When the foam is compressed very slowly, it acts as a spring
whose resistance pushes back, called stiffness, but the
stiffness is not linearly related to the amount of deflection. In
fact, it softens or experiences less resistance to compression
as the deflection increases.
This behavior manifest itself dynamically in the response,
being nominally below the linear natural frequency and
having two amplitudes of vibration that exist depending
on the initial position and velocity of the mass. Figure 5
illustrates the model's prediction of this behavior for an Arcel
®
sample at three different input acceleration levels.
Impact Response
The complex constitutive behavior of the foam is also
responsible for its impact response. Typically, the impact
response of expanded polymer foam is studied experimentally
using cushion curves through the ASTM procedure, ASTM
D1596 – "Dynamic Shock Cushioning Characteristics
of Packaging Material". Experimentally determining
cushion curves take countless hours; however, understanding
the material behavior of the foam allows us to develop
mathematical models able to predict cushion curves in
minutes.
Comparing numerical predictions with experimental results
reveals an acceptable variation between the predicted and
experimental response per the expected lab-to-lab variability
of 18% documented in ASTM D1596 for all but one point
at a static stress of 0.57 kPa (Fig. 6). Furthermore, the
model illustrates the link between stress-strain behavior and
the predicted shock pulse and resulting cushion curve as
illustrated in Figure 7.
Figure 5: Frequency response of the nonlinear system at various input acceleration levels.
0 1 2 3 4 5
0
20
40
60
80
100
120
140
Static Stress (kPa)
Peak
Deaccleration
(G's)
Simulation
Experimental Impact
+18%
-18%
Figure 6: Experimental validation of the impact model simulation.
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