Anisotropic elasticity in hexagonal crystals

2007 ◽  
Vol 515 (17) ◽  
pp. 7020-7024 ◽  
Author(s):  
Jian-Min Zhang ◽  
Yan Zhang ◽  
Ke-Wei Xu ◽  
Vincent Ji
Keyword(s):  
Anisotropic Elasticity ◽  
Hexagonal Crystals

Origin of the alternate bright/dark contrast in HREM images of hexagonal crystals, particularly 6H-SiC

1993 ◽  
Vol 51 ◽  
pp. 914-915
Author(s):  
J.S. Bow ◽  
R.W. Carpenter ◽  
M.J. Kim
Keyword(s):  
High Resolution ◽  
Incident Beam ◽  
Hexagonal Crystal ◽  
Detailed Explanation ◽  
Similar Character ◽  
High Resolution Images ◽  
The Difference ◽  
Zigzag Shape ◽  
Hexagonal Crystals ◽  
Dark Contrast

A prominent characteristic of high-resolution images of 6H-SiC viewed from [110] is a zigzag shape with a period of 6 layers as shown in Fig.1. Sometimes the contrast is same through the 6 layers of (0006) planes (Fig.1a), but in most cases it appears as in Fig.1b -- alternate bright/dark contrast among every three (0006) planes. Alternate bright/dark contrast is most common for the thicker specimens. The SAD patterns of these two types of image are almost same, and there is no indication that the difference results from compositional ordering. O’Keefe et al. concluded this type of alternate contrast was due to crystal tilt in thick parts of the specimen. However, no detailed explanation was given. Images of similar character from Ti3Al, which is also a hexagonal crystal, were reported by Howe et al. Howe attributed the bright/dark contrast among alternate (0002) Ti3Al planes to phase shifts produced by incident beam tilt.

Anisotropic Elasticity

1996 ◽  
Author(s):  
T. T. C. Ting
Keyword(s):  
Composite Materials ◽  
Elastic Constants ◽  
Piezoelectric Materials ◽  
Anisotropic Materials ◽  
Anisotropic Elasticity ◽  
Stress Singularities ◽  
Comprehensive Survey ◽  
The Subject ◽  
Key Topics ◽  
First Time

Anisotropic Elasticity offers for the first time a comprehensive survey of the analysis of anisotropic materials that can have up to twenty-one elastic constants. Focusing on the mathematically elegant and technically powerful Stroh formalism as a means to understanding the subject, the author tackles a broad range of key topics, including antiplane deformations, Green's functions, stress singularities in composite materials, elliptic inclusions, cracks, thermo-elasticity, and piezoelectric materials, among many others. Well written, theoretically rigorous, and practically oriented, the book will be welcomed by students and researchers alike.

Observations on crystals found in the intestine of Nematodirus battus during the development of immunity to this nematode in lambs

Parasitology ◽  
1976 ◽  
Vol 72 (1) ◽  
pp. 75-80 ◽  
Author(s):  
J. Martin ◽  
D. L. Lee
Keyword(s):  
X Ray ◽  
Infective Larvae ◽  
Adult Nematode ◽  
Hexagonal Crystals

Lambs which were given 60000 infective larvae ofNematodirus battus progressively threw off adult nematodes from day 20 onwards. Large, hexagonal crystals appeared in the intestine of the adult nematode at about this time and caused blockage of the intestinal-rectal or -cloacal junction. Lambs which were given 1000–2000 infective larvae did not throw off the infection, and adult nematodes from lambs which had been infected for up to 74 days did not contain these crystals. Chemical, histo-chemical and X-ray microanalysis tests on the crystals indicated that they are lipoprotein in composition. The crystals arise within the lumen of the nematode and appear to be associated with the development of immunity to this nematode in lambs.

scholarly journals Viscoelastic phase-field fracture using the framework of representative crack elements

2021 ◽  
Author(s):  
Bo Yin ◽  
Johannes Storm ◽  
Michael Kaliske
Keyword(s):  
Phase Field ◽  
Consistency Condition ◽  
Field Method ◽  
Anisotropic Elasticity ◽  
Phase Field Method ◽  
Internal Variables ◽  
Crack Model ◽  
Material Degradation ◽  
Discrete Crack ◽  
Deformation State

AbstractThe promising phase-field method has been intensively studied for crack approximation in brittle materials. The realistic representation of material degradation at a fully evolved crack is still one of the main challenges. Several energy split formulations have been postulated to describe the crack evolution physically. A recent approach based on the concept of representative crack elements (RCE) in Storm et al. (The concept of representative crack elements (RCE) for phase-field fracture: anisotropic elasticity and thermo-elasticity. Int J Numer Methods Eng 121:779–805, 2020) introduces a variational framework to derive the kinematically consistent material degradation. The realistic material degradation is further tested using the self-consistency condition, which is particularly compared to a discrete crack model. This work extends the brittle RCE phase-field modeling towards rate-dependent fracture evolution in a viscoelastic continuum. The novelty of this paper is taking internal variables due to viscoelasticity into account to determine the crack deformation state. Meanwhile, a transient extension from Storm et al. (The concept of representative crack elements (RCE) for phase-field fracture: anisotropic elasticity and thermo-elasticity. Int J Numer Methods Eng 121:779–805, 2020) is also considered. The model is derived thermodynamic-consistently and implemented into the FE framework. Several representative numerical examples are investigated, and consequently, the according findings and potential perspectives are discussed to close this paper.

Contributions to the Shear Constants of Hexagonal Crystals

1940 ◽  
Vol 57 (1) ◽  
pp. 60-60 ◽  
Author(s):  
H. B. Huntington
Keyword(s):  
Hexagonal Crystals
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