On fractional and fractal formulations of gradient linear and nonlinear elasticity
From MaRDI portal
Publication:2285567
DOI10.1007/s00707-019-2373-xzbMath1428.74039arXiv1808.04452OpenAlexW2885411887WikidataQ128388099 ScholiaQ128388099MaRDI QIDQ2285567
Elias C. Aifantis, Vasily E. Tarasov
Publication date: 8 January 2020
Published in: Acta Mechanica (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1808.04452
Classical linear elasticity (74B05) Nonlinear elasticity (74B20) Fractional derivatives and integrals (26A33)
Related Items
Ulam stabilities of nonlinear coupled system of fractional differential equations including generalized Caputo fractional derivative, On inverse problems arising in fractional elasticity, Gradient extension of classical material models: from nuclear \& condensed matter scales to Earth \& cosmological scales, Fractional single-phase lag heat conduction and transient thermal fracture in cracked viscoelastic materials, Numerical investigation of the nonlinear modified anomalous diffusion process, Modelling flexural wave propagation by the nonlocal strain gradient elasticity with fractional derivatives
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Lattice fractional calculus
- Flow of fractal fluid in pipes: non-integer dimensional space approach
- Ten equivalent definitions of the fractional Laplace operator
- On scale invariance in anisotropic plasticity, gradient plasticity and gradient elasticity
- Barenblatt profiles for a nonlocal porous medium equation
- Variational principle of stationary action for fractional nonlocal media and fields
- Generalized Taylor's formula
- Non-standard extensions of gradient elasticity: fractional non-locality, memory and fractality
- Fractional vector calculus and fractional Maxwell's equations
- On turbulence in fractal porous media
- Fractional dynamics. Applications of fractional calculus to dynamics of particles, fields and media
- On the role of gradients in the localization of deformation and fracture
- Fractals and fractional calculus in continuum mechanics
- On a Riemann-Liouville generalized Taylor's formula
- A simple approach to solve boundary-value problems in gradient elasticity
- The physics of plastic deformation
- Detailed error analysis for a fractional Adams method
- Acoustic waves in fractal media: non-integer dimensional spaces approach
- Exact discretization by Fourier transforms
- Fractional thermoelasticity
- A class of linear viscoelastic models based on Bessel functions
- Exact discretization of fractional Laplacian
- On the propagation of transient waves in a viscoelastic Bessel medium
- Partial fractional derivatives of Riesz type and nonlinear fractional differential equations
- Towards thermomechanics of fractal media
- Continuous medium model for fractal media
- Fractional generalization of the Ginzburg-Landau equation: an unconventional approach to critical phenomena in complex media
- Fractional hydrodynamic equations for fractal media
- Vector calculus in non-integer dimensional space and its applications to fractal media
- Elasticity theory of materials with long range cohesive forces
- Linear theory of nonlocal elasticity and dispersion of plane waves
- Micro-structure in linear elasticity
- United lattice fractional integro-differentiation
- REVIEW OF SOME PROMISING FRACTIONAL PHYSICAL MODELS
- Toward lattice fractional vector calculus
- Nonlocal Continuum Field Theories
- Equations of motion in a non-integer-dimensional space
- Anisotropic fractal media by vector calculus in non-integer dimensional space
- Fractal solids, product measures and fractional wave equations
- Axiomatic basis for spaces with noninteger dimension
- Fractional Kinetics in Solids
- An Extension Problem Related to the Fractional Laplacian
- Psi-series solution of fractional Ginzburg–Landau equation
- Renormalization
- DYNAMICS OF FRACTAL SOLIDS
- Fractional Calculus with Applications in Mechanics
- Riemann's Form of Taylor's Series
- The numerical solution of fractional differential equations: speed versus accuracy
