Solution of Crack Problems: The Distributed Dislocation Technique

Hills, D.A.; Kelly, Piaras; Dai, Dao‐Qing; Korsunsky, Alexander M.; Keer, Leon M.

doi:10.1115/1.2789094

Cited by 256 publications

(400 citation statements)

References 0 publications

Supporting

Mentioning

396

Contrasting

Unclassified

Order By: Relevance

“…The integral operator L ij is non-local and hypersingular (see Mogilevskaya (2014);Bonnet (1999); Hills et al (1996) for more details on elastic fracture problems and their integral representations). Its numerical discretization results in a fully populated matrix.…”

Section: Linear Elasticitymentioning

confidence: 99%

Numerical methods for hydraulic fracture propagation: A review of recent trends

Lecampion

Bunger

Zhang

2018

Journal of Natural Gas Science and Engineering

350

172

View full text Add to dashboard Cite

Section: Linear Elasticitymentioning

confidence: 99%

Numerical methods for hydraulic fracture propagation: A review of recent trends

Lecampion

Bunger

Zhang

2018

Journal of Natural Gas Science and Engineering

350

172

View full text Add to dashboard Cite

“…For example, Comninou and Barber [13] considered the problem of a layer of thickness a pressed against a half space of the same material by a uniform pressure p 0 and then subjected to an oscillating tangential load Q at x = 0 on the free surface. Tractions due to slip displacements were represented by convolution on a distribution of glide dislocations B x (x) in the slip regions-a technique which has been widely used for two dimensional crack problems [14]. They tracked the extent of the slip zones throughout the cycle and hence established the maximum amplitude of the load Q for which shakedown occurred.…”

Section: Counter Examplesmentioning

confidence: 99%

Shakedown in frictional contact problems for the continuum

Barber

Klarbring

Ciavarella

2008

Comptes Rendus. Mécanique

View full text Add to dashboard Cite

Elastic systems with frictional interfaces subjected to periodic loading are often found to 'shake down' in the sense that frictional slip ceases after the first few loading cycles. The similarities in behaviour between such systems and monolithic bodies with elasticplastic constitutive behaviour have prompted various authors to speculate that Melan's theorem might apply to them-i.e. that the existence of a state of residual stress sufficient to prevent further slip is a sufficient condition for the system to shake down.In this article, we prove this result for 'complete' contact problems in the continuum formulation for systems with no coupling between relative tangential displacements at the interface and the corresponding normal contact tractions. This condition is satisfied for the contact of two half spaces, or of a rigid body with a half space if Dundurs' constant β = 0. It is also satisfied for the contact of two symmetric bodies of similar materials at the plane of symmetry. RésuméAdaptation dans les problèmes de contact avec frottement de milieux continus. Les systèmes élastiques comportant des interfaces en contact frottant, soumis à des chargements périodiques, « s'adaptent » souvent dans le sens où le glissement cesse après les premiers cycles de chargement. Les similitudes entre le comportement de tels systèmes et celui de corps monolithiques à comportement constitutif élasto-plastique ont incité divers auteurs à penser que le théorème de Melan pourrait s'y appliquer-ce qui signifierait que l'existence d'un état d'efforts résiduels suffisants pour empêcher la poursuite du glissement est une condition suffisante pour que le système s'adapte. Dans cet article, nous prouvons ce résultat pour des problèmes « complets » de contact entre milieux continus, dans le cas de systèmes sans couplage entre les déplacements tangentiels relatifs à l'interface et les tractions normales de contact correspondantes. Cette condition est satisfaite pour le contact de deux demi-espaces, ou d'un corps rigide et d'un demi-espace, si la constante β de Dundurs est nulle. Elle est également satisfaite pour le contact de deux corps symétriques constitués de matériaux semblables. J.R. Barber et al. / C. R. Mecanique 336 (2008) 34-41 35 Version française abrégéeDans un article précédent [6] nous avons établi une version du théorème de Melan pour le frottement de Coulomb et pour les systèmes discrets « désaccouplés », dans lesquels les déplacements relatifs tangentiels à l'interface (glissement) ne produisent pas de tractions normales de contact et le secteur de contact reste constant. Ici nous prouvons le théorème correspondant pour les milieux continus.Nous commençons, dans l'Éq. (4), par définir l'opérateur linéaire L 1 reliant la traction tangentielle q au point (x, y) au déplacement tangentiel s en (ξ, η). Une condition nécessaire pour l'adaptation est l'existence d'une distribution de glissements et d'une traction correspondanteq qui, superposée à la solution ne comportant aucun glissement, engendre une traction su...

show abstract

“…The shape/geometry of the flow domain depends not only on and but also on the factor m defined as m = 1 cos sin (29) and on the length 0 given by (see Figure 2) Indeed, four different flow configurations arise depending on , , 0 , and m. If m = ∞, the front is parallel to one of the fixed coordinate axes ( or ) and S is a rectangle. If m = ∞, S is either a triangle, quadrilateral, or a pentagon depending on whether 0< < 0 , or 0 < < − 0 , or − 0 < < , respectively.…”

Section: Calculating the Front Positionmentioning

confidence: 99%

“…The equation relating the displacement and stress field in the homogeneous elastic medium can be condensed into a hypersingular integral equation between the fracture aperture w and the fluid pressure p f [28,29] …”

Section: Elasticitymentioning

confidence: 99%

An Eulerian moving front algorithm with weak‐form tip asymptotics for modeling hydraulically driven fractures

Peirce

Detournay

2008

Commun. Numer. Meth. Engng.

View full text Add to dashboard Cite

SUMMARYThe coupled equations for a propagating hydraulic fracture (HF) exhibit a multi-scale structure for which resolution on all length scales becomes computationally prohibitive. Asymptotic analysis is able to identify the dominant physical process active at the computational length scale. This paper describes a novel algorithm that uses weak-form tip asymptotics on a rectangular Eulerian mesh to solve the problem of a propagating HF. The location of the fracture front is determined within each tip element by matching the volume associated with the known asymptotic solution to the flux of fluid into the given element. Even if the fracture front is curved, the algorithm is able to capture the solution on a relatively coarse rectangular mesh by implementing a weak form of the tip asymptotic solution, based on averaging the volume over a tip element to determine the fracture widths at tip element centers. The fracture is divided into a 'channel' region made up of elements that are filled with fluid and a 'tip' region comprising partially filled elements. An iterative procedure is used to determine the fracture widths and fluid pressures in the channel region and the fracture font locations in the tip regions. The algorithm is tested by analyzing an HF propagating in a viscosity-dominated regime within an impermeable homogeneous elastic material for which a similarity solution is available. The numerical results show close agreement with the exact solution even though a relatively coarse mesh is used.

show abstract

Solution of Crack Problems: The Distributed Dislocation Technique

Cited by 256 publications

References 0 publications

Numerical methods for hydraulic fracture propagation: A review of recent trends

Numerical methods for hydraulic fracture propagation: A review of recent trends

Shakedown in frictional contact problems for the continuum

An Eulerian moving front algorithm with weak‐form tip asymptotics for modeling hydraulically driven fractures

Contact Info

Product

Resources

About