Zum Materialgesetz eines elastischen Mediums mit Momentenspannungen

1965 ◽  
Vol 20 (3) ◽  
pp. 336-359 ◽  
Author(s):  
F. Hehl ◽  
E. Kröner
Keyword(s):  
Constitutive Relations ◽  
Short Review ◽  
Local Effect ◽  
Classical Elasticity ◽  
Couple Stresses ◽  
State Of Stress ◽  
Order Of Magnitude ◽  
Non Local ◽  
Peierls Model ◽  
Edge Dislocations

If through an element of area of a continuum there acts not only a force but also a couple, we have to introduce besides the force-stresses the so-called couple-stresses. In this article we emphasize the importance of couple-stresses in dislocated solids.—§ 2 gives a short review of the present state of the theory of couple-stresses. In classical elasticity couple-stresses are to be interpreted as a non-local effect intimately connected with the range of the atomic forces. The couplestresses are of a higher order in this range than force-stresses and can therefore usually be neglected.In the field theory of dislocations couple-stresses generally are of the same order of magnitude as force-stresses, however. Hence they cause considerable effects. In § 3 we determine the macroscopic observable couple-stresses of homogeneously distributed screw and edge dislocations through averaging over their microscopic fluctuating stress field. With the PEIERLS model we show in § 4 that the core of a dislocation produces an asymmetric state of stress and for that reason also couple-stresses, which are negligibly small under certain circumstances. Introducing a simple polycrystal model we derive in § 5 the constitutive relations for couple-stresses and dislocation density in an isotropic form. The results are discussed in § 6.

scholarly journals Static and Dynamic Solutions of Functionally Graded Micro/Nanobeams under External Loads Using Non-Local Theory

Vibration ◽  
2020 ◽  
Vol 3 (2) ◽  
pp. 51-69
Author(s):  
Reza Moheimani ◽  
Hamid Dalir
Keyword(s):  
Power Index ◽  
Linear Equations ◽  
Local Effect ◽  
Functionally Graded ◽  
Local Theory ◽  
Classical Elasticity ◽  
Graded Materials ◽  
Nano Scale ◽  
Non Local ◽  
External Loads

Functionally graded materials (FGMs) have wide applications in different branches of engineering such as aerospace, mechanics, and biomechanics. Investigation of the mechanical behaviors of structures made of these materials has been performed widely using classical elasticity theories in micro/nano scale. In this research, static, dynamic and vibrational behaviors of functional micro and nanobeams were investigated using non-local theory. Governing linear equations of the problem were driven using non-local theory and solved using an analytical method for different boundary conditions. Effects of the axial load, the non-local parameter and the power index on the natural frequency of different boundary condition are assessed. Then, the obtained results were compared with those obtained from classical theory. These results showed that a non-local effect could greatly affect the behaviors of these beams, especially at nano scale.

scholarly journals Author Correction: Non-local effect of impurity states on the exchange coupling mechanism in magnetic topological insulators

2021 ◽  
Vol 6 (1) ◽  
Author(s):  
Thiago R. F. Peixoto ◽  
Hendrik Bentmann ◽  
Philipp Rüßmann ◽  
Abdul-Vakhab Tcakaev ◽  
Martin Winnerlein ◽  
...  
Keyword(s):  
Exchange Coupling ◽  
Topological Insulators ◽  
Local Effect ◽  
Coupling Mechanism ◽  
Impurity States ◽  
Non Local

A Correction to this paper has been published: https://doi.org/10.1038/s41535-021-00314-9

TEM investigation of defect reduction and etch pit formation in GaN

2003 ◽  
Vol 798 ◽  
Author(s):  
Angelika Vennemann ◽  
Jens Dennemarck ◽  
Roland Kröger ◽  
Tim Böttcher ◽  
Detlef Hommel ◽  
...  
Keyword(s):  
Electron Microscopy ◽  
Dislocation Density ◽  
Line Tension ◽  
Threading Dislocations ◽  
Dislocation Loops ◽  
Etch Pits ◽  
Defect Reduction ◽  
Transmission Electron ◽  
Order Of Magnitude ◽  
Edge Dislocations

ABSTRACTGaN samples of this study were chemically wet etched to gain easier access to the dislocation sturcture. The scanning electron microscopy and transmission electron microscopy investigations revealed four different types of etch pits. After brief etching, several dislocations with screw component showed large etch pits, which may be correlated with the core of the screw dislocation. By means of SiNx micromasking the dislocation density could be reduced by more than one order of magnitude. The reduction of threading dislocations in the SiNx region in GaN grown on 〈0001〉 sapphire is due to bending of the threading dislocations into the {0001} plane, such that they form dislocation loops if they meet dislocations with opposite Burgers vectors. Accordingly, the achievable reduction of the dislocation density is limited by the probability that these dislocations interact. Edge dislocations bend more easily on account of their low line tension. This results in a preferential bending and reduction of dislocations with edge character.

scholarly journals Non-Local Buckling Analysis of Functionally Graded Nanoporous Metal Foam Nanoplates

Coatings ◽  
2018 ◽  
Vol 8 (11) ◽  
pp. 389 ◽  
Author(s):  
Yanqing Wang ◽  
Zhiyuan Zhang
Keyword(s):  
Metal Foam ◽  
Plate Theory ◽  
Constitutive Relations ◽  
Equations Of Motion ◽  
Local Buckling ◽  
Functionally Graded ◽  
Small Scale ◽  
Refined Plate Theory ◽  
Nanoporous Metal ◽  
Non Local

In this study, the buckling of functionally graded (FG) nanoporous metal foam nanoplates is investigated by combining the refined plate theory with the non-local elasticity theory. The refined plate theory takes into account transverse shear strains which vary quadratically through the thickness without considering the shear correction factor. Based on Eringen’s non-local differential constitutive relations, the equations of motion are derived from Hamilton’s principle. The analytical solutions for the buckling of FG nanoporous metal foam nanoplates are obtained via Navier’s method. Moreover, the effects of porosity distributions, porosity coefficient, small scale parameter, axial compression ratio, mode number, aspect ratio and length-to-thickness ratio on the buckling loads are discussed. In order to verify the validity of present analysis, the analytical results have been compared with other previous studies.

Wave propagation in a non-local piezoelectric phononic crystal Timoshenko nanobeam

2020 ◽  
pp. 2150064
Author(s):  
Feiyang He ◽  
Denghui Qian ◽  
Musai Zhai
Keyword(s):  
Wave Propagation ◽  
Phononic Crystal ◽  
Local Effect ◽  
Geometric Parameters ◽  
Width Ratio ◽  
Plane Wave Expansion ◽  
Mechanical Coupling ◽  
Non Local ◽  
Influencing Parameters ◽  
Scale Coefficient

By applying non-local elasticity theory and plane wave expansion (PWE) method to Timoshenko beam, the calculation method of band structure of a non-local piezoelectric phononic crystal (PC) Timoshenko nanobeam is proposed and formulized. In order to investigate the properties of wave propagating in the nanobeam in detail, bandgaps of first four orders are picked, and the corresponding influence rules of thermo-electro-mechanical coupling fields, non-local effect and geometric parameters on bandgaps are studied. During the research works, temperature variation, external electrical voltage and axial force are chosen as the influencing parameters related to the thermo-electro-mechanical coupling fields. Scale coefficient is chosen as the influencing parameter corresponding to non-local effect. Length ratio between materials PZT-4 and epoxy and height-width ratio are chosen as the influencing parameters of geometric parameters. Moreover, all the band structures and influence rules of Timoshenko nanobeam are compared to those of Euler nanobeam. The results are expected to be of help for the design of micro and nanodevices based on piezoelectric periodic nanobeams.

scholarly journals Empirical surface gravities

1997 ◽  
Vol 189 ◽  
pp. 119-124
Author(s):  
P. F. L. Maxted
Keyword(s):  
Binary Stars ◽  
Short Review ◽  
Limited Range ◽  
Stellar Atmospheres ◽  
Fundamental Parameter ◽  
Dwarf Stars ◽  
Eclipsing Binary ◽  
White Dwarf Stars ◽  
Eclipsing Binary Stars ◽  
Order Of Magnitude

The surface gravity of a star (log g) is a fundamental parameter in models of stellar atmospheres. Given suitable spectra, log g can be determined from such models with an accuracy of 0.1dex, at best. Detached eclipsing binary stars can provide values of log g an order of magnitude more accurate than this, though for a more limited range of stars. Naturally, less accurate surface gravities can be obtained for a wider range of eclipsing binary stars.These facts are well known, so in this short review I will outline the types of stars to which the two methods have be usefully applied and might be applied in the near future. This naturally leads to the question of where the two ranges overlap and the comparison of results from the two methods. Techniques for allowing this comparison to made directly will be described. Surface gravities derived from winds in hot stars and (indirectly) from gravitational redshifts in white dwarf stars will also be covered briefly.

Non-local constitutive relations and the quasi-homogeneous approximation

2005 ◽  
Vol 342 (5-6) ◽  
pp. 363-367 ◽  
Author(s):  
Robert W. Schoonover ◽  
Joseph M. Rutherford ◽  
Ole Keller ◽  
P. Scott Carney
Keyword(s):  
Constitutive Relations ◽  
Non Local ◽  
Homogeneous Approximation

Study on Non-Local Damage Constitutive Model of Concrete under Freeze-Thaw Action

2010 ◽  
Vol 452-453 ◽  
pp. 133-136 ◽  
Author(s):  
Zong Min Liu ◽  
Ji Ze Mao ◽  
Hai Yan Song
Keyword(s):  
Constitutive Model ◽  
Internal State ◽  
Constitutive Relations ◽  
Irreversible Thermodynamics ◽  
Local Damage ◽  
Variable Theory ◽  
Freeze Thaw ◽  
Adjacent Point ◽  
Damage Constitutive Model ◽  
Non Local

Concrete is multi-phase composites. Due to the inhomogeneity of mechanical properties and complexity of physical properties, constitutive relations of concrete are more complicated. Starting from irreversible thermodynamics theory, internal state variable theory and nonlocal field theory, non-local damage constitutive model of concrete under freeze-thaw action is established in this paper. In the model, non-local influence functions are discussed which are used to describe interplay of damage between adjacent point.

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