11.9.5. 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 11.12: Input Data

Name	Symbol	Units	Notes
Parameter A1	A₁	Stress	Often equivalent to the material bulk modulus
Parameter A2	A₂	Stress
Parameter A3	A₃	Stress
Parameter B0	B₀	None
Parameter B1	B₁	None
Parameter T1	T₁	Stress	This value will be automatically set to the material bulk modulus if entered as zero.
Parameter T2	T₂	Stress

Custom results variables available for this model:

Name	Description	Solids	Shells	Beams
PRESSURE	Pressure	Yes	No	No
DENSITY	Density	Yes	No	No
COMPRESSION	Compression	Yes	No	No
VISC_PRESSURE	Viscous Pressure	Yes	No	No
INT_ENERGY	Internal Energy	Yes	No	No
TEMPERATURE	Temperature	Yes	No	No