A Simple Explicit Formula for the Voigt-Reuss-Hill Average of Elastic Polycrystals with Arbitrary Crystal and Texture Symmetries

Man, Chi‐Sing; Huang, Mojia

doi:10.1007/978-94-007-1884-5_28

Cited by 11 publications

(12 citation statements)

References 16 publications

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“…Also we provide the empirical VRH-average for the bulk and shear modulus. This empirical average is known to represent the bulk and shear modulus of polycrystalline materials with comparable accuracy as more advanced polycrystalline homogenization schemes such as those by Hashin and Strickman 14 , 55 . Other properties computed in this work are the index of elastic anisotropy 56 and the Poisson ratio in the isotropic approximation.…”

Section: Data Recordsmentioning

confidence: 99%

Charting the complete elastic properties of inorganic crystalline compounds

et al. 2015

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The elastic constant tensor of an inorganic compound provides a complete description of the response of the material to external stresses in the elastic limit. It thus provides fundamental insight into the nature of the bonding in the material, and it is known to correlate with many mechanical properties. Despite the importance of the elastic constant tensor, it has been measured for a very small fraction of all known inorganic compounds, a situation that limits the ability of materials scientists to develop new materials with targeted mechanical responses. To address this deficiency, we present here the largest database of calculated elastic properties for inorganic compounds to date. The database currently contains full elastic information for 1,181 inorganic compounds, and this number is growing steadily. The methods used to develop the database are described, as are results of tests that establish the accuracy of the data. In addition, we document the database format and describe the different ways it can be accessed and analyzed in efforts related to materials discovery and design.

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Section: Data Recordsmentioning

confidence: 99%

Charting the complete elastic properties of inorganic crystalline compounds

et al. 2015

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“…First, we recall some basics of tensorial algebra, following the presentation of Moakher and Norris [8] (see also [15,16]). Since we are investigating elastic behaviors, we are mainly concerned with fourth-order and second-order tensors in a three-dimensional Cartesian space.…”

Section: Preliminariesmentioning

confidence: 99%

“…In order to facilitate some calculations, we take advantage of the Kelvin notation in elasticity (see [15,16] for a comprehensive description of the Kelvin notation). Fourth-order elasticity tensors in three dimensions are equivalent to second-order tensors in six dimensions; the tensor C can be represented by the 6 × 6 matrix C defined by…”

Section: Preliminariesmentioning

confidence: 99%

Generalized Euclidean Distances for Elasticity Tensors

Morin

Pierre

Derrien

2019

J Elast

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The aim of this short paper is to provide, for elasticity tensors, generalized Euclidean distances that preserve the property of invariance by inversion. First, the elasticity law is expressed under a non-dimensional form by means of a gauge, which leads to an expression of elasticity (stiffness or compliance) tensors without units. Based on the difference between functions of the dimensionless tensors, generalized Euclidean distances are then introduced. A subclass of functions is proposed, which permits the retrieval of the classical log-Euclidean distance and the derivation of new distances, namely the arctan-Euclidean and power-Euclidean distances. Finally, these distances are applied to the determination of the closest isotropic tensor to a given elasticity tensor.

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“…Let C : Sym → Sym be the fourth-order elasticity tensor; it is a symmetric linear transformation on Sym. In the Kelvin notation [10], the Cauchy stress T and the infinitesimal strain E are treated as 6-dimensional vectors in Sym, and the elasticity tensor C as a symmetric second-order tensor in Sym ⊗ Sym…”

Section: Anisotropic Linear Elasticitymentioning

confidence: 99%

Remarks on isotropic extension of anisotropic constitutive functions via structural tensors

Man

Goddard

2017

Mathematics and Mechanics of Solids

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The following is an elaboration on the linear non-local model of viscoelastic fluids proposed in a previous work (Int. J. Eng. Sci. 48 (2010), 1279-1288). As a recapitulation of that work, the basic theory is presented in terms of the temporal frequency and spatial wave number in the Laplace-Fourier domain. Taylor-series expansions in these variables provides a weakly non-local theory in spatio-temporal gradients that is more comprehensive than the "bi-velocity" model of Brenner. The linearized Chapman-Enskog kinetic theory is shown to provide a confirmation of the more general theory, from which one can reconstruct a fully non-local integral model. Following the work of Davis and Brenner (J. Acoust. Soc. Am. 132 (2012), 2963-2969), the general theory is employed to derive dispersion relations for acoustic, thermal and shear-wave propagation in compressible viscoelastic fluids. At Burnett order the Chapman-Enskog theory gives a cubic polynomial in wave number squared which reduces in the dissipative quasi-static limit to a quadratic like that given by the classical Navier-Stokes-Fourier model and the bi-velocity modification of that model. With minor modification, the present analysis applies to viscoelastic shear and dilatational wave propagation in solids with higher-gradient and Cosserat effects, where it may, for example, find application to the field of rotational seismology.

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A Simple Explicit Formula for the Voigt-Reuss-Hill Average of Elastic Polycrystals with Arbitrary Crystal and Texture Symmetries

Cited by 11 publications

References 16 publications

Charting the complete elastic properties of inorganic crystalline compounds

Charting the complete elastic properties of inorganic crystalline compounds

Generalized Euclidean Distances for Elasticity Tensors

Remarks on isotropic extension of anisotropic constitutive functions via structural tensors

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