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loading [20]. Displacement, force, and time values are recorded during tests.
The obtained experimental curves are used to determine the values of mate-
rialparameterssothatthetheoreticaldescriptioncorrespondstoexperiments.
The elastic parameters are usually identified before by standard experimental
procedures.
In order to estimate the inelastic parameters analytically, it is necessary to
reduce the constitutive equations to the uniaxial form. Since these nonlinear
equationscontainalotofparameters,allambiguityinidentificationresultmust
beremovedbyarobustidentificationscheme.Consideredinthispaperanalyt-
ical methodology of parametersidentification is presented in details in [13]. A
simplifiedschematicalgorithmispresentedinthissection.
Theexpressionfortheinelasticstrainrateisgivenasfollows:
√
3
D
0
exp
R
2
n
I
=
2
1
2
+
D
n
+1
n
sgn
(
ʵ
˙
−
˃
)
(1)
˃
Here,theisotropichardening
R
isdefinedbythefollowingdifferentialequation
(withtheinitialvalue
R
0
)
˙
)
˙
I
R
=
m
1
(
R
1
−
R
W
R
(0)=
R
0
(2)
The kinematic hardening
D
is given by the set of equations with initial
condition:
=
2
D
3
X
sgn
(
˃
,
)
(3)
3
2
D
1
sgn
(
˙
˙
I
X
=
m
2
˃
)
−
X
W
X
(0)=0
,
(4)
˙
I
=
I
W
˃
ʵ
˙
(5)
Inthisformbothhardeningfunctionscanbeexplicitlyintegrated:
R
1
1
I
)
+
I
)
R
=
−
exp(
−
m
1
W
R
0
exp(
−
m
1
W
,
(6)
D
1
1
I
)
.
D
=
−
exp(
−
m
2
W
(7)
=
3
)
1
I
)
,
2
D
1
sgn
(
X
˃
−
exp(
−
m
2
W
(8)
I
=
I
W
˃
ʵ
˙
.
(9)
In the Bodner-Partom formulation, the elastic limit does not appear. The
inelastic effects are incorporated already from the beginning of the deforma-
tionprocess,butuntiltheconventionalelasticlimittheirinfluenceaccordingto
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