Laminar flow through fractal porous materials: the fractional-order transport equation

Abstract The anomalous transport of a viscous fluid across a porous media with power-law scaling of the geometrical features of the pores is dealt with in the paper. It has been shown that, assuming a linear force–flux relation for the motion in a porous solid, then a generalized version of the Hagen–Poiseuille equation has been obtained with the aid of Riemann–Liouville fractional derivative. The order of the derivative is related to the scaling property of the considered media yielding an appropriate mechanical picture for the use of generalized fractional-order relations, as recently used in scientific literature.

FRACTIONAL-ORDER GENERALIZATION OF TRANSPORT EQUATIONS IN FRACTAL POROUS MEDIA

A fractional-order model of ultra-high molecular weight polyethylene for biomedical implantation

A new design approach to the use of composite materials for heavy transport vehicles

In order to keep or to reach a high level of competitiveness and performance of a product, it is necessary to explore all the possible solutions that allow the best compromise between costs and project requirements. By this point of view the study of alternative designs and/or materials to use, is an important aspect that can identify a new concept or way of thinking about a product. This paper presents how to make use of composite materials in the field of heavy vehicles transportation. A new semitrailer in composite material has been designed, using a methodical redesign approach and an optimisation process. The main innovation in this project is, besides the use of the Glass Fibre Reinfo…

A physical description of fractional-order Fourier diffusion

In this paper the authors introduce a physical picture of anomalous heat transfer in rigid conductor. The analysis shows that a fractional-order Fourier transport is obtained by the analysis of the heat transport in a functionally graded conductor. The order of the fractional-type operator obtained is related to the grading of the physical properties of the conductor.

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

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…

A fractional order theory of poroelasticity

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, …

Fractional-order theory of thermoelasticicty. I: Generalization of the Fourier equation

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…

Multi-objective optimization of nitinol stent design.

Nitinol stents continuously experience loadings due to pulsatile pressure, thus a given stent design should possess an adequate fatigue strength and, at the same time, it should guarantee a sufficient vessel scaffolding. The present study proposes an optimization framework aiming at increasing the fatigue life reducing the maximum strut strain along the structure through a local modification of the strut profile.The adopted computational framework relies on nonlinear structural finite element analysis combined with a Multi Objective Genetic Algorithm, based on Kriging response surfaces. In particular, such an approach is used to investigate the design optimization of planar stent cell.The r…