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TakingtheLaplacetransformationofthegoverningequationsofthis model
[11],thefinalformoftheconstitutivemodelcanbepresentedas:
+
ʻ
E
˙
+
ʻ
+
ʻ
1
E
1
+
ʻʻ
1
+
ʻʻ
1
˃
˃
EE
1
¨
˃
=
ʻ
ʵ
˙
E
1
¨
ʵ,
(1)
where:
-strain.
Basing on the experimental data presented in [3] or [12] we can introduce
an empirical relationship between Young modulus (
E
-Youngmodulus,
ʻ,ʻ
1
,E
1
-materialparameters,
˃
-stress,
E
) values of investigated
specimensandinternalunderpressure-p.
10
6
E
(
p
)=2
.
7
∗
exp
(2
.
65
p
)
(2)
)is
nonlinear (Fig. 5). For the calibration process, in the first step the discrete
experimentaldatahastobeinterpolatedbyasuitablemathematicalfunction.
Forthispurposethe
Interpolate
functioninthe
Mathematica
environmenthas
beenused.
For the considered case the experimentally applied loading function
ʵ
(
t
Fig. 5.
Interpolationofthe
ʵ
(
t
)function;blue-experimentaldata,red-interpolation
function(superposed)
),
NDSolvefunctionhasbeenchosen.ToidentifytheparametersoftheGubanov
model(1),i.e.tocalibrateittotherealresponseoftheVPPstheoptimization
proceduresbasedonEvolutionaryAlgorithms(EA)canbeapplied.Inthiswork
aspecificversionofEA-GeneticAlgorithm(GA)wasused.
To solve Eq. (1) assuming a nonlinear character of the strain function
ʵ
(
t
4 Genetic Algorithms
Inthepaper,theidentificationofmaterialparametersisformulatedastheop-
timizationproblemandsolvedbymeansoftheGA.Geneticalgorithmsarenon
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