The G2 constant displacement discontinuity method – Part II: Solution of half-plane crack problems

Exadaktylos, G.; Xiroudakis, George

doi:10.1016/j.ijsolstr.2010.05.014

Cited by 7 publications

(4 citation statements)

References 8 publications

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“…where A zz,C denotes the combined element transformation-influence coefficients matrix of the classical elasticity, and A zz, G2 denotes the matrix of the additional coefficients of the g2 theory. 17 For the known solution of crack opening displacements along the uniformly pressurized crack as is expressed by the first of Equation (15) and the above Equation 16, it may be found that the gradient term for each ith crack element gives identical results in terms of normal displacement discontinuities and internal pressure with the classical solution…”

Section: Calibration Of the Gradient Term Using The Benchmark Problmentioning

confidence: 99%

“…This desired feature rests on the well-known fact that strain gradient elasticity and other types of nonlocal constitutive models should be used for the prediction of size effects exhibited by elasticity or strength and wave dispersion effects of solids with microstructure and for the regularization of ill-posed postfailure models. [11][12][13] Moreover, in a series of previous papers, the applicability of a simple variant of strain gradient elasticity theory for the improvement of the accuracy of CDDM in two-dimensional (2D) applications [14][15][16] has been demonstrated. So, the next natural step is to generalize the method in 3D.…”

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confidence: 99%

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Three‐dimensional elastic analysis of cracks with the g2 constant displacement discontinuity method

Xiroudakis

Stavropoulou

Exadaktylos

2019

Num Anal Meth Geomechanics

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Summary A new triangular element was created that could be used for the improvement of the accuracy of the constant displacement discontinuity method (CDDM). This element is characterized by three degrees of freedom in the three‐dimensional space as in the classical CDDM approach. The element is based on strain gradient elasticity theory that accounts for the difference of the average value of stress with the local stress at surfaces with large curvature (eg, crack borders, corners, and notches) in elastic bodies. The new element is characterized by a strain gradient term in addition to the two Lamè constants that gives a more representative value of the stresses at the centroid of crack edge elements compared with the classical elasticity solution and thus an accurate stress intensity factor. In this approach, special crack border elements with square‐root radius dependent displacements and numerical integrations are avoided. The extra strain gradient term is calibrated once only on the analytical solution for the penny‐shaped crack. In a verification stage, the accuracy of the computational algorithm for the elliptic and rectangular crack problems is demonstrated. Then, the algorithm, which also accounts for crack closure in compression, is applied for the modeling of crack propagation and crack interaction in uniaxial tension and compression loading. It is illustrated that the numerical predictions are in accordance with experimental evidence pertaining to uniaxial compression of transparent precracked specimens in the lab.

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Section: Calibration Of the Gradient Term Using The Benchmark Problmentioning

confidence: 99%

mentioning

confidence: 99%

Three‐dimensional elastic analysis of cracks with the g2 constant displacement discontinuity method

Xiroudakis

Stavropoulou

Exadaktylos

2019

Num Anal Meth Geomechanics

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“…By the way it is pointed that a new approach for the significant improvement of the accuracy of the constant displacement discontinuity technique without resort to special crack tip elements is presented recently by Exadaktylos and Xiroudakis [28][29][30].…”

Section: Implementation Of the Hybrid Displacement Discontinuity Methmentioning

confidence: 99%

A numerical analysis of a center circular-hole crack in a rectangular tensile sheet

Miao

Wei

Yan

2015

Applied Mathematics and Computation

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“…6. Quasistatic crack propagation was simulated by the code G2TWODD (i.e., acronym for Grade-2 Two-Dimensional Displacement Discontinuity) that is dedicated for fast and accurate calculations of Stress Intensity Factors (SIFs), as well as of displacements and stresses in cracked elastic bodies (Exadaktylos and Xiroudakis 2009, 2010aand 2010b. The initial crack occupying the line segment AB was discretized with ten tractionless linear displacement discontinuity elements of equal size.…”

Section: Crack Trajectory Inside the Muckpilementioning

confidence: 99%

Analytical model for estimation of digging forces and specific energy of cable shovel

Stavropoulou¹,

Xiroudakis²,

Exadaktylos³

2013

Coupled Systems Mechanics

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An analytical algorithm for the estimation of the resistance forces exerted on the dipper of a cable shovel and the specific energy consumed in the cutting-loading process is presented. Forces due to payload and to cutting of geomaterials under given initial conditions, cutting trajectory of the bucket, bucket's design, and geomaterial properties are analytically computed. The excavation process has been modeled by means of a kinematical shovel model, as well as of dynamic payload and cutting resistance models. For the calculation of the cutting forces, a logsandwich passive failure mechanism of the geomaterial is considered, as has been found by considering that a slip surface propagates like a mixed mode crack. Subsequently, the Upper-Bound theorem of Limit Analysis Theory is applied for the approximate calculation of the maximum reacting forces exerted on the dipper of the cable shovel. This algorithm has been implemented into an Excel™ spreadsheet to facilitate user-friendly, "transparent" calculations and built-in data analysis techniques. Its use is demonstrated with a realistic application of a medium-sized shovel. It was found, among others, that the specific energy of cutting exhibits a size effect, such that it decreases as the (-1)-power of the cutting depth for the considered example application.

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The G2 constant displacement discontinuity method – Part II: Solution of half-plane crack problems

Cited by 7 publications

References 8 publications

Three‐dimensional elastic analysis of cracks with the g2 constant displacement discontinuity method

Three‐dimensional elastic analysis of cracks with the g2 constant displacement discontinuity method

A numerical analysis of a center circular-hole crack in a rectangular tensile sheet

Analytical model for estimation of digging forces and specific energy of cable shovel

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