Cauchy–Born rule and stability of crystalline solids at finite temperature

2021 ◽  
Vol 19 (6) ◽  
pp. 1461-1490
Author(s):  
Tao Luo ◽  
Yang Xiang ◽  
Jerry Zhijian Yang ◽  
Cheng Yuan
Keyword(s):  
Finite Temperature ◽  
Crystalline Solids ◽  
Born Rule

Finite Temperatue Cauchy--Born Rule and Stability of Crystalline Solids with Point Defects

2021 ◽  
Vol 19 (4) ◽  
pp. 1710-1735
Author(s):  
Tao Luo ◽  
Yang Xiang ◽  
Jerry Zhijian Yang
Keyword(s):  
Point Defects ◽  
Crystalline Solids ◽  
Born Rule

A finite temperature continuum theory based on interatomic potential in crystalline solids

2008 ◽  
Vol 42 (4) ◽  
pp. 531-541 ◽  
Author(s):  
Albert C. To ◽  
Wing Kam Liu ◽  
Adrian Kopacz
Keyword(s):  
Finite Temperature ◽  
Interatomic Potential ◽  
Continuum Theory ◽  
Crystalline Solids

Contrast From Point Defects in The Infinitesimal Approximation

1980 ◽  
Vol 38 ◽  
pp. 350-351
Author(s):  
L. J. Sykes ◽  
J. J. Hren
Keyword(s):  
Electron Microscope ◽  
Point Defects ◽  
Broad Class ◽  
Stacking Fault ◽  
Crystalline Solids ◽  
Dislocation Loops ◽  
Analytical Expression ◽  
Stacking Fault Tetrahedra

In electron microscope studies of crystalline solids there is a broad class of very small objects which are imaged primarily by strain contrast. Typical examples include: dislocation loops, precipitates, stacking fault tetrahedra and voids. Such objects are very difficult to identify and measure because of the sensitivity of their image to a host of variables and a similarity in their images. A number of attempts have been made to publish contrast rules to help the microscopist sort out certain subclasses of such defects. For example, Ashby and Brown (1963) described semi-quantitative rules to understand small precipitates. Eyre et al. (1979) published a catalog of images for BCC dislocation loops. Katerbau (1976) described an analytical expression to help understand contrast from small defects. There are other publications as well.

Cosserat Modeling of Size Effects in Crystalline Solids

2000 ◽  
Vol 653 ◽  
Author(s):  
Samuel Forest
Keyword(s):  
Stress State ◽  
Size Effects ◽  
Elastic Inclusion ◽  
Characteristic Size ◽  
Infinite Matrix ◽  
Crystalline Solids ◽  
Generalized Continua ◽  
Absolute Size ◽  
Kink Bands ◽  
The Matrix

AbstractThe mechanics of generalized continua provides an efficient way of introducing intrinsic length scales into continuum models of materials. A Cosserat framework is presented here to descrine the mechanical behavior of crystalline solids. The first application deals with the problem of the stress field at a crak tip in Cosserat single crystals. It is shown that the strain localization patterns developping at the crack tip differ from the classical picture : the Cosserat continuum acts as a bifurcation mode selector, whereby kink bands arising in the classical framework disappear in generalized single crystal plasticity. The problem of a Cosserat elastic inclusion embedded in an infinite matrix is then considered to show that the stress state inside the inclusion depends on its absolute size lc. Two saturation regimes are observed : when the size R of the inclusion is much larger than a characteristic size of the medium, the classical Eshelby solution is recovered. When R is much small than the inclusion, a much higher stress is reached (for an inclusion stiffer than the matrix) that does not depend on the size any more. There is a transition regime for which the stress state is not homogeneous inside the inclusion. Similar regimes are obtained in the study of grain size effects in polycrystalline aggregates of Cosserat grains.

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