A Review of Mixture and Non-Local Continuum Mechanics with Example Applications to Cohesive Sediments

2013 ◽  
pp. 429-455
Author(s):  
A.D. Kirwan
Keyword(s):  
Continuum Mechanics ◽  
Cohesive Sediments ◽  
Non Local

scholarly journals Fractional calculus for continuum mechanics – anisotropic non-locality

2016 ◽  
Vol 64 (2) ◽  
pp. 361-372 ◽  
Author(s):  
W. Sumelka
Keyword(s):  
Fractional Calculus ◽  
Continuum Mechanics ◽  
General Framework ◽  
Deformation Gradient ◽  
Theoretical Discussion ◽  
Geometrical Meaning ◽  
Numerical Examples ◽  
Non Local ◽  
Fractional Continuum ◽  
Non Locality

Abstract In this paper, a generalisation of previous author’s formulation of fractional continuum mechanics for the case of anisotropic non-locality is presented. The discussion includes a review of competitive formulations available in literature. The overall concept is based on the fractional deformation gradient which is non-local due to fractional derivative definition. The main advantage of the proposed formulation is its structure, analogous to the general framework of classical continuum mechanics. In this sense, it allows to define similar physical and geometrical meaning of introduced objects. The theoretical discussion is illustrated by numerical examples assuming anisotropy limited to single direction.

Group velocity of wave propagation in carbon nanotubes

2008 ◽  
Vol 464 (2094) ◽  
pp. 1423-1438 ◽  
Author(s):  
Lifeng Wang ◽  
Wanlin Guo ◽  
Haiyan Hu
Keyword(s):  
Carbon Nanotubes ◽  
Cylindrical Shell ◽  
Dispersion Relation ◽  
Phase Velocity ◽  
Group Velocity ◽  
Continuum Mechanics ◽  
Flexural Wave ◽  
Multi Walled Carbon Nanotubes ◽  
Non Local ◽  
Walled Carbon Nanotubes

The group velocities of longitudinal and flexural wave propagations in single- and multi-walled carbon nanotubes are studied in the frame of continuum mechanics. The dispersion relations between the group velocity and the wavenumber for flexural and longitudinal waves, described by a beam model and a cylindrical shell model, are established for both single- and multi-walled carbon nanotubes. The effect of microstructures in carbon nanotubes on the wave dispersion is revealed through the non-local elastic models of a beam and a cylindrical shell, including the second-order gradient of strain and a parameter of microstructure. It is shown that the microstructures in the carbon nanotubes play an important role in the dispersion of both longitudinal and flexural waves. In addition, the non-local elastic models predict that the cut-off wavenumber of the dispersion relation between the group velocity and the wavenumber is approximately 2×10 10  m −1 for the longitudinal and flexural wave propagations in both single- and multi-walled carbon nanotubes. This may explain why the direct molecular dynamics simulation cannot give a proper dispersion relation between the phase velocity and the wavenumber when the wavenumber approaches approximately 2×10 10  m −1 , much lower than the cut-off wavenumber for the dispersion relation between the phase velocity and the wavenumber predicted by continuum mechanics.

A morphing strategy to couple non-local to local continuum mechanics

2012 ◽  
Vol 60 (6) ◽  
pp. 1088-1102 ◽  
Author(s):  
Gilles Lubineau ◽  
Yan Azdoud ◽  
Fei Han ◽  
Christian Rey ◽  
Abe Askari
Keyword(s):  
Continuum Mechanics ◽  
Non Local
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