A model of cavitational flows for initial stages of cavitation

Galin, L. A.; Markov, V. G.; Frolov, A. P.

doi:10.1007/bf00916227

Cited by 3 publications

(4 citation statements)

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“…A normalized-corrected meshless method (smoothed particle hydrodynamics method) was employed to solve the resulting system [5][6]: Figure 1(a). The particle resolution is sufficient to resolve all characteristics of the thermal plastic-elastic stress-strain state.…”

Section: Smoothed Particle Hydrodynamicsmentioning

confidence: 99%

Uncertainty analysis for hydraulic fracturing modeling in porous media containing oil and gas

Lukyanov¹,

Chugunov²

2015

AIP Conference Proceedings

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The hydraulic fracturing process (HFP) includes irreversible deformation, fluid-rock interactions, and fluid flow with phase transitions. Performance of a HFP may be quantitatively assessed through prescribed measures: length and height of the macro-fractures, incremental increase or decrease in porosity around main fractures, incremental increase in elastic deformation and temperature, fluid pressure distribution in the pore space etc. Given that formation and fluid properties are characterized poorly, performance predictions of HFP process are likely to be uncertain. Development and assessment of HFP strategy necessitates uncertainty quantification of formation and fluid properties. We perform Global Sensitivity Analysis to quantify and rank contributions to the uncertainty in HFP performance from individual input parameters of the model. All the processes (i.e., irreversible deformation, fracturing, micro-damaging, heat transfer) in the proposed mathematical model are strongly coupled. The explicit normalized-corrected meshless method (SPH method) is used to solve the resulting governing equations. The flexibility of the proposed numerical technique allows running efficiently using a great number of micro-and macro-fractures. The results are presented, discussed and future studies are outlined.

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Section: Smoothed Particle Hydrodynamicsmentioning

confidence: 99%

Uncertainty analysis for hydraulic fracturing modeling in porous media containing oil and gas

Lukyanov¹,

Chugunov²

2015

AIP Conference Proceedings

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“…However, the Oliver and Pharr approach is rather empirical and suffers from the lack of theoretical justification. The BASh relation ( 19) is often attributed either to Oliver and Pharr [87] or to Sneddon [31], however if one would read these papers then one could see that Sneddon just gave another interpretation of the known Galin solution and neither Sneddon [31] nor Galin [22,30] studied the inverse problem of extracting elastic modulus from the experiments; while Oliver and Pharr [87] have referred to papers published by Bulychev, Alekhin, Shorshorov and their co-workers.…”

Section: Bash Relation and Its Modificationsmentioning

confidence: 99%

“…In 1946 Galin extended the classical axisymmetric problems of the frictonless indentation of an isotropic elastic half-space by convex indenters and presented a solution of the axisymmetric problem from which were deduced simple formulae for the depth of penetration of the tip of a punch of arbitrary profile and for the total load acting on the indenter [30]. As an example, he gave explicit formulae for axisymmetric indenter whose shape is given by a monomial function of arbitrary degree d ,…”

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confidence: 99%

Contact Problems at Nano/Microscale and Depth Sensing Indentation Techniques

Borodich

2010

MSF

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An overview of development of indentation techniques and connections between contact mechanics and methods of extracting mechanical characteristics from indentation data is given. Observed disagreements between the experimental observations and the models of indentation are discussed. It is shown that this disagreement is often caused by violation of hypotheses that are used in the formulation of the appropriate boundary-value contact problems and strictly speaking one cannot apply directly the solutions of Hertz type contact problems to indentation tests employing the sharp indenters. It is shown that commonly used experimental test involving sharp pyramidal and conical indenters may be applied to study plastic properties of materials while this approach is not very accurate for estimations of elastic modulus of the test solid. The recently proposed by Borodich and Galanov non-direct method that employs data of elastically loading of a spherical indenter is described. It is argued that the non-direct method can be used for determination of both the work of adhesion and elastic modulus of the tested material.

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“…To take into account the non-ideal shape of a three-dimensional indenter, others have used equivalent cones connected with spheres or power-law functions of revolution (see, e.g., [29,30]). Note that the solution to the elastic contact problem for an arbitrary indenter of revolution was obtained by Galin [16,31] in 1946, in particular for an arbitrary power-law indenter. This solution can be used to solve the problem for an indenter described as a power-law series of the radius [32,33].…”

Section: Similarity Approachmentioning

confidence: 99%

Analytical study of fundamental nanoindentation test relations for indenters of non-ideal shapes

Borodich¹,

Keer²,

Korach³

2003

Nanotechnology

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Nanoindentation techniques provide a unique opportunity to obtain mechanical properties of materials of very small volumes. The load-displacement and load-area curves are the basis for nanoindentation tests, and their interpretation is usually based on the main assumptions of the Hertz contact theory and formulae obtained for ideally shaped indenters. However, real indenters have some deviation from their nominal shapes leading researchers to develop empirical 'area functions' to relate the apparent contact area to depth. We argue that for both axisymmetric and three-dimensional cases, the indenter shape near the tip can be well approximated by monomial functions of radius. In this case problems obey the self-similar laws. Using Borodich's similarity considerations of three-dimensional contact problems and the corresponding formulae, fundamental relations are derived for depth of indentation, size of the contact region, load, hardness, and contact area, which are valid for both elastic and non-elastic, isotropic and anisotropic materials. For loading the formulae depend on the material hardening exponent and the degree of the monomial function of the shape. These formulae are especially important for shallow indentation (usually less than 100 nm) where the tip bluntness is of the same order as the indentation depth. Uncertainties in nanoindentation measurements that arise from geometric deviation of the indenter tip from its nominal geometry are explained and quantitatively described.

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A model of cavitational flows for initial stages of cavitation

Cited by 3 publications

References 1 publication

Uncertainty analysis for hydraulic fracturing modeling in porous media containing oil and gas

Uncertainty analysis for hydraulic fracturing modeling in porous media containing oil and gas

Contact Problems at Nano/Microscale and Depth Sensing Indentation Techniques

Analytical study of fundamental nanoindentation test relations for indenters of non-ideal shapes

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