Difference between revisions of "JWLPlusPlus Material"
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<math>P_{solid} = {1\over nK}\left({1\over J^n}-1\right)</math> | <math>P_{solid} = {1\over nK}\left({1\over J^n}-1\right)</math> | ||
where <i>K</i> is bulk modulus, <i>n</i> is JWL material property, and <i>J</i> is relative volume change (<i>i.e.</i>, determinant of the deformation gradient). | where <i>K</i> is bulk modulus, <i>n</i> is a [[Material Properties|JWL material property]], and <i>J</i> is relative volume change (<i>i.e.</i>, determinant of the deformation gradient). The pressure of the gas phase is | ||
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<math>P_{gas} = A\exp(-R_1J) + B\exp(-R_2J) + {C\over J^{1+\omega}}</math> | |||
where <i>A</i>, <i>B</i>, <i>C</i>, <i>R</i><sub>1</sub>, <i>R</i><sub>2</sub>, and ω are [[Material Properties|JWL material properties]]. The total pressure for each particle is then given by | |||
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<math>P_{gas} = (1-F)P_{solid} + FP_{gas}</math> | |||
where <i>F</i> is the fraction of the particle that has reacted. | |||
== Material Properties == | == Material Properties == | ||
Revision as of 15:39, 12 May 2020
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 siple mixture of unreacted solid material with a reacted gas phase. The equation of state is described in Souers et al.[1]
The solid material 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 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.
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:
- 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
- ↑ 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</b, 54-58 (2000).