II II II II II I - Waste Isolation Pilot Plant - U.S. Department of Energy

~=$s:s . (4.6.9)
J
The yield condition is checked to determine whether ~ < Oyd. If this is the case, the trial stress is the correct
deviatoric stress at the end of the time step, Sn+ 1 = S‘r. If yield is exceeded, a simple radial return is performed to
calculate the deviatoric stress at the end of the time step
(4.6.10)
Finally, the total stress is determined by
CT”+l =s ‘+1+pn+’ 5 .
(4.6.11)
The Soils and Crushable
Foams model uses four internal state variables:
EVMAX - maximum compressive volumetric strain experienced (always positive),
EVFRAC - current value of volumetric fracture strain (positive in compression),
EV - current value of volumetric strain (positive in compression),
NUM - integer pointing to the last increment in the pressure function where the interpolate was
found.
The PROP array contains the following entries for this material:
PROP(1)
PROP(2)
PROP(3)
PROP(4)
PROP(5)
PROP(6)
- 2p
- Bulk Modulus, K
-W
- al
- a2
- Function ID number.
4.7 Low Density Foams
The low density foams model presented here was developed by Neilsen, Morgan, and Krieg (1987) and is based
on results from experimental tests on low density, closed-cell polyurethane foams. These foams having densities
ranging from 2 to 10 pounds per cubic foot have been proposed for use as energy absorbers in nuclear waste
shipping containers. Representative responses of closed-cell polyurethane foams for various hydrostatic, uniaxial,
and triaxial laboratory test conditions are shown in Figures 4.7.1 and 4.7.2. These results indicate that the ‘
volumetric response of the foam is highly dependent on load history. This implies that typical decompositions of
total foam response into an independent volumetric part and a mean stress (pressure) dependent deviatoric part are
not valid for this class of foam. Many “soil and crushable foam” models, including the other foam model described
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