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Finite Element Techniques for Rolling Rubber Wheels 133
Fig. 4 Cyclic tensile test: comparison between experimental and computational
results from the pseudo-elastic damage model.
In [27] the first derivative of the damage function
−φ ′ (α ps
D )=m erf−1 [r(α ps
D − 1)] + Wm, (25)
with a set of positive constitutive parameters r and m is proposed, where
erf −1 (•) is the inverse of the error function. Substituting (25) in (21), the
damage variable can be finally expressed by
α ps
D
1
=1−
r erf
�
1
m [Wm − W ◦ ( ¯ �
C)]
, (26)
which vanishes for virgin loading. The deviatoric part of the second Piola–
Kirchhoff stress tensor
¯S(t) =α ps
D ¯S ◦ (t) − J −2/3 DEV [αV (t)] (27)
is obtained from the first derivative of (19) with respect to C.
A comparison between experimental data and computational results is
depicted in Figure 4. In the experiment a rubber specimen is subjected to
the uniaxial tension test under 10mm/min deformation rate and stretched
in steps to 10, 20, 30, ..., 90, 100 and 120% strain. At each strain level five
load cycles are performed until a stationary response is obtained. For the
simulation similar loading conditions are applied to a single brick element.
The computed material response is plotted as dotted lines. A quite good
agreement between the experiment and simulation is obtained.
It should be noted that the pseudo-elastic model significantly simplifies
the identification of constitutive parameters. Since damage is only activated
during unloading and reloading, one can identify the viscoelastic parameters,