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

[+] Author and Article Information
G. Alotta

Engineering and Architecture Faculty,
University of Enna “Kore,”
Viale delle Olimpiadi,
Enna 94100, Italy
e-mail: gioacchino.alotta@unikore.it

N. Colinas-Armijo

Dipartimento di Ingegneria Civile,
Ambientale e Aerospaziale (DICAM),
Universitá degli Studi di Palermo,
Viale delle Scienze Ed. 8,
Palermo 90128, Italy
e-mail: natalia.colinasarmijo@unipa.it

Manuscript received June 22, 2016; final manuscript received January 4, 2017; published online June 12, 2017. Assoc. Editor: Mario Di Paola.

ASME J. Risk Uncertainty Part B 3(3), 030906 (Jun 12, 2017) (7 pages) Paper No: RISK-16-1096; doi: 10.1115/1.4036704 History: Received June 22, 2016; Revised January 04, 2017

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) subjected to deterministic stresses is presented. It is found that the first- and second-order statistical moments of the response can be easily evaluated only by the knowledge of the PDF of the temperature and the behavior of the parameters with the temperature. Comparison with Monte Carlo simulations is also performed in order to assess the accuracy and the reliability of the method.

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Fig. 1

The springpot model

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Fig. 2

The fractional Maxwell model

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Fig. 3

Stress excitation σ(t) (continuous line—theoretical and dotted line—experimental)

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Fig. 4

Strain response ε(t) (continuous line—theoretical and dotted line—experimental)

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Fig. 5

Coefficient β variation function of T

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Fig. 6

Coefficient Cβ variation function of T

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Fig. 7

Coefficient E0 variation function of T

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Fig. 8

Modeled creep function for the different temperatures under study

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Fig. 9

Mean of the creep test with uniformly distributed temperature

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Fig. 10

Variance of the creep test with uniformly distributed temperature

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Fig. 11

Mean of the creep test with normally distributed temperature

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Fig. 12

Variance of the creep test with normally distributed temperature




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