Fractional viscoelastic beam under torsion

Abstract This paper introduces a study on twisted viscoelastic beams, having considered fractional calculus to capture the viscoelastic behaviour. Further another novelty of this paper is extending a recent numerical approach, labelled line elementless method (LEM), to viscoelastic beams. The latter does not require any discretization neither in the domain nor in the boundary. Some numerical applications have been reported to demonstrate the efficiency and accuracy of the method.

Statistical Methods for Parameter Identification of Temperature Dependent Viscoelastic Models

Fractional characteristic times and dissipated energy in fractional linear viscoelasticity

Abstract In fractional viscoelasticity the stress–strain relation is a differential equation with non-integer operators (derivative or integral). Such constitutive law is able to describe the mechanical behavior of several materials, but when fractional operators appear, the elastic and the viscous contribution are inseparable and the characteristic times (relaxation and retardation time) cannot be defined. This paper aims to provide an approach to separate the elastic and the viscous phase in the fractional stress–strain relation with the aid of an equivalent classical model (Kelvin–Voigt or Maxwell). For such equivalent model the parameters are selected by an optimization procedure. Once …

Step-by-step integration for fractional operators

Abstract In this paper, an approach based on the definition of the Riemann–Liouville fractional operators is proposed in order to provide a different discretisation technique as alternative to the Grunwald–Letnikov operators. The proposed Riemann–Liouville discretisation consists of performing step-by-step integration based upon the discretisation of the function f(t). It has been shown that, as f(t) is discretised as stepwise or piecewise function, the Riemann–Liouville fractional integral and derivative are governing by operators very similar to the Grunwald–Letnikov operators. In order to show the accuracy and capabilities of the proposed Riemann–Liouville discretisation technique and th…

Analysis of Fractional Viscoelastic Material With Mechanical Parameters Dependent on Random Temperature

It is well known that mechanical parameters of polymeric materials, e.g., epoxy resin, are strongly influenced by the temperature. On the other hand, in many applications, the temperature is not known exactly during the design process and this introduces uncertainties in the prevision of the behavior also when the stresses are deterministic. For this reason, in this paper, the mechanical behavior of an epoxy resin is characterized by means of a fractional viscoelastic model at different temperatures; then, a simple method to characterize the response of the fractional viscoelastic material at different temperatures modeled as a random variable with assigned probability density function (PDF…

Analytical approach for the mix design optimisation of bituminous mixtures with crumb rubber

The present paper provides a basis for defining a mix design method specifically tailored to rubberised asphalt that takes into account the behaviour of crumb rubber. An analytical approach to quantifying the recovered deformation of crumb rubber in the post-compaction phase has been developed in order to adjust the number of gyrations proposed by the Superpave method for compacting specimens of hot mix asphalt using a Superpave gyratory compactor. The maximum allowable amount of rubber has been calculated. Finally, a step-by-step protocol has been proposed in order to fabricate and compact crumb rubber modified mixtures with the gyratory compactor.

Evaluation of the temperature effect on the fractional linear viscoelastic model for an epoxy resin

The paper deals with the evolution of the parameters of a fractional model for different values of temperature. An experimental campaign has been performed on epoxy resin at different levels of temperature. It is shown that epoxy resin is very sensitive to the temperature.

Markovian approximation of linear systems with fractional viscoelastic term

It is well known that the response of a linear system enforced by a Gaussian white noise is Markovian. The order of Markovianity is n-1 being n the maximum order of the derivative of the equation ruling the evolution of the system. However when a fractional operator appears, the order of Markovianity of the system becomes infinite. Then the main aim developed in the proposed paper, consists of rewriting the system with fractional term of order r with an "equivalent" one, in which the fractional operator is substituted by two classical differential terms with integer order of derivative int(r) and int(r + 1) (for a real r). In this way the fractional differential equation reverts into a clas…

Fractional viscoelastic behaviour under stochastic temperature process

Abstract This paper deals with the mechanical behaviour of a linear viscoelastic material modelled by a fractional Maxwell model and subject to a Gaussian stochastic temperature process. Two methods are introduced to evaluate the response in terms of strain of a material under a deterministic stress and subjected to a varying temperature. In the first approach the response is determined making the material parameters change at each time step, due to the temperature variation. The second method, takes advantage of the Time–Temperature Superposition Principle to lighten the calculations. In this regard, a stochastic characterisation for the Time–Temperature Superposition Principle method is p…