JWL EOS

The JWL equation of state describes the detonation product expansion down to a pressure of 1 kbar for high energy explosive materials and has been proposed by Jones, Wilkins and Lee according to the following equation

, where ρ0 is the reference density, ρ the density and η = ρ/ρ0.

The values of the constants A, B, R1, R2 and ω for many common explosives have been determined from dynamic experiments.

Figure 54:  Pressure as function of density for the JWL equation of state

Pressure as function of density for the JWL equation of state

The standard JWL equation of state can be used in combination with an energy release extension whereby additional energy is deposited over a user-defined time interval. Thermobaric explosives show this behavior and produce more explosive energy than conventional high energy explosives through combustion of inclusions, like aluminum, with atmospheric oxygen after detonation.

This option is activated when the additional specific energy is specified different from zero.

Burn on Compression

In this process the detonation wave is not predefined but the unburned explosive is initially treated similarly to any other inert material. However, as an initiating shock travels through the unburned explosive and traverses elements within the explosive the compression of all explosive elements is monitored. If and when the compression in a cell reaches a predefined value the chemical energy is allowed to be released at a controlled rate.

Burn on compression may be defined in one of two ways:

The critical threshold compression and the release rate are parameters that must be chosen with care in order to obtain realistic results. The burn on compression option may give unrealistic results for unconfined regions of explosive since the material is free to expand at the time of initial shock arrival and may not achieve sufficient compression to initiate energy release in a realistic time scale.

Typically, a burn logic based upon compression is more successful in Lagrangian computations rather than Eulerian.


Note:  The constants A, B, R1, R2 and ω should be considered as a set of interdependent parameters and one constant cannot be changed unilaterally without considering the effect of this change on the other parameters.

This equation of state can only be applied to solid bodies.

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 128:  Input Data

NameSymbolUnitsNotes
Parameter AAStress 
Parameter BBStress 
Parameter R1R1None 
Parameter R2R2None 
Parameter ωωNone 
C-J Detonation VelocityDCJVelocity 
C-J Energy/unit mass Energy/mass 
C-J PressurePCJStressBurn on compression logic
Burn on compression fractionBCJNoneBurn on compression logic
Pre-burn bulk modulusKBKStressBurn on compression logic
Adiabatic constant None 
Additional specific internal energy/unit mass Energy/massAdditional energy release
Begin Time TimeStart time of additional energy release
End Time TimeEnd time of additional energy release

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

Custom results variables available for this model:

NameDescriptionSolidsShellsBeams
PRESSUREPressureYesNoNo
DENSITYDensityYesNoNo
COMPRESSIONCompressionYesNoNo
INT_ENERGYInternal EnergyYesNoNo
TEMPERATURETemperatureYesNoNo
BURN_FRACBurn FractionYesNoNo

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