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/ρ_{0}-1 |

ρ_{0} = solid, zero pressure density |

e = internal energy per unit mass |

_{A1}, _{A2}, _{A3}, _{B0,}, _{B1}, _{T1} and _{T2} are
material constants |

If T_{1} is input as 0.0 it is reset to
T_{1} = A_{1} 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**

Name | Symbol | Units | Notes |
---|---|---|---|

Parameter A1 | A_{1} | Stress | Often equivalent to the material bulk modulus |

Parameter A2 | A_{2} | Stress | |

Parameter A3 | A_{3} | Stress | |

Parameter B0 | B_{0} | None | |

Parameter B1 | B_{1} | None | |

Parameter T1 | T_{1} | Stress | This value will be automatically set to the material bulk modulus if entered as zero. |

Parameter T2 | T_{2} | 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 |