Stress–strain field around elliptic cavities in elastic continuum

Lukić, Dragan; Prokić, Aleksandar; Anagnosti, Petar

doi:10.1016/j.euromechsol.2008.04.005

Cited by 12 publications

(10 citation statements)

References 23 publications

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“…For example, Xu et al [11] examined Sadowsky and Sternberg's work and proposed an approximate solution for the stresses at a three-dimensional notch tip. Also using elliptic curvilinear coordinates, Lukić et al [4] studied the stresses around an oblong ellipsoid cavity in elastic homogeneous continuum with constant body forces and presented a solution in the form of infinite series. Meanwhile, studies on the stress concentrations around cavities in the shape of an ellipsoid of revolution can be found in, for example the work by Neuber [7].…”

Section: Introductionmentioning

confidence: 99%

Elastic Fields for the Ellipsoidal Cavity Problem

Zhao

Wang

2009

J Elasticity

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Lur'e (Three-dimensional Problem of the Theory of Elasticity. Interscience, New York, 1964, §6.9) presented an approach to solve the problem of an ellipsoidal cavity in a linear, elastic and isotropic medium loaded by uniform principal stresses at infinity. In this paper we show that the approach by Lur'e may have no solution. Derivation mistakes are first pointed out in his (6.9.22), (6.9.23), (6.9.30) and (6.9.31). With the correct expressions, we then prove the coefficient matrix in his (6.9.32) to be singular. Therefore constants A, A 4 , A 5 may have no solution. The problem lies in the harmonic functions chosen by Lur'e for the Papkovich-Neuber solution. From the solutions obtained by the Eshelby equivalent inclusion method, the present paper derives new Papkovich-Neuber harmonic functions for the ellipsoidal cavity problem.

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Section: Introductionmentioning

confidence: 99%

Elastic Fields for the Ellipsoidal Cavity Problem

Zhao

Wang

2009

J Elasticity

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“…There is no closed-form analytical solution available for such a system to describe the stress field. There have been some attempts made by other researchers [7,8] for a cavity system with a symmetrical configuration using numerical methods that are often very lengthy and timeconsuming to solve. Also, the solution for a geometrically asymmetric cavity pair, as shown in Fig.…”

Section: Unequal-sized Cavity Problemmentioning

confidence: 99%

“…An analytical closed-form solution for such a system is not available, although some numerical methods have been proposed in past research. Chiang used the Eshelby tensor and equivalent inclusion principle to describe the stress concentration around an ellipsoidal cavity [7,8]. Sternberg and Sadowsky proposed using Papcovich-Boussinesq displacement functions to solve the stress distribution around a pair of equal-sized cavities in an infinite continuum [9].…”

Section: Introductionmentioning

confidence: 99%

Empirical formulation of stress concentration factor around an arbitrary-sized spherical dual-cavity system and its application to aluminum die castings

Bidhar

Kuwazuru

Shiihara

et al. 2015

Applied Mathematical Modelling

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a b s t r a c tAn empirical formula for the stress concentration factor is developed for an unequal-sized cavity pair in an arbitrary orientation. Three-dimensional finite element linear elastic analyses are performed to evaluate the stress concentration factors for different sizes, orientations, and separations of cavities. A suitable mathematical function is chosen to fit the numerical results of the finite element analyses. An application is given for evaluating the maximum stress concentration factor, which governs fatigue crack initiation in aluminum die cast test pieces from an engine block. From the X-ray CT image, the location and geometry of the gas pores are evaluated so as to develop the proposed empirical formula for this actual multi-pore system simplified to a dual spherical pore system. A proof of the formula is shown by comparison with voxel finite element analysis. The proposed empirical formula can be satisfactorily used as a scientific guideline for selecting a casting method for car engine blocks from a fatigue crack initiation perspective.

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“…Introducing the relation (5), the stresses may be written in the following form [1,4,5,6,7] 3 3 2 2 2 2 2 2 2 3 2 2 2 2 3 2 2 2 2 2 1 0 2 2 2 2 2 2 0 0 2 2 2 2 1 0 2 2 2 3 2 2 2 2 2 3 2 2 2 2 2 2 …”

Section: Definition Of Stresses and The Ultimate Degeneration Processmentioning

confidence: 99%

Definition of Cracks for the Ultimate Degeneration Process of Revolving Ellipsoids

Lukić¹,

Zlatanović²

2014

AFST

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<p>The state of stress around cavities of the revolving ellipsoidal shape (prolate or oblate) in the extreme cases of their degeneration is a very complex problem. Namely, the shape of cavities is defined by an appropriate curvilinear coordinate system, which contains hyperbolic and trigonometric functions. In this paper, the treatment of revolving ellipsoid coordinates has been presented, along with transformations of ellipsoids for corresponding limiting values of their coordinates. Various forms of cracking can be defined through the ellipsoid degeneration process. In addition, the paper is dealing with a definition of the stress state for the limiting cases of degeneration.</p>

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Stress–strain field around elliptic cavities in elastic continuum

Cited by 12 publications

References 23 publications

Elastic Fields for the Ellipsoidal Cavity Problem

Elastic Fields for the Ellipsoidal Cavity Problem

Empirical formulation of stress concentration factor around an arbitrary-sized spherical dual-cavity system and its application to aluminum die castings

Definition of Cracks for the Ultimate Degeneration Process of Revolving Ellipsoids

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