Embedded representation of fracture in concrete with mixed finite elements

Lotfi, Hamid Reza; Shing, P. Benson

doi:10.1002/nme.1620380805

Cited by 90 publications

(67 citation statements)

References 12 publications

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“…This transmission to + and − can be done according to a scalar factor (Klisinski et al 1991;Lofti and Shing 1995;Ohlsson and Olofsson 1997;Alfaiate et al 2003;Remmers 2006) or alternatively by using independent enhanced displacement fields,ũ + andũ − (Bolzon 2001;Alfaiate and Sluys 2004). The Heaviside function used to transmit the total jump is defined as:…”

Section: Kinematics Of a Strong Discontinuitymentioning

confidence: 99%

“…The development of finite elements with strong embedded discontinuities became a powerful technique for the efficient modelling of strain localization (Simo and Rifai 1990;Dvorkin et al 1990;Klisinski et al 1991;Simo et al 1993;Lofti and Shing 1995;Larsson and Runesson 1996;Oliver 1996;Armero and Garikipati 1996;Wells and Sluys 2000;Oliver et al 2002;Sancho et al 2005). The element enrichment is performed in the displacement field allowing to incorporate localized strain modes.…”

Section: Introductionmentioning

confidence: 99%

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A comparative study on the modelling of discontinuous fracture by means of enriched nodal and element techniques and interface elements

et al. 2009

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In this paper, three different approaches used to model strong discontinuities are studied: a new strong embedded discontinuity technique, designated as the discrete strong embedded discontinuity approach (DSDA), introduced in Dias-da-Costa et al. [773][774][775][776][777][778][779][780][781] 1976). First, it is shown that all three descriptions are based on the same variational formulation. However, the main differences between these models lie in the way the discontinuity is represented in the finite element mesh, which is explained in the paper. Main focus is on the differences between the element enrichment technique, used in the DSDA and the nodal

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Section: Kinematics Of a Strong Discontinuitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A comparative study on the modelling of discontinuous fracture by means of enriched nodal and element techniques and interface elements

et al. 2009

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“…Eqs. (11) and (12) enforce traction continuity across the discontinuity surface C d , where the tractions are denoted by t. As depicted in Fig. 1 In Alfaiate et al [35], the variational formulation is reviewed as a common basis for various approaches.…”

Section: Variational Formulationmentioning

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%

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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“…Finite element models with so-called embedded discontinuities provide a more elegant approach to implement cohesive-zone models in a smeared context [26][27][28][29][30][31]. There are two versions of these models, namely the strong discontinuity approach and the weak discontinuity approach.…”

Section: Smeared Numerical Representations Of Cohesive-zone Modelsmentioning

confidence: 99%

Cohesive‐zone models, higher‐order continuum theories and reliability methods for computational failure analysis

Borst

Gutiérrez

Wells

et al. 2004

Numerical Meth Engineering

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SUMMARYA concise overview is given of various numerical methods that can be used to analyse localization and failure in engineering materials. The importance of the cohesive-zone approach is emphasized and various ways to incorporate the cohesive-zone methodology in discretization methods are discussed. Numerical representations of cohesive-zone models suffer from a certain mesh bias. For discrete representations this is caused by the initial mesh design, while for smeared representations it is rooted in the ill-posedness of the rate boundary value problem that arises upon the introduction of decohesion. A proper representation of the discrete character of cohesive-zone formulations which avoids any mesh bias can be obtained elegantly when exploiting the partition-of-unity property of finite element shape functions. The effectiveness of the approach is demonstrated for some examples at different scales. Moreover, examples are shown how this concept can be used to obtain a proper transition from a plastifying or damaging continuum to a shear band with gross sliding or to a fully open crack (true discontinuum). When adhering to a continuum description of failure, higher-order continuum models must be used. Meshless methods are ideally suited to assess the importance of the higher-order gradient terms, as will be shown. Finally, regularized strain-softening models are used in finite element reliability analyses to quantify the probability of the emergence of various possible failure modes.

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Embedded representation of fracture in concrete with mixed finite elements

Cited by 90 publications

References 12 publications

A comparative study on the modelling of discontinuous fracture by means of enriched nodal and element techniques and interface elements

A comparative study on the modelling of discontinuous fracture by means of enriched nodal and element techniques and interface elements

A discrete strong discontinuity approach

Cohesive‐zone models, higher‐order continuum theories and reliability methods for computational failure analysis

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