Finite Element with Inner Softening Band

Klisinski, Marek; Runesson, Kenneth; Sture, Stein

doi:10.1061/(asce)0733-9399(1991)117:3(575)

Cited by 82 publications

(55 citation statements)

References 9 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%

“…This is due to the following specific features: i) the DSDA is based on a discrete approach, ii) a one dimensional interface element is explicitly embedded in the parent element to model the discontinuity, iii) a non-homogeneous jump displacement field is introduced in each parent element, which is approximated by the shape functions of the interface element, iv) the additional degrees of freedom are located at the discontinuity, v) these additional degrees of freedom are global, vi) both continuous jumps and tractions across element boundaries are obtained and vii) the enhanced displacement field induced by the jumps consists of a rigid body motion. For clarity, in the following, the former strong discontinuity approach (Simo and Rifai 1990;Dvorkin et al 1990;Klisinski et al 1991) will be designated as the EAS approach, whereas the present approach will be referred to as DSDA.…”

Section: Introductionmentioning

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%

See 2 more Smart Citations

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%

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 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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“…Some authors indicate that each change of the discontinuity path needs remeshing process [5][6][7][8]. Other authors propose to enhance the trial function of the finite element in order to represent a jump of the displacement field [9][10][11]. The concept of partition of unity enhances the shape function of standard finite elements and ensures a uniqueness result [3].…”

Section: Introductionmentioning

confidence: 99%

Simplified Qualitative Discrete Numerical Model to Determine Cracking Pattern in Brittle Materials by Means of Finite Element Method

Avendaño

Garzón‐Alvarado

Linero

et al. 2017

Mathematical Problems in Engineering

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This paper presents the formulation, implementation, and validation of a simplified qualitative model to determine the crack path of solids considering static loads, infinitesimal strain, and plane stress condition. This model is based on finite element method with a special meshing technique, where nonlinear link elements are included between the faces of the linear triangular elements. The stiffness loss of some link elements represents the crack opening. Three experimental tests of bending beams are simulated, where the cracking pattern calculated with the proposed numerical model is similar to experimental result. The advantages of the proposed model compared to discrete crack approaches with interface elements can be the implementation simplicity, the numerical stability, and the very low computational cost. The simulation with greater values of the initial stiffness of the link elements does not affect the discontinuity path and the stability of the numerical solution. The exploded mesh procedure presented in this model avoids a complex nonlinear analysis and regenerative or adaptive meshes.

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Finite Element with Inner Softening Band

Cited by 82 publications

References 9 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

Simplified Qualitative Discrete Numerical Model to Determine Cracking Pattern in Brittle Materials by Means of Finite Element Method

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