Journal ArticleDOI
Calculation of Polycrystal Elastic Constants from Single-Crystal Data
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In this article, a new calculation method of determining the elastic constants of a polycrystalline material from single-crystal elastic coefficients is presented, which can be applied to any crystal symmetry and allows to take texture into account.Abstract:
A new calculation method of determining the elastic constants of a polycrystalline material from single-crystal elastic coefficients is presented. The averaging procedure satisfies the condition of commutation with the inversion operation. It can be applied to any crystal symmetry and allows to take texture into account. The properties of the averaging procedure are given and compared to the corresponding properties of the arithmetic averaging method.
Eine neue Berechnungsmethode zur Bestimmung der elastischen Konstanten von polykristallinem Material aus Einkristallkonstanten wird dargestellt. Die Vertauschungsrelation zwischen der Mittelungsprozedur und der Inversionsoperation ist erfullt. Die Methode kann fur jede Kristallsymmetrie angewandt werden und erlaubt die Berucksichtigung der Textur. Die Eigenschaften der vorgeschlagenen Mittelungsprozedur werden gezeigt und mit den entsprechenden Eigenschaften der arithmetischen Mittelung verglichen.read more
Citations
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Book ChapterDOI
The Seismic Anisotropy of the Earth's Mantle: from Single Crystal to Polycrystal
TL;DR: In this paper, the anisotropic single crystal seismic properties are reviewed in the light of recent experimental and theoretical determinations and it is emphasized that simple seismic symmetry pattern of upper mantle rocks are a direct result of the interaction of olivine, opx and cpx.
Journal ArticleDOI
Methods of calculating petrophysical properties from lattice preferred orientation data
David Mainprice,Michel Humbert +1 more
TL;DR: In this paper, the authors consider the theoretical problems of calculating the physical properties of an aggregate from the constituent crystal properties and the lattice preferred orientation, and show that the Voigt and Reuss bounds become increasingly separated with inceasing anisotropy, emphasising the need for better methods.
Journal ArticleDOI
On the Averaging of Symmetric Positive-Definite Tensors
TL;DR: In this article, the authors present properly invariant averaging procedures for symmetric positive-definite tensors which are based on different measures of nearness of symmetric PDF tensors.
Journal ArticleDOI
Seismic properties and anisotropy of the continental crust: Predictions based on mineral texture and rock microstructure
Bjarne Almqvist,David Mainprice +1 more
TL;DR: In this paper, the authors use the Christoffel equation to estimate the seismic velocities and anisotropy of the continental crust of the United States using a microfabric-based approach.
Journal ArticleDOI
On the diffractive determination of single-crystal elastic constants using polycrystalline samples
TL;DR: The diffractive determination of single-crystal elastic constants using polycrystalline samples represents the inverse problem to the (direct) experiment of conventional diffractive residual-stress analysis as discussed by the authors.
References
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Journal ArticleDOI
The Elastic Behaviour of a Crystalline Aggregate
TL;DR: The connection between the elastic behavior of an aggregate and a single crystal is considered in this article, with special reference to the theories of Voigt, Reuss, and Huber and Schmid.
Journal ArticleDOI
A variational approach to the theory of the elastic behaviour of multiphase materials
Zvi Hashin,S. Shtrikman +1 more
TL;DR: In this paper, the authors derived upper and lower bounds for the effective elastic moduli of quasi-isotropic and quasi-homogeneous multiphase materials of arbitrary phase geometry.
Journal ArticleDOI
Berechnung der Fließgrenze von Mischkristallen auf Grund der Plastizitätsbedingung für Einkristalle .
Journal ArticleDOI
Berechnung der elastischen Konstanten des Vielkristalls aus den Konstanten des Einkristalls
TL;DR: In this article, anwendungsmoglichkeiten der Methode werden besprochen, in which experimentelle Vergleichswerte weichen von den berechneten etwas ab, was beweist, das die Experimente nicht den von der Theorie geforderten idealen Bedingungen genugt haben.