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RESEARCH PRODUCT

The Multiscale Stochastic Model of Fractional Hereditary Materials (FHM)

Mario Di PaolaMassimiliano Zingales

subject

Multiscale FractanceRandom modelsStochastic modellingMathematical analysisModel parametersGeneral MedicineFractional HereditarinessDashpotFractional calculusMassless particleFractional DerivativesFractional Derivatives; Fractional Hereditariness; Multiscale Fractance; Random modelsFractional HereditarineCalculusExponentNewtonian fluidLinear independenceFractional DerivativeMathematics

description

Abstract In a recent paper the authors proposed a mechanical model corresponding, exactly, to fractional hereditary materials (FHM). Fractional derivation index 13 E [0,1/2] corresponds to a mechanical model composed by a column of massless newtonian fluid resting on a bed of independent linear springs. Fractional derivation index 13 E [1/2, 1], corresponds, instead, to a mechanical model constituted by massless, shear-type elastic column resting on a bed of linear independent dashpots. The real-order of derivation is related to the exponent of the power-law decay of mechanical characteristics. In this paper the authors aim to introduce a multiscale fractance description of FHM in presence of stochastic fluctuations of model parameters. In this setting the random multiscale fractance may be used to capture the fluctuations of material parameters observed in experimental tests by means of proper analytical evaluation of the model statistics.

yearjournalcountryeditionlanguage
2013-01-01Procedia IUTAM
https://doi.org/10.1016/j.piutam.2013.01.006