When modeling with continuum elements, certain material models will require that an equation-of-state (EOS) be defined. This is done using the keyword *EOS_option and the variable EOSID in *PART.
For details on when an EOS is required, see the MATERIAL MODEL REFERENCE TABLES in the beginning of the *MAT section of the User's Manual. In that table, there's a column labeled EOS. If a "Y" appears in that column, then the corresponding material model requires an equation-of-state when used with solid elements, shell formulations 13/14/15, or tshell formulations 3/5/7.
For more information on equations-of-state, see
the *EOS section of the User's Manual,
http://www.dynasupport.com/howtos/general/equation-of-state, and
p. 10.6 in Du Bois's crash notesi (no longer available).
In some situations, an EOS is required in order to accurately simulate material
behavior. An EOS determines the hydrostatic, or bulk, behavior of the material
by calculating pressure as a function of density and perhaps, energy and/or
temperature. Situations that call for an EOS are characterized by very high
strain rates, material pressures far in excess of yield stress, and propagation
of shock waves. Of course, these phenomena are very much interrelated.
EOS_LINEAR_POLYNOMIAL or EOS_GRUNEISEN are probably the most commonly used
EOS forms for non-gaseous materials. Gruneisen parameters are available for many
materials including metals.
Total stress is the sum of deviatoric stress and pressure.
The mean stress (sig1 + sig2 + sig3)/3 is equal to the pressure.
Constitutive models which do NOT employ an EOS calculate total stress directly.
In these models, the pressure component of total stress is based only on
volumetric strain. For instance, for an elastic material, p = K * mu where K is
the bulk modulus and mu = rho/rho0 - 1.
Material models that require an accompanying EOS calculate only the
deviatoric component of stress, i.e. the strength behavior, whereas the
EOS calculates the pressure component of total stress, i.e., the
hydrostatic behavior.
If you're using a material model where an EOS is required, you can achieve
simple bulk behavior by using *eos_linear_polynomial and setting C1 to the
bulk modulus = E/(3 * (1-2*PR))
and all the other C terms to zero. I would only recommend this approach
if strain rates are low to moderate.
Strain rates in an auto crash would qualify as moderate.
The user has the option of providing a user-defined subroutine
to describe an equation-of-state. A template of such user-defined subroutines
is included in the file dyn21b.f. See Appendix B in the Users Manual and
the command *EOS_USER_DEFINED.
The book "High Velocity Impact Dynamics",
edited by Zukas (1990, John Wiley and Sons) is a good
reference on the subject of material behavior at high strain rates.
EOS parameters for approximately 50 materials are given in
"Equation of State and Strength Properties
of Selected Materials", Daniel J. Steinberg, Lawrence Livermore National Laboratory,
1991 (Change 1 issued 1996), UCRL-MA-106439.
LLNL prohibits this work from being posted electronically, but in an email to jpd
from Stephanie Black, LLNL, 8/31/2011, 8:14 am, it can be shared with
customers in "hard copy only".
Regarding EOS_TABULATED_COMPACTION and EOS_TABULATED:
The manual isn't very specific. The notes I have indicate the following:
- The eVi terms (abscissa of the curve) represent ln(relative volume) and
thus are negative in compression.
- eVi = ln(relative volume) values should be given in descending order, that is,
tensile (positive) value first and largest compression (most negative) value last.
- Pressure is positive in compression. If gamma = 0, Ci is equal to pressure on the
loading curve. Thus Ci should have an algebraic sign opposite of eVi.
When there's an EOS, the initial stress values given in *initial_stress are adjusted
so that the mean stress (pressure) is in agreement with the EOS. In other words,
-(SIGXX + SIGYY + SIGZZ)/3 - stress adjustment = initial pressure from EOS
or
stress adjustment = -(SIGXX + SIGYY + SIGZZ)/3 - initial pressure from EOS
actual initial sigxx = SIGXX + stress adjustment
actual initial sigyy = SIGYY + stress adjustment
actual initial sigzz = SIGZZ + stress adjustment
See http://ftp.lstc.com/anonymous/outgoing/support/FAQ_kw/mat16.initstress.k
______________________________________________________________________
The following comes from James M. Kennedy
KBS2 Inc.
April 23, 2010
An excellent reference book you might consider:
Zukas, J.A., "Intoduction to Hydrocodes", Studies in Applied Mechanics,
Vol. 49, Elsevier, 2004.
http://www.elsevier.com/wps/find/bookdescription.authors/701885/description#description
Perhaps the following report and paper may have some information you
desire:
Davydov, B.I., "Equation of State for Solid Bodies", Report AD0600614,
Foreign Techology Division Air Force Systems Command Wright-Patterson
AFB Ohio, March, 1964.
http://oai.dtic.mil/oai/oai?verb=getRecord&metadataPrefix=html&identifier=AD0600614
http://www.ntis.gov/search/product.aspx?ABBR=AD600614
Men''shikov, G.P., "An Equation of State for Solids at High Pressure",
Combustion, Explosion, and Shock Waves, Vol. 17, No. 2, pp. 215-222,
March, 1981.
http://www.springerlink.com/content/xn701j6277t72h30/
A review article on Gruneisen equation of state
Mendoza, E., "The Equation of State for Solids 1843-1926", European
Journal of Physics, Vol. 3, pp. 181-187, 1982.
http://www.iop.org/EJ/abstract/0143-0807/3/3/010
An abstract that might be helpful:
http://gsa.confex.com/gsa/2003AM/finalprogram/abstract_60195.htm
An introductory note:
http://www.ccl.net/cca/documents/dyoung/topics-orig/eq_state.html