the weak form. Moreover, in [17] the mathematical representation of the shape function implied the use of the Dirac delta function; and to get around the obstacle of dealing with delta functions a regularization via delta-sequences and a regularization parameter was introduced.…”

Section: Introductionmentioning

confidence: 90%

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An embedded crack in a constant strain triangle utilizing extended finite element concepts

Olesen¹,

Poulsen²

2013

Computers & Structures

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This paper revisits the formulation of the CST element with an embedded discrete crack taking advantage of the direct formulations developed within the framework of the extended finite element method, XFEM. The result is a simple element for modeling cohesive fracture processes in quasi-brittle materials. The element is easily fitted a standard FEM code, and as such it is an alternative to more cumbersome XFEM elements which require special d.o.f.'s and extra administration. The crack description is embedded, in the sense that extra d.o.f.'s controlling the crack opening are eliminated at the element level. The cracked element is stress-compatible in the sense that stresses are continuous across the crack. A special shape function is introduced to allow for the discontinuous displacements without eradicating the stress compatibility. The simplicity of the element comes at the cost of inter-element discontinuity of displacements. The formulation is based on a variational principle of virtual work involving only the interpolation of displacements. The good performance of the element is demonstrated through the comparison with three benchmark tests in which a single crack is propagated: The center cracked sheet in uni-axial tension, the three-point bending test and the four-point shear beam test.

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Section: Introductionmentioning

confidence: 90%

“…Also, at any state of deformation we may, analogously to (14), establish a relation between the variations given by δV d = Z δV c , keeping in mind that Z is a function of V d . Then by utilizing (4) and (7) we may rewrite (18) in the form…”

Section: Variational Fem Formulationsmentioning

confidence: 99%

An embedded crack in a constant strain triangle utilizing extended finite element concepts

Olesen¹,

Poulsen²

2013

Computers & Structures

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“…Detailed descriptions of the theory of plasticity considering displacement discontinuities can be found, e.g. in References [7,20], and referring in particular to the present model in Reference [51]. Hence, in the following only the specialization of the general model to the Rankine criterion will be reviewed briefly, which is suitable for fracture simulations of plain concrete.…”

Section: Determination Of the Displacement Jumpmentioning

confidence: 99%

Three‐dimensional fracture simulations based on the SDA

Feist

Hofstetter

2006

Num Anal Meth Geomechanics

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SUMMARYA numerical model within the framework of a non-symmetric strong discontinuity approach (SDA) suitable for fracture simulations of plain concrete is presented. The model is based on the fixed crack concept and is formulated within the framework of elements with embedded discontinuities. Discontinuity segments of individual elements are considered to form a C 0 -continuous surface. Enforcement of continuity of the crack surface across adjacent elements is established by the so-called partial domain crack tracking algorithm (PDTA). Orientation of individual crack segments is derived from a non-local strain field. Within the present work emphasis is put on the formulation for the three-dimensional case. The implications on the respective algorithms are highlighted. The capabilities of the model are shown by means of numerical examples.

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“…Several justifications can be taken from literature, namely incorrect assessment of material parameters as well as spurious bending occurring in the experimental tests and giving rise to different crack paths at the front and rear faces of the specimen [56][57][58]. This is why some authors tend to focus on the crack path only, disregarding the comparison between numerical and experimental load-displacement curves, namely [59].…”

Section: Nooru-mohamed Testmentioning

confidence: 99%

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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An embedded strong discontinuity model for cracking of plain concrete

Cited by 57 publications

References 34 publications

An embedded crack in a constant strain triangle utilizing extended finite element concepts

An embedded crack in a constant strain triangle utilizing extended finite element concepts

Three‐dimensional fracture simulations based on the SDA

A discrete strong discontinuity approach

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