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Fractional Vector Calculus and Fractional Continuum Mechanics |
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PP: 85-104 |
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doi:10.18576/pfda/020202
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Author(s) |
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Konstantinos A. Lazopoulos,
Anastasios A. Lazopoulos,
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Abstract |
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| Since modern continuum mechanics is mainly characterized by the strong influence of microstructure, Fractional Continuum
Mechanics has been a promising research field, satisfying both experimental and theoretical demands. The geometry of the fractional
differential is corrected and the geometry of the tangent spaces of a manifold is clarified providing the bases of the missing Fractional
Differential Geometry. The Fractional Vector Calculus is revisited along with the basic field theorems of Green, Stokes and Gauss. New
concepts of the differential forms, such as fractional gradient, divergence and rotation are introduced. Application of the Fractional
Vector Calculus to Continuum Mechanics is presented. The Fractional right and left Cauchy-Green deformation tensors and Green
(Lagrange) and Euler-Almanssi strain tensors are exhibited. The change of volume and the surface due to deformation (configuration
change) of a deformable body are also discussed. Fractional stress tensors are also introduced. Further the Fractional Continuum
Mechanics principles yielding the fractional continuity and motion equations are also derived. |
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