Axial symmetric stress distributions in aeolotropic hexagonal crystals. The problem of the plane and related problems

Elliott, Harold

doi:10.1017/s0305004100025305

Cited by 95 publications

(33 citation statements)

References 9 publications

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“…It should be noted that Eqs (9)-(11) are similar to the results for a transversely isotropic elastic body (Noda, et al, 1983, Elliott, 1949 and that Eqs (12) and (13) govern the unique coupling behavior, as depicted in Fig. 1, through 14 e .…”

Section: Potential Functionssupporting

confidence: 63%

Thermoelectroelastic response of a piezoelectric cylinder with D<sub>∞</sub> symmetry under axisymmetric mechanical and thermal loading

Ootao

Kameo

Saito

2017

Mechanical Engineering Journal

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Carbon-neutral and biodegradable materials such as wood and poly-L-lactic acid play an important role in reducing environmental loads. Therefore, this study theoretically analyzed the thermoelectroelastic problem for a solid cylinder with D ∞ symmetry subjected to a distributed torsional shear stress as a mechanical input and to a nonuniform temperature distribution as a thermal disturbance, in order to gain an elementary understanding of the thermal effects on the electroelastic field in cylindrical bodies with D ∞ symmetry. The displacement components are expressed in terms of the elastic displacement potential function, the piezoelastic displacement potential function, and the thermoelastic displacement potential functions, and the electric field components are expressed in terms of the electric potential function. Subsequent to presenting the fundamental equations for thermoelectroelasticity, the governing equations for the above potential functions are derived based on the above fundamental equations. These governing equations are solved by a Fourier transform technique, and the theoretical solutions of the thermoelectroelastic field quantities are obtained. Furthermore, by performing numerical calculations, the distributions of the field quantities are illustrated graphically, and the structures of the thermoelectroelastic field are discussed qualitatively and quantitatively. Moreover, by quantitatively evaluating the ratio of the thermally disturbed electric displacement to the undisturbed electric displacement reflecting the mechanical input, the necessity of the thermoelectroelastic analyses, as treated in this paper, is clearly demonstrated.

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Section: Potential Functionssupporting

confidence: 63%

Thermoelectroelastic response of a piezoelectric cylinder with D<sub>∞</sub> symmetry under axisymmetric mechanical and thermal loading

Ootao

Kameo

Saito

2017

Mechanical Engineering Journal

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“…For instance, in the case of a transverse isotropic material, the indentation modulus obtained by indentation in the axis x3 of symmetry relates to the five independent C ijkl coefficients of the material in the following way [9,12]:…”

Section: Nanoindentation On Natural Compositesmentioning

confidence: 99%

The nanogranular nature of shale

2006

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Despite their ubiquitous presence as sealing formations in hydrocarbon bearing reservoirs affecting many fields of exploitation, the source of anisotropy of this earth material is still an enigma that has deceived many decoding attempts from experimental and theoretical sides. Sedimentary rocks, such as shales, are made of highly compacted clay particles of submicrometer size, nanometric porosity and different mineralogy. In this paper, we present, for the first time, results from a new experimental technique that allows one to rationally assess the elasticity content of the highly heterogeneous clay fabric of shales from nanoand microindentation. Based on the statistical analysis of massive nanoindentation tests, we find (1) that the in-situ elasticity content of the clayfabric at a scale of a few hundred to thousands nanometers is almost an order of magnitude smaller than reported clay stiffness values of clay minerals, and (2) that the elasticity and the anisotropy scale linearly with the clay packing density beyond a percolation threshold of roughly 50%. Furthermore, we show that the elasticity content sensed by nano-and microindentation tests is equal to the one that is sensed by (small strain) velocity measurements. From those observations, we conclude that shales are nanogranular composite materials, whose mechanical properties are governed by particle-toparticle contact and by characteristic packing densities, and that the much stiffer mineral properties play a secondary role.

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“…The basic results in the solution of elastic problems in a transversely isotropic body belong to Elliott [2,3], where he gave the general solution for the case of traditional axis orientation. A more elegant solution can be found in Fabrikant [5], as well as additional references to other relevant publications.…”

Section: Introductionmentioning

confidence: 99%

General flat crack located in the plane perpendicular to the planes of isotropy in transversely isotropic body

Fabrikant¹

2015

Acta Mech

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The published traditional crack problem solutions usually consider cracks located in the planes parallel to the plane of isotropy, which is usually denoted as z = 0. The case of a crack located in the plane x = 0 and subjected to arbitrary normal or tangential loading was solved recently in Fabrikant (Eur J Mech A 30:902-912, 2011). This article may be considered as its logical continuation. We consider here a transversely isotropic body, related to the system of axes (x 1 , x 2 , x 3 ), weakened in the plane x 1 = 0 by a flat crack of arbitrary shape. The plane x 1 = 0 is perpendicular to the planes of isotropy of the transversely isotropic body. The axis Ox 1 coincides with the major axis Ox, and the axes Ox 2 and Ox 3 are obtained by rotation about the axis Ox by arbitrary angle ϕ. The governing integral equation is derived for such a general case. The case of an elliptical crack is considered in detail. The complete solution for the fields of displacements and stresses is presented as single contour integrals of elementary integrands. Stress intensity factors are computed explicitly.

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Axial symmetric stress distributions in aeolotropic hexagonal crystals. The problem of the plane and related problems

Cited by 95 publications

References 9 publications

Thermoelectroelastic response of a piezoelectric cylinder with D<sub>∞</sub> symmetry under axisymmetric mechanical and thermal loading

Thermoelectroelastic response of a piezoelectric cylinder with D<sub>∞</sub> symmetry under axisymmetric mechanical and thermal loading

The nanogranular nature of shale

General flat crack located in the plane perpendicular to the planes of isotropy in transversely isotropic body

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