Weak formulation of axi-symmetric frictionless contact problems with boundary elements

Graciani, E.; Mantič, V.; Parı́s, F.; Blázquez, Antonio

doi:10.1016/j.compstruc.2004.09.011

Cited by 54 publications

(21 citation statements)

References 21 publications

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“…The BEM, which is very suitable for solving these kinds of problems where all nonlinearities are placed on the boundaries of the subdomains, is employed in the present work. Implementation details of the collocational 2D BEM code employed and an overall description of the solution algorithm can be found in (Távara et al 2011(Távara et al , 2010Távara 2010;Graciani et al 2005). This algorithm uses an incremental formulation and a very efficient solution procedure, usually referred to as sequentially linear (elastic) analysis, appropriate for the present nonlinear problem (Távara et al 2011(Távara et al , 2010.…”

Section: The Numerical Procedures Used To Analyse the Fibre-matrix Debmentioning

confidence: 99%

“…In order to make the Model more simple, only frictionless contact is considered here, although for situations with relatively large contact zones and high friction coefficient under relevant compressions, friction could be included, e.g., following either Bialas and Mróz (2005a,b), Graciani et al (2005), or Raous (2011) and Kšiñan et al (2014).…”

Section: (C) and (D)mentioning

confidence: 99%

“…The BEM mesh has 1472 continuous linear boundary elements: two uniform meshes of 720 elements discretizing both sides of the fibre-matrix interface (therefore, the polar angle of each element is 0.5 • ) and 32 elements for the external boundary of the matrix, where the remote stresses σ ∞ x and σ ∞ y are applied. Rigid body motions are removed by Method F2 introduced in Blázquez et al (1996), see also Graciani et al (2005). …”

Section: The Numerical Procedures Used To Analyse the Fibre-matrix Debmentioning

confidence: 99%

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A linear elastic-brittle interface model: application for the onset and propagation of a fibre-matrix interface crack under biaxial transverse loads

et al. 2015

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A new linear elastic and perfectly brittle interface model for mixed mode is presented and analysed. In this model, the interface is represented by a continuous distribution of springs which simulates the presence of a thin elastic layer. The constitutive law for the continuous distribution of normal and tangential initially-linear-elastic springs takes into account possible frictionless elastic contact between adherents once a portion of the interface is broken. A perfectly brittle failure criterion is employed for the springs, which enables the study of crack onset and propagation. This interface failure criterion takes into account the variation of the interface fracture toughness with the fracture mode mixity. A unified way to represent several phenomenological both energy and stress based failure criteria is introduced. A proof relating the energy release rate and tractions at an interface point (not necessarily a crack tip point) is introduced for this interface model by adapting Irwin's crack closure technique for the first time. The main advantages of the present interface model are its simplicity, robustness and computational efficiency, even in the presence of snap-back and snap-through instabilities, when the so-called sequentially linear (elastic) analysis is applied. This model is applied here in order to study crack onset and propagation at the fibre-matrix interface in a composite under tensile/compressive remote biaxial transverse loads. Firstly, this model is used to obtain analytical predictions about interface crack onset, while investigating a single fibre embedded in a matrix which is subjected to uniform remote transverse loads. Then, numerical results provided by a 2D boundary element analysis show that a fibre-matrix interface failure is initiated by the onset of a finite debond in the neighbourhood of the interface point where the failure criterion is first reached (under increasing proportional load); this debond further propagates along the interface in mixed mode or even, in some configurations, with the crack tip under compression. The analytical predictions of the debond onset position and associated critical load are used for several parametric studies of the influence of load biaxiality, fracture-mode sensitivity and brittleness number, and for checking the computational procedure implemented.

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Section: The Numerical Procedures Used To Analyse the Fibre-matrix Debmentioning

confidence: 99%

Section: (C) and (D)mentioning

confidence: 99%

Section: The Numerical Procedures Used To Analyse the Fibre-matrix Debmentioning

confidence: 99%

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A linear elastic-brittle interface model: application for the onset and propagation of a fibre-matrix interface crack under biaxial transverse loads

et al. 2015

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“…Regarding computational cost, note that, if all sparse matrix-vector multiplications are ignored, applying an iterative solver to the full Hermite matrix requires 3N 2 operations per iteration (i.e. each matrix-vector multiplication), due to the three dense matrices A 1 j in the first row of Equation (10). On the other hand, Equation (11) requires only N 2 operations per inner iteration, plus an overhead of 2N 2 operations to compute the right-hand side for each outer iteration.…”

Section: Iterative Algorithmmentioning

confidence: 99%

Iterative solution of Hermite boundary integral equations

Gray

Fata

Ma³

2007

Numerical Meth Engineering

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SUMMARYAn efficient iterative method for solution of the linear equations arising from a Hermite boundary integral approximation has been developed. Along with equations for the boundary unknowns, the Hermite system incorporates equations for the first-order surface derivatives (gradient) of the potential, and is therefore substantially larger than the matrix for a corresponding linear approximation. However, by exploiting the structure of the Hermite matrix, a two-level iterative algorithm has been shown to provide a very efficient solution algorithm. In this approach, the boundary function unknowns are treated separately from the gradient, taking advantage of the sparsity and near-positive definiteness of the gradient equations. In test problems, the new algorithm significantly reduced computation time compared with iterative solution applied to the full matrix. This approach should prove to be even more effective for the larger systems encountered in three-dimensional analysis, and increased efficiency should come from pre-conditioning of the non-sparse matrix component.

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“…The numerical study has been carried out using a tool based on BEM, París and Cañas [15], that makes it possible to perform the numerical analysis of plane elastic problems considering contact and interface cracks, in a similar way to that described in Blázquez et al [16] for planar problems and Graciani et al [17] for axisymmetric problems. Two BEM models are used in this analysis.…”

Section: Single Fibre Modelmentioning

confidence: 99%

Effect of thermal residual stresses on matrix failure under transverse tension at micromechanical level: A numerical and experimental analysis

Correa¹,

Mantič²,

Parı́s³

2011

Composites Science and Technology

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To cite this version:E. Correa, V. Mantič, F. París. Effect of thermal residual stresses on matrix failure under transverse tension at micromechanical level. A numerical and experimental analysis. Composites Science and Technology, Elsevier, 2011, 71 (5) This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. Abstract. In the present work the influence at micromechanical scale of thermal residual stresses, originated in the cooling down associated to the curing process of fibrous composites, on interfibre failure under transverse tension is studied. In particular, the effect of the presence of thermal residual stresses on the appearance of the first debonds is discussed analytically, whereas later steps of the mechanism of damage, i.e. the growth of interface cracks and their kinking towards

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Weak formulation of axi-symmetric frictionless contact problems with boundary elements

Cited by 54 publications

References 21 publications

A linear elastic-brittle interface model: application for the onset and propagation of a fibre-matrix interface crack under biaxial transverse loads

A linear elastic-brittle interface model: application for the onset and propagation of a fibre-matrix interface crack under biaxial transverse loads

Iterative solution of Hermite boundary integral equations

Effect of thermal residual stresses on matrix failure under transverse tension at micromechanical level: A numerical and experimental analysis

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