JWLPlusPlus Material

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Introduction

This MPM material is a programmed-burn model for simulating certain detonation scenarios. It is only available in OSParticulas

Constitutive Law

This material tracks only pressure, which is modeled as simple mixture of unreacted solid phase with a reacted gas phase. The equation of state is described in Souers et al.[1]

The solid phase is modeled using a Murnahan equation of state:

     [math]\displaystyle{ P_{solid} = {1\over nK}\left({1\over J^n}-1\right) }[/math]

where K is bulk modulus, n is a JWL material property, and J is relative volume change (i.e., determinant of the deformation gradient). The pressure of the gas phase[1] is

     [math]\displaystyle{ P_{gas} = A\exp(-R_1J) + B\exp(-R_2J) + {C\over J^{1+\omega}} }[/math]

where A, B, C, R1, R2, and ω are JWL material properties. The total pressure for each particle is then given by

     [math]\displaystyle{ P_{gas} = (1-F)P_{solid} + FP_{gas} }[/math]

where F is the fraction of the particle that has reacted.

Detonation Wave

The fraction reacted is modeling by assuming a detonation wave moving through a collection of JWLPlusPlus material points. The wave starts at a specified position (see StartPositionX(Y)(Z)) and a given ignition time (see time0). If no normal vector is defined, the detonation wave will be a spherical wave emanating from the starting point. If a normal vector is defined (see NormX(Y)(Z)), the detonation wave will be planar wave defined by the plane through the starting point with the provided normal vector. The wave front propagates at a constant detonation velocity (see Dv)

All particles started as unreacted (fraction reacted F=0). They start to react when the detonation wave reaches the particle and finish reacting when the wave is a distance Dw past the particle. Within the wave front, the fraction reacted varies linear from 0 to 1. In other words, Dw is the width of the detonation front and Dw/Dt is the time it takes each particle to fully react.

Material Properties

The properties for a Tait liquid are:

Property Description Units Default
time0 Detonation start time time units 0
StartX Detonation starting x position length units 0
StartY Detonation starting y position length units 0
StartZ Detonation starting z position length units 0
NormX Planar wave normal in x direction length units 0
NormY Planar wave normal in y direction length units 0
NormZ Planar wave normal in z direction length units 0
Dv Detonation velocity alt velocity units none
Dw Detonation front width. The extent of reaction of these particle goes from 0 to 1 over a length equal to this width. The time for a given partile to burn once it starts is thus Dw/Dv. length units none
DeleteDist Particle deletion distance. If a particle is greater than this distance from the starting location (for spherical wave) or starting plane (for planar wave), the particle is deleted from the simulation. length units none
nm none none
Ajwl pressure units none
Bjwl pressure units none
Cjwl pressure units none
R1 none none
R2 none none
Omega none none
(other) Properties common to all materials varies varies

History Variables

This material tracks two history variables:

  1. J or the volumetric strain (i.e., the determinant of the deformation gradient).
  2. Fraction reacted. The fracture reacted is zero for particle ahead of the detonation wave front, one behind in, and transitions for zero to one across the detonation wave front defined by the Dw material property.

Examples

The following commands are for water for scripted or XML input files

  1. 1.0 1.1 P. Clark Souers*, Steve Anderson, James Mercer, Estella McGuire and Peter Vitello, "JWL  : A Simple Reactive Flow Code Package for Detonation." Propellants, Explosives, Pyrotechnics 25, 54-58 (2000).