Topic
Anisotropy
About: Anisotropy is a research topic. Over the lifetime, 55875 publications have been published within this topic receiving 1076026 citations.
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TL;DR: A new universal anisotropy index is introduced that overcomes the above limitations and is applicable to all types of elastic single crystals, and thus fills an important void in the existing literature.
Abstract: Practically all elastic single crystals are anisotropic, which calls for an appropriate universal measure to quantify the extent of anisotropy. A review of the existing anisotropy measures in the literature leads to a conclusion that they lack universality in the sense that they are nonunique and ignore contributions from the bulk part of the elastic stiffness (or compliance) tensor. Proceeding from extremal principles of elasticity, we introduce a new universal anisotropy index that overcomes the above limitations. Furthermore, we establish special relationships between the proposed anisotropy index and the existing anisotropy measures for special cases. A new elastic anisotropy diagram is constructed for over 100 different crystals (from cubic through triclinic), demonstrating that the proposed anisotropy measure is applicable to all types of elastic single crystals, and thus fills an important void in the existing literature.
1,628 citations
TL;DR: In this paper, the authors examined the modeling of the pressure-strain correlation of turbulent flows from a basic theoretical standpoint with a view toward developing improved second-order closure models and proved that for plane homogeneous turbulent flows the equilibrium structure of this hierarchy of models is encapsulated by a relatively simple model which is only quadratically nonlinear in the anisotropy tensor.
Abstract: The modeling of the pressure-strain correlation of turbulence is examined from a basic theoretical standpoint with a view toward developing improved second-order closure models. Invariance considerations along with elementary dynamical systems theory are used in the analysis of the standard hierarchy of closure models. In these commonly used models, the pressure-strain correlation is assumed to be a linear function of the mean velocity gradients with coefficients that depend algebraically on the anisotropy tensor. It is proven that for plane homogeneous turbulent flows the equilibrium structure of this hierarchy of models is encapsulated by a relatively simple model which is only quadratically nonlinear in the anisotropy tensor. This new quadratic model - the SSG model - is shown to outperform the Launder, Reece, and Rodi model (as well as more recent models that have a considerably more complex nonlinear structure) in a variety of homogeneous turbulent flows. Some deficiencies still remain for the description of rotating turbulent shear flows that are intrinsic to this general hierarchy of models and, hence, cannot be overcome by the mere introduction of more complex nonlinearities. It is thus argued that the recent trend of adding substantially more complex nonlinear terms containing the anisotropy tensor may be of questionable value in the modeling of the pressure-strain correlation. Possible alternative approaches are discussed briefly.
1,556 citations
TL;DR: In this article, an inextensive system of magnetic susceptibility anisotropy factors is suggested which is sufficient in the majority of practical applications for characterizing the magnetic fabric of rocks.
1,508 citations
TL;DR: In this paper, the authors considered the elastic equations for the case in which the state of the solid is independent of one of the three Cartesian coordinates, and the stresses due to a dislocation, a wall of parallel dislocations, and a crack in an arbitrary non-uniform stress field were obtained.
Abstract: The solution of the elastic equations is considered for the case in which the state of the solid is independent of one of the three Cartesian coordinates. The stresses due to a dislocation, a wall of parallel dislocations, and a crack in an arbitrary non-uniform stress field are obtained. The results hold for the most general anisotropy in which no symmetry elements of the crystal are assumed.
1,479 citations
TL;DR: In this article, a theoretical formalism to calculate the single crystal elastic constants for orthorhombic crystals from first principle calculations is described, and the elastic constants using a full potential linear muffin-tin orbital method using the local density approximation (LDA) and generalized gradient approximation (GGA).
Abstract: A theoretical formalism to calculate the single crystal elastic constants for orthorhombic crystals from first principle calculations is described. This is applied for TiSi2 and we calculate the elastic constants using a full potential linear muffin-tin orbital method using the local density approximation (LDA) and generalized gradient approximation (GGA). The calculated values compare favorably with recent experimental results. An expression to calculate the bulk modulus along crystallographic axes of single crystals, using elastic constants, has been derived. From this the calculated linear bulk moduli are found to be in good agreement with the experiments. The shear modulus, Young’s modulus, and Poisson’s ratio for ideal polycrystalline TiSi2 are also calculated and compared with corresponding experimental values. The directional bulk modulus and the Young’s modulus for single crystal TiSi2 are estimated from the elastic constants obtained from LDA as well as GGA calculations and are compared with the ...
1,469 citations