0000000000873880

AUTHOR

Valentina Piccolo

showing 3 related works from this author

Fractional-Order Theory of Thermoelasticity. II: Quasi-Static Behavior of Bars

2018

This work aims to shed light on the thermally-anomalous coupled behavior of slightly deformable bodies, in which the strain is additively decomposed in an elastic contribution and in a thermal part. The macroscopic heat flux turns out to depend upon the time history of the corresponding temperature gradient, and this is the result of a multiscale rheological model developed in Part I of the present study, thereby resembling a long-tail memory behavior governed by a Caputo's fractional operator. The macroscopic constitutive equation between the heat flux and the time history of the temperature gradient does involve a power law kernel, resulting in the anomaly mentioned previously. The interp…

PhysicsWork (thermodynamics)Order theoryStrain (chemistry)Anomalous heat transferMechanical EngineeringMathematical analysisFractional derivatives02 engineering and technologyFractional derivative01 natural sciencesFractional calculusAnomalous thermoelasticity010101 applied mathematicsMultiscale hierarchical heat conductorsMultiscale hierarchical heat conductor020303 mechanical engineering & transports0203 mechanical engineeringMechanics of MaterialsMechanics of Material0101 mathematicsSettore ICAR/08 - Scienza Delle CostruzioniQuasistatic process
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A fractional order theory of poroelasticity

2019

Abstract We introduce a time memory formalism in the flux-pressure constitutive relation, ruling the fluid diffusion phenomenon occurring in several classes of porous media. The resulting flux-pressure law is adopted into the Biot’s formulation of the poroelasticity problem. The time memory formalism, useful to capture non-Darcy behavior, is modeled by the Caputo’s fractional derivative. We show that the time-evolution of both the degree of settlement and the pressure field is strongly influenced by the order of Caputo’s fractional derivative. Also a numerical experiment aiming at simulating the confined compression test poroelasticity problem of a sand sample is performed. In such a case, …

Constitutive equationPoromechanics02 engineering and technology01 natural sciencesPressure fieldDarcy–Weisbach equationPhysics::Geophysics010305 fluids & plasmas0203 mechanical engineeringFractional operators0103 physical sciencesCaputo's fractional derivative; Fractional operators; PoroelasticityApplied mathematicsGeneral Materials ScienceCaputo's fractional derivative Fractional operators PoroelasticityCaputo's fractional derivativeCivil and Structural EngineeringMathematicsOrder theoryBiot numberMechanical EngineeringPoroelasticityCondensed Matter PhysicsFractional calculus020303 mechanical engineering & transportsMechanics of MaterialsFractional operatorSettore ICAR/08 - Scienza Delle CostruzioniPorous medium
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Fractional-order theory of thermoelasticicty. I: Generalization of the Fourier equation

2018

The paper deals with the generalization of Fourier-type relations in the context of fractional-order calculus. The instantaneous temperature-flux equation of the Fourier-type diffusion is generalized, introducing a self-similar, fractal-type mass clustering at the micro scale. In this setting, the resulting conduction equation at the macro scale yields a Caputo's fractional derivative with order [0,1] of temperature gradient that generalizes the Fourier conduction equation. The order of the fractional-derivative has been related to the fractal assembly of the microstructure and some preliminary observations about the thermodynamical restrictions of the coefficients and the state functions r…

Uses of trigonometryGeneralization01 natural sciences010305 fluids & plasmasScreened Poisson equationsymbols.namesakeFractional operators0103 physical sciencesFractional Fourier equationMechanics of Material010306 general physicsFourier seriesMathematicsFourier transform on finite groupsEntropy functionsHill differential equationPartial differential equationMechanical EngineeringFourier inversion theoremMathematical analysisTemperature evolutionMechanics of MaterialssymbolsFractional operatorSettore ICAR/08 - Scienza Delle CostruzioniEntropy function
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