An X‐FEM approach for large sliding contact along discontinuities

Nistor, Ionel; Guiton, Martin; Massin, Patrick; Moës, Nicolas; Geniaut, Samuel

doi:10.1002/nme.2532

Cited by 56 publications

(47 citation statements)

References 44 publications

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“…Remark that the coherent imperfect interface model appropriate for modelling the interface effect in nanomaterials and nanostructures can also be derived from (22) and (23) by taking the interphase to be very stiff with respect to the surrounding phases. In the coherent imperfect interface model, the displacement vector is continuous but the traction vector is discontinuous across the interface.…”

mentioning

confidence: 99%

Three‐dimensional numerical modelling by XFEM of spring‐layer imperfect curved interfaces with applications to linearly elastic composite materials

Zhu

Yvonnet

et al. 2011

Numerical Meth Engineering

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SUMMARYThe spring-layer interface model is widely used in describing some imperfect interfaces frequently involved in materials and structures. Typically, it is appropriate for modelling a thin soft interphase layer between two relatively stiff bulk media. According to the spring-layer interface model, the displacement vector suffers a jump across an interface whereas the traction vector is continuous across the same interface and is, in the linear case, proportional to the displacement vector jump. In the present work, an efficient three-dimensional numerical approach based on the extended finite element method is first proposed to model linear spring-layer curved imperfect interfaces and then applied to predict the effective elastic moduli of composites in which such imperfect interfaces intervene. In particular, a rigorous derivation of the linear spring-layer interface model is provided to clarify its domain of validity. The accuracy and convergence rate of the elaborated numerical approach are assessed via benchmark tests for which exact analytical solutions are available. The computated effective elastic moduli of composites are compared with the relevant analytical lower and upper bounds.

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mentioning

confidence: 99%

Three‐dimensional numerical modelling by XFEM of spring‐layer imperfect curved interfaces with applications to linearly elastic composite materials

Zhu

Yvonnet

et al. 2011

Numerical Meth Engineering

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“…In the elements where K α is discontinuous, a technique similar to the ghost node interpolation used in [41] is preferred. The principle consists in using two continuous interpolations by prolongation of the one on + and the one on − to the whole domain (an example is given Fig.…”

Section: New "Bubble" Approximation Spacementioning

confidence: 99%

On the construction of approximation space to model discontinuities and cracks with linear and quadratic extended finite elements

Ndeffo

Massin

Moës

et al. 2017

Adv. Model. and Simul. in Eng. Sci.

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This paper presents a robust enrichment strategy to model weak and strong discontinuities as well as cracks for industrial applications. First, numerical issues encountered with popular extended finite element approximation spaces are pointed out. Then, the paper gives indications on how to circumvent those issues. The very originality of the paper relies on questioning the theoretical approximation spaces with respect to numerical results and to modify accordingly their design. The relationship between the new design and the previous designs is clearly established, in order to highlight the very small implementation cost of the modifications exposed here. Hence with minimal additional computational cost, gains in accuracy can be significant as shown later in the paper.

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“…As in the previous subsection, the continuous terms of the approximation (12) are cancelled when evaluating the differences (u P −u Q ). Note that F 1 (r, ) is the only enrichment function that is discontinuous in (11).…”

Section: Crack-tip Elementmentioning

confidence: 99%

Crack face contact in X‐FEM using a segment‐to‐segment approach

Giner

Tur

Tarancón

et al. 2009

Numerical Meth Engineering

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SUMMARYIn this study, we propose a segment-to-segment contact formulation (mortar-based) that uses Lagrange's multipliers to establish the contact between crack faces when modeled with the extended finite element method (X-FEM) in 2D problems. It is shown that, in general, inaccuracies arise when the contact is formulated following a point-to-point approach. This is due to the non-linear character of the X-FEM interpolation along the crack faces that leads to crack face interpenetration. However, the segment-tosegment approach optimizes the fulfilment of the contact constraints along the whole crack segment, and in practice the contact is modeled precisely. Convergence studies for mesh sequences have been performed, showing the advantages of the proposed methodology.

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An X‐FEM approach for large sliding contact along discontinuities

Cited by 56 publications

References 44 publications

Three‐dimensional numerical modelling by XFEM of spring‐layer imperfect curved interfaces with applications to linearly elastic composite materials

Three‐dimensional numerical modelling by XFEM of spring‐layer imperfect curved interfaces with applications to linearly elastic composite materials

On the construction of approximation space to model discontinuities and cracks with linear and quadratic extended finite elements

Crack face contact in X‐FEM using a segment‐to‐segment approach

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