scholarly journals Analytical calculation of electron group velocity surfaces in uniform strained graphene

2016 ◽  
Vol 30 (03) ◽  
pp. 1550263 ◽  
Author(s):  
Wilfrido A. Gómez-Arias ◽  
Gerardo G. Naumis
Keyword(s):  
Shear Strain ◽  
Group Velocity ◽  
Pure Shear ◽  
Reciprocal Lattice ◽  
Tight Binding ◽  
Analytical Calculation ◽  
Fermi Velocity ◽  
Strained Graphene ◽  
Electron Group ◽  
Analytical Expressions

Electron group velocity for graphene under uniform strain is obtained analytically by using the tight-binding (TB) approximation. Such closed analytical expressions are useful in order to calculate the electronic, thermal and optical properties of strained graphene. These results allow to understand the behavior of electrons when graphene is subjected to strong strain and nonlinear corrections, for which the usual Dirac approach is no longer valid. Some particular cases of uniaxial and shear strain were analyzed. The evolution of the electron group velocity indicates a break-up of the trigonal warping symmetry, which is replaced by a warping consistent with the symmetry of the strained reciprocal lattice. To do this, analytical expressions for the shape of the first Brillouin zone (BZ) of the honeycomb strained reciprocal lattice are provided. Finally, the Fermi velocity becomes strongly anisotropic, i.e., for a strong pure shear strain (20% of the lattice parameter), the two inequivalent Dirac cones merge and the Fermi velocity is zero in one of the principal axis of deformation. We found that nonlinear terms are essential to describe the effects of deformation for electrons near or at the Fermi energy.

Observation of spatially-varying Fermi velocity in strained-graphene directly grown on hexagonal boron nitride

Carbon ◽  
2014 ◽  
Vol 74 ◽  
pp. 139-145 ◽  
Author(s):  
Won-Jun Jang ◽  
Howon Kim ◽  
Yong-Ro Shin ◽  
Min Wang ◽  
Sung Kyu Jang ◽  
...  
Keyword(s):  
Boron Nitride ◽  
Hexagonal Boron Nitride ◽  
Fermi Velocity ◽  
Strained Graphene ◽  
Spatially Varying

scholarly journals Dodecagonal bilayer graphene quasicrystal and its approximants

2019 ◽  
Vol 5 (1) ◽  
Author(s):  
Guodong Yu ◽  
Zewen Wu ◽  
Zhen Zhan ◽  
Mikhail I. Katsnelson ◽  
Shengjun Yuan
Keyword(s):  
Large Scale ◽  
Lattice Mismatch ◽  
Tight Binding ◽  
Bilayer Graphene ◽  
Dominant Factor ◽  
Honeycomb Lattice ◽  
Fermi Velocity ◽  
Band Theory ◽  
Incommensurate Structures ◽  
Unfolding Method

AbstractDodecagonal bilayer graphene quasicrystal has 12-fold rotational order but lacks translational symmetry which prevents the application of band theory. In this paper, we study the electronic and optical properties of graphene quasicrystal with large-scale tight-binding calculations involving more than ten million atoms. We propose a series of periodic approximants which reproduce accurately the properties of quasicrystal within a finite unit cell. By utilizing the band-unfolding method on the smallest approximant with only 2702 atoms, the effective band structure of graphene quasicrystal is derived. The features, such as the emergence of new Dirac points (especially the mirrored ones), the band gap at $$M$$M point and the Fermi velocity are all in agreement with recent experiments. The properties of quasicrystal states are identified in the Landau level spectrum and optical excitations. Importantly, our results show that the lattice mismatch is the dominant factor determining the accuracy of layered approximants. The proposed approximants can be used directly for other layered materials in honeycomb lattice, and the design principles can be applied for any quasi-periodic incommensurate structures.

More hyperelastic models for rubber-like materials: consistent tangent operators and comparative study

2013 ◽  
Vol 22 (1-2) ◽  
pp. 27-50 ◽  
Author(s):  
Mokarram Hossain ◽  
Paul Steinmann
Keyword(s):  
Large Deformations ◽  
Pure Shear ◽  
Three Dimensional ◽  
Network Models ◽  
Polymeric Materials ◽  
Chain Molecules ◽  
Current Contribution ◽  
Dimensional Network ◽  
Analytical Expressions ◽  
Order Tangent

AbstractRubber-like materials can deform largely and nonlinearly upon loading, and they return to the initial configuration when the load is removed. Such rubber elasticity is achieved due to very flexible long-chain molecules and a three-dimensional network structure that is formed via cross-linking or entanglements between molecules. Over the years, to model the mechanical behavior of such randomly oriented microstructures, several phenomenological and micromechanically motivated network models for nearly incompressible hyperelastic polymeric materials have been proposed in the literature. To implement these models for polymeric material (undoubtedly with widespread engineering applications) in the finite element framework for solving a boundary value problem, one would require two important ingredients, i.e., the stress tensor and the consistent fourth-order tangent operator, where the latter is the result of linearization of the former. In our previous work, 14 such material models are reviewed by deriving the accurate stress tensors and tangent operators from a group of phenomenological and micromechanical models at large deformations. The current contribution will supplement some further important models that were not included in the previous work. For comparison of all selected models in reproducing the well-known Treloar data, the analytical expressions for the three homogeneous defomation modes, i.e., uniaxial tension, equibiaxial tension, and pure shear, have been derived and the performances of the models are analyzed.

scholarly journals Investigation on shear strain of reinforced concrete membrane panels subjected to pure shear

2019 ◽  
Vol 11 (8) ◽  
pp. 168781401986948
Author(s):  
Je-Pyong Jeong ◽  
Dae-Hung Kang
Keyword(s):  
Reinforced Concrete ◽  
Shear Strain ◽  
Pure Shear ◽  
Failure Criteria ◽  
Principal Compressive Stress ◽  
Strain Relationship ◽  
Trial And Error Method ◽  
Shear Strain Energy ◽  
Relationship Of ◽  
The Relationship

Hsu recently conducted a shear test on nine reinforced concrete panel elements subjected to applying pure shear using a shear testing device. Modern truss models (i.e. modified compression field theory and a rotating angle softened truss model) are used to perform a complex nonlinear analysis through a trial and error method based on a double loop. This analysis is conducted by employing equilibrium conditions, compatibility conditions, and a ductile stress–strain relationship of a reinforced concrete membrane panel in a biaxial state. In this study, an effective algorithm that uses a revised Mohr compatibility method based on the failure criteria of struts and ties is proposed. This algorithm is used to improve the convergence rate in the analysis of shear history, which was performed in the experiment of Hsu. The result of the analysis indicates that the shear strain energy in a state of extended shear strain is influenced by the relationship between principal compressive stress and strain (crushing failure).

Effect of pure shear strain on mechanical properties and microstructural evolution

2017 ◽  
Vol 679 ◽  
pp. 133-142 ◽  
Author(s):  
Farhad Rahimi ◽  
Ali Reza Eivani ◽  
Hamid Reza Jafarian ◽  
Tilak Bhattacharjee
Keyword(s):  
Mechanical Properties ◽  
Shear Strain ◽  
Microstructural Evolution ◽  
Pure Shear

Poloidal eigenmode of the geodesic acoustic mode in the limit of high safety factor

2009 ◽  
Vol 75 (6) ◽  
pp. 721-729 ◽  
Author(s):  
M. SASAKI ◽  
K. ITOH ◽  
A. EJIRI ◽  
Y. TAKASE
Keyword(s):  
Spatial Structure ◽  
Phase Velocity ◽  
Group Velocity ◽  
Safety Factor ◽  
Acoustic Mode ◽  
Higher Order ◽  
Expansion Parameter ◽  
Geodesic Acoustic Mode ◽  
Analytical Expressions

AbstractThe poloidal eigenmode of the geodesic acoustic mode (GAM) is studied in the limit of high safety factor. In this limit, the poloidal gyroradius cannot be treated as a perturbation or as an expansion parameter. Analytical expressions for the poloidal structure of the GAM potential, the radial wavenumber dependence of the frequency, the phase velocity, and the group velocity are obtained. The spatial structure of the poloidal eigenmode including the higher-order gyroradius effect is revealed theoretically.

Digital pure shear-strain moiré patterns

1992 ◽  
Vol 31 (11) ◽  
pp. 1813 ◽  
Author(s):  
Qifeng Yu ◽  
K. Andresen ◽  
Dongsheng Zhang
Keyword(s):  
Shear Strain ◽  
Pure Shear ◽  
Moire Patterns ◽  
Moiré Patterns

The role of pure shear strain on the site of crack initiation in notches

1977 ◽  
Vol 8 (5) ◽  
pp. 729-740 ◽  
Author(s):  
Vincent J. Russo ◽  
Amiya K. Chakrabarti ◽  
Joseph W. Spretnak
Keyword(s):  
Crack Initiation ◽  
Shear Strain ◽  
Pure Shear

Soliton-Like Light Propagation through Coupled Resonators Constructed with Periodic Metal-Dielectric Layers

2013 ◽  
Vol 339 ◽  
pp. 706-713
Author(s):  
Yu Guang Zhu ◽  
Yun Tuan Fang ◽  
Wei Li Hu ◽  
Wei Zhong Yan
Keyword(s):  
Group Velocity ◽  
Free Space ◽  
Light Propagation ◽  
Tight Binding ◽  
Coupled Resonators ◽  
Light Velocity ◽  
One Dimensional ◽  
Resonator Structure ◽  
Transmission Mechanisms ◽  
Dielectric Layers

in order to obtain a soliton-like light propagation, we design a coupled resonator structure constructed with one-dimensional periodic metal-dielectric layers. Through tight-binding analysis and the Blochs theorem, we study its transmission mechanisms. Basing on the transmission mechanisms, we achieve a soliton-like light propagation in it with a group velocity being smaller light velocity in free space.

scholarly journals Generalizing the Fermi velocity of strained graphene from uniform to nonuniform strain

2015 ◽  
Vol 379 (40-41) ◽  
pp. 2645-2651 ◽  
Author(s):  
M. Oliva-Leyva ◽  
Gerardo G. Naumis
Keyword(s):  
Fermi Velocity ◽  
Strained Graphene ◽  
Nonuniform Strain
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