Polynomial EOS

This is a general form of the Mie-Gruneisen form of the equation of state and it has different analytic forms for states of compression and tension.

This equation of state defines the pressure as

µ> 0 (compression):

µ< 0 (tension)

where

µ = compression = ρ/ρ0-1
ρ0 = solid, zero pressure density
e = internal energy per unit mass
A1, A2, A3, B0,, B1, T1 and T2 are material constants

If T1 is input as 0.0 it is reset to T1 = A1 in the solver.

The validity of this equation depends upon the ability to represent the variation of pressure at e = 0 (or some other reference curve) as a simple polynomial in µ of no more than three terms. This is probably true as long as the range in density variation (and hence range in µ) is not too large.

The Polynomial equation of state defines the Gruneisen parameter as

This allows a number of useful variants of the Gruneisen parameter to be described:


Note:  This equation of state can only be used with solid elements.

The Poisson's ratio is assumed to be zero when calculating effective strain.

A specific heat capacity should be defined with this property to allow the calculation of temperature.


Table 125:  Input Data

NameSymbolUnitsNotes
Parameter A1A1StressOften equivalent to the material bulk modulus
Parameter A2A2Stress 
Parameter A3A3Stress 
Parameter B0B0None 
Parameter B1B1None 
Parameter T1T1StressThis value will be automatically set to the material bulk modulus if entered as zero.
Parameter T2T2Stress 

Custom results variables available for this model:

NameDescriptionSolidsShellsBeams
PRESSUREPressureYesNoNo
DENSITYDensityYesNoNo
COMPRESSIONCompressionYesNoNo
VISC_PRESSUREViscous PressureYesNoNo
INT_ENERGYInternal EnergyYesNoNo
TEMPERATURETemperatureYesNoNo

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