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

By Alberto Carpinteri, Pietro Cornetti. 2002

169 citations recorded by the source corpus.

Subfields: Condensed Matter Physics, Fluid Flow and Transfer Processes, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/e800c45595de373a1c1280d5f26b842815f55fca

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In Condensed Matter Physics

In Fluid Flow and Transfer Processes

In Modeling and Simulation

Citations in the corpus

From criticality to final collapse: Evolution of the ''b-value" from 1.5 to 1.0 (2009, background): “Among the results obtained by the senior author, we could cite the modelling of the size-scale effects on strength, toughness [5,6,11,12] and critical strain [13] of heterogeneous materials and the optimization of the mechanical properties of advanced materials [14].”
Long-range cohesive interactions of non-local continuum faced by fractional calculus (2008, background): “…decade, to several fields of applied mechanics such as the description of damage and fatigue in heterogeneous media (Carpinteri et al., 2001, 2004; Carpinteri and Cornetti, 2002), the representation of viscous forces (Narahari Achar et al., 2004) and in stochastic dynamics setting (Cottone and Di…”
Advanced Local Fractional Calculus and Its Applications (2012, unknown): “[50] A.”
A Fractional Model of Continuum Mechanics (2012, background): “Thus the generalization of the geometric interpretation of derivatives in terms of tangents given in [ 9 ] remains valid: all the curves with the same order α form an equivalence class denoted by x α .”
Generalizations of Hölder’s and Some Related Integral Inequalities on Fractal Space (2011, background): “Fractal calculus (also called local fractional calculus) has played an important role in not only mathematics but also in physics and engineers [2-15].”
Fractional order constitutive model of geomaterials under the condition of triaxial test (2013, methodology): “To date, it has already been successfully applied to viscoelastic mechanics [3], electromagnetics [4], signal processing [5], chaos systems [6], and other areas [7].”