JWLPlusPlus Material
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 particle 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 and moved into the Material Point Reservoir. | length units | none |
| K | Bulk modulus in the solid phase equation of state | pressure units | none |
| nm | Factor in the solid phase equation of state | none | none |
| Ajwl | A term in gas phase equation of state | pressure units | none |
| Bjwl | B term in gas phase equation of state | pressure units | none |
| Cjwl | C term in gas phase equation of state | pressure units | none |
| R1 | R1 term in gas phase equation of state | none | none |
| R2 | R2 term in gas phase equation of state | none | none |
| Omega | ω term in gas phase equation of state | none | none |
| (other) | Properties common to all materials | varies | varies |
History Variables
This material tracks two history variables:
- J or the volumetric strain (i.e., the determinant of the deformation gradient).
- 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