A fractional model of continuum mechanics

DOI10.1007/s10659-011-9346-1zbMath1451.74219OpenAlexW2039517642MaRDI QIDQ1937177

Corina S. Drapaca, Siv Sivaloganathan

Publication date: 11 February 2013

Published in: Journal of Elasticity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10659-011-9346-1

zbMATH Keywords

continuum mechanicsfractional calculusdeformable media

Mathematics Subject Classification ID

Fractional derivatives and integrals (26A33) Applications of fractional calculus in solid mechanics (74S40)

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Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Elastic media with microstructure. I: One-dimensional models. (Transl. from the Russian)
• Probability calculus of fractional order and fractional Taylor's series application to Fokker-Planck equation and information of non-random functions
• Deformation of a peridynamic bar
• Long-range cohesive interactions of non-local continuum faced by fractional calculus
• A theoretical study of the effect of intraventricular pulsations on the pathogenesis of hydroce\-phalus
• Mechanically-based approach to non-local elasticity: variational principles
• Non-local continuum mechanics and fractional calculus
• The fractional calculus. Theory and applications of differentiation and integration to arbitrary order
• Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
• Reformulation of elasticity theory for discontinuities and long-range forces
• Fractional partial differential equations and modified Riemann-Liouville derivative new methods for solution
• On nonlocal elasticity
• Operators and Fractional Derivatives for Viscoelastic Constitutive Equations
• Fractional mechanical model for the dynamics of non-local continuum
• Convergence, adaptive refinement, and scaling in 1D peridynamics
• Static-kinematic fractional operators for fractal and non-local solids
• Fractional calculus - A different approach to the analysis of viscoelastically damped structures
• A Theoretical Basis for the Application of Fractional Calculus to Viscoelasticity
• Construction of a nonisothermal model of electrohydrodynamics with a nonsymmetric stress tensor
• Fractional differentiability of nowhere differentiable functions and dimensions
• On the Fractional Calculus Model of Viscoelastic Behavior
• Advances in Fractional Calculus
• Fluid Mechanical Aspects of Antisymmetric Stress
• A fractional calculus approach to the description of stress and strain localization in fractal media
• Static-kinematic duality and the principle of virtual work in the mechanics of fractal media

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