A general material model requires equations that relate stress to deformation and internal energy (or temperature). In most cases, the stress tensor may be separated into a uniform hydrostatic pressure (all three normal stresses equal) and a stress deviatoric tensor associated with the resistance of the material to shear distortion.

Then the relation between the hydrostatic pressure, the local density (or specific volume) and local specific energy (or temperature) is known as an equation of state.

Hooke's law is the simplest form of an equation of state and is implicitly assumed when you use linear elastic material properties. Hooke's law is energy independent and is only valid if the material being modeled undergoes relatively small changes in volume (less than approximately 2%). One of the alternative equation of state properties should be used if the material is expected to experience high volume changes during an analysis.

Before looking at the various equations of state available, it is good to understand some of the fundamental physics behind their formulations. See the links in the following sections.

One of the simplest forms of equation of state is that for an ideal polytropic gas which may be used in many applications involving the motion of gases. This material property is used by the Explicit Materials library in Engineering Data. See the description in Ideal Gas EOS for additional information.

This property requires that you also define Density and Specific Heat Constant Volume, Cv.

Written as *EOS_IDEAL_GAS and *MAT_NULL.

See the description in Bulk Modulus.

See the description in Shear Modulus.

See the description in Polynomial EOS.

Written as *EOS_LINEAR_POLYNOMIAL.

See Keywords used by LS-DYNA in Workbench for more information.

See the description in Shock EOS Linear.

Written as *EOS_GRUNEISEN.

See Keywords used by LS-DYNA in Workbench for more information.

See the description in Shock EOS Bilinear.

Written as *EOS_GRUNEISEN.

See Keywords used by LS-DYNA in Workbench for more information.

The JWL equation of state describes the detonation product expansion. This material property is used by the Explicit Materials library in Engineering Data. See the description in JWL EOS for additional information.

This property requires that you also define Density.

Written as *EOS_JWL and *MAT_HIGH_EXPLOSIVE_BURN.