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.

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 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:

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