A fractional calculus approach to the description of stress and strain localization in fractal media

DOI10.1016/S0960-0779(00)00238-1zbMath1030.74045OpenAlexW2083085165MaRDI QIDQ5951024

Publication date: 2 January 2002

Published in: Chaos, Solitons and Fractals (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0960-0779(00)00238-1

zbMATH Keywords

heterogeneous materials static-kinematic duality virtual work principle fractal dimensions local fractional calculus operators

Mathematics Subject Classification ID

Fracture and damage (74R99) Fractional derivatives and integrals (26A33) Fractals (28A80)

Related Items

Fractional derivatives and strain gradient elasticity ⋮ Calculation of the tensile and flexural strength of disordered materials using fractional calculus ⋮ Long-range cohesive interactions of non-local continuum faced by fractional calculus ⋮ The stiffness of self-similar fractals ⋮ Self-similarity in concrete fracture: size-scale effects and transition between different collapse mechanisms ⋮ Anisotropic fractal media by vector calculus in non-integer dimensional space ⋮ Flow of fractal fluid in pipes: non-integer dimensional space approach ⋮ FRACTIONAL RANDOM FIELDS ON DOMAINS WITH FRACTAL BOUNDARY ⋮ Analytical solutions for heat transfer on fractal and pre-fractal domains ⋮ Exact local fractional differential equations ⋮ Fractal and multifractal approaches for the analysis of crack-size dependent scaling laws in fatigue ⋮ Feedback control in fractal mechanics ⋮ Fractal analysis of damage detected in concrete structural elements under loading ⋮ Nonlinear dynamics of a novel fractional-order Francis hydro-turbine governing system with time delay ⋮ A fractional model of continuum mechanics ⋮ Local fractional Fourier series with application to wave equation in fractal vibrating string ⋮ Yang-Fourier transforms of Lipschitz local fractional continuous functions ⋮ Laminar flow through fractal porous materials: the fractional-order transport equation ⋮ Generalized theory of diffusive stresses associated with the time-fractional diffusion equation and nonlocal constitutive equations for the stress tensor ⋮ Local fractional variational iteration and decomposition methods for wave equation on Cantor sets within local fractional operators ⋮ Some further generalizations of Hölder's inequality and related results on fractal space ⋮ Advanced analysis of local fractional calculus applied to the Rice theory in fractal fracture mechanics ⋮ Fundamental solutions to three-dimensional diffusion-wave equation and associated diffusive stresses ⋮ Mathematical aspects of the Heisenberg uncertainty principle within local fractional Fourier analysis ⋮ A generalized Tu formula and Hamiltonian structures of fractional AKNS hierarchy ⋮ Analytical solutions for vibrating fractal composite rods and beams ⋮ Discrete self-similarity of multiscale materials and systems. Universality of scaling exponents ⋮ Nonlocal elasticity: an approach based on fractional calculus ⋮ Local fractional series expansion method for solving wave and diffusion equations on Cantor sets ⋮ Intermediate processes and critical phenomena: theory, method and progress of fractional operators and their applications to modern mechanics ⋮ Fractal mechanics ⋮ Free vibration analysis of a von Koch beam ⋮ Criteria of asymptotic \(\omega\)-periodicity and their applications in a class of fractional differential equations ⋮ Scaling of Effective Moduli of Generalised Continua ⋮ Multi-term time fractional diffusion equations and novel parameter estimation techniques for chloride ions sub-diffusion in reinforced concrete ⋮ Application of the Local Fractional Fourier Series to Fractal Signals ⋮ A GENERALIZED METHOD AND ITS APPLICATIONS TO n-DIMENSIONAL FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS IN FRACTAL DOMAIN

Cites Work