ABAQUS/CAE User's Manual


12.10.6 Defining equations of state

The Edit Material dialog box allows you to define a hydrodynamic model in the form of an equation of state. See the following sections for details:

Defining an equation of state

You can use the Edit Material dialog box to define a hydrodynamic material model in which the material's volumetric strength is determined by an equation of state. For more information, see “Equation of state,” Section 17.9.1 of the ABAQUS Analysis User's Manual.

To define an equation of state:

  1. From the menu bar in the Edit Material dialog box, select Other EOS.

    (For information on displaying the Edit Material dialog box, see “Creating or editing a material,” Section 12.6.1.)

  2. Click the arrow to the right of the Type field, and select the type of equation of state that you want to define:

  3. If you selected Ideal Gas in Step 2, enter the following in the Data table:

    Gas Constant

    Gas constant, R. (Units of JM–1K–1.)

    Ambient Pressure

    The ambient pressure, (Units of FL–2).

    For detailed information on how to enter data, see “Entering tabular data,” Section 3.2.7.

  4. If you selected JWL in Step 2, enter the following in the Data table:

    Detonation Wave Speed

    Detonation wave speed, . (Units of LT–1.)

    A and B

    Material constants A, and b. (Units of FL–2.)

    omega, R1, and R2

    Material constants , , and . (Dimensionless.)

    Pre-deton bulk modulus

    Pre-detonation bulk modulus, . (Units of FL–2.)

    For detailed information on how to enter data, see “Entering tabular data,” Section 3.2.7.

  5. If you selected Us-Up in Step 2, enter the following in the Data table:

    c0

    Reference sound speed, . (Units of LT–1.)

    s

    Slope of the Us – Up curve, s. (Dimensionless.)

    Gamma0

    Grüneisen ratio, . (Dimensionless.)

    For detailed information on how to enter data, see “Entering tabular data,” Section 3.2.7.

  6. If desired, select Eos Shear from the Suboptions menu to define deviatoric behavior. For detailed instructions, see “Defining shear behavior for an equation of state” in “Defining equations of state,” Section 12.10.6.

  7. If you selected JWL in Step 2, select Detonation Point from the Suboptions menu to define detonation points for the explosive material. For detailed instructions, see “Defining detonation points for an explosive material” in “Defining equations of state,” Section 12.10.6.

  8. If you selected Us-Up in Step 2, you can select Eos Compaction from the Suboptions menu to specify plastic compaction behavior for a ductile porous material. For detailed instructions, see “Defining plastic compaction behavior for an equation of state” in “Defining equations of state,” Section 12.10.6.

  9. Click OK to close the Edit Material dialog box. Alternatively, you can select another material behavior to define from the menus in the Edit Material dialog box (see “Browsing and modifying material behaviors,” Section 12.6.2, for more information).

Defining shear behavior for an equation of state

An equation of state defines only the material's hydrostatic behavior. If used by itself, the material has only volumetric strength (the material is assumed to have no shear strength). Alternatively, ABAQUS/Explicit allows you to define deviatoric behavior, assuming that the deviatoric and volumetric responses are uncoupled. Two models, a linear isotropic deviatoric model or a Newtonian viscous deviatoric model, are available. The material's volumetric response is governed by the equation of state model, while its deviatoric response is governed by either the linear isotropic elastic model or the Newtonian viscous fluid model that you define.

For more information, see “Deviatoric behavior” in “Equation of state,” Section 17.9.1 of the ABAQUS Analysis User's Manual.

To define shear behavior:

  1. From the Suboptions menu in the Edit Material dialog box, select Eos Shear.

    A Suboption Editor appears.

  2. Click the arrow to the right of the Type field, and select the type of deviatoric model that you want to define:

    • Select Elastic to define a linear isotropic deviatoric model.

    • Select Viscous to define a Newtonian viscous deviatoric model.

  3. Toggle on Use temperature-dependent data to define the data as a function of temperature.

    A column labeled Temp appears in the Data table.

  4. Click the arrows to the right of the Number of field variables field to increase or decrease the number of field variables on which the data depend.

  5. In the Data table, enter shear modulus or viscosity data (depending on your selection in Step 3). Include temperature or field variable data if applicable. For detailed information on how to enter data, see “Entering tabular data,” Section 3.2.7.

  6. Click OK to return to the Edit Material dialog box.

Defining plastic compaction behavior for an equation of state

If you define a linear Us – Up equation of state (as described in “Defining an equation of state” in “Defining equations of state,” Section 12.10.6), you can use the Suboption Editor to specify plastic compaction behavior for a ductile porous material. For more information, see “P– equation of state” in “Equation of state,” Section 17.9.1 of the ABAQUS Analysis User's Manual.

To define plastic compaction:

  1. From the Suboptions menu in the Edit Material dialog box, select Eos Compaction.

    A Suboption Editor appears.

  2. In the Reference sound speed in the porous material field, enter a value for . (Units of LT–1.)

  3. In the Value of the porosity of the unloaded material field, enter a value for . (Dimensionless.)

  4. In the Pressure required to initialize plastic behavior field, enter a value for . (Units of FL–2.)

  5. In the Compaction pressure at which all pores are crushed field, enter a value for . (Units of FL–2.)

  6. Click OK to return to the Edit Material dialog box.

Defining detonation points for an explosive material

You can define any number of detonation points for an explosive material. Coordinates of the points must be defined along with a detonation delay time. Each material point responds to the first detonation point that it sees. For more information, see “JWL high explosive equation of state” in “Equation of state,” Section 17.9.1 of the ABAQUS Analysis User's Manual.

To define detonation points:

  1. Define a Jones-Wilkens-Lee (JWL) equation of state, as described in “Defining an equation of state” in “Defining equations of state,” Section 12.10.6.”

  2. From the Suboptions menu in the Edit Material dialog box, select Detonation Point.

    A Suboption Editor appears.

  3. Enter the following in the Data table:

    X

    Coordinate 1 of the detonation point.

    Y

    Coordinate 2 of the detonation point.

    Z

    Coordinate 3 of the detonation point.

    Detonation Delay Time

    Detonation delay time (total time, as defined in “Conventions,” Section 1.2.2 of the ABAQUS Analysis User's Manual). The default is 0.

    For detailed information on how to enter data, see “Entering tabular data,” Section 3.2.7.

  4. Click OK to return to the Edit Material dialog box.