We have implemented the burn model in LS-DYNA. At present, the damage (porosity and specific surface area) is specified as initial conditions. However, history variables that are used by the strength model are reserved as placeholders for the next major revision, which will be a completely interactive model. We have implemented an improved strength model for explosives based on a model for concrete. The model exhibits peak strength and subsequent strain softening in uniaxial compression. The peak strength increases with increasing strain rate and/or reduced ambient temperature. Under triaxial compression compression, the strength continues to increase (or at least not decrease) with increasing strain. This behaviour is common to both concrete and polymer-bonded explosives (PBX) because the microstructure of these composites is similar. Both have aggregate material with a broad particle size distribution, although the length scale for concrete aggregate is two orders of magnitude larger than for PBX. The (cement or polymer) binder adheres to the aggregate, and is both pressure and rate sensitive. There is a larger bind binder content in concrete, compared to the explosive, and the aggregates have different hardness. As a result we expect the parameter values to differ, but the functional forms to be applicable to both. The models have been fit to data from tests on an AWE explosive that is HMX based. The decision to implement the models in LS-DYNA was based on three factors: LS-DYNA is used routinely by the AWE engineering analysis group and has a broad base of experienced users; models implemented in LS-DYNA can be transferred easily to LLNL's ALE 3D using a material model wrapper developed by Rich Becker; and LS-DYNA could accommodate the model requirements for a significant number of additional history variables without the significant time delay associated with code modification.

Plastic-bonded explosives are heterogeneous materials. Experimentally, shock initiation is sensitive to small amounts of porosity, due to the formation of hot spots (small localized regions of high temperature). This leads to the Ignition and Growth concept, introduced by Lee and Tarver in 1980, as the basis for reactive burn models. A homogeneized burn rate needs to account for three mesoscale physical effects (i) the density of burnt hot spots, which depends on the lead shock strength; (ii) the growth of the burn fronts triggered by hot spots, which depends on the local deflagration speed; (iii) a geometric factor that accounts for the overlap of deflagration wavelets from adjacent hot spots. These effects can be combined and the burn model defined by specifying the reaction progress variable [lambda](t) as a function of a dimensionless reaction length [tau]{sub hs}(t)/l{sub hs}, rather than by xpecifying an explicit burn rate. The length scale l{sub hs} is the average distance between hot spots, which is proportional to [N{sub hs}(P{sub s})]−13, where N{sub hs} is the number density of hot spots activated by the lead shock. The reaction length [tau]{sub hs}(t) = {line_integral}0{sup t} D(P(t'))dt' is the distance the burn front propagates from a single hot spot, where D is the deflagration speed and t is the time since the shock arrival. A key implementation issue is how to determine the lead shock strength in conjunction with a shock capturing scheme. They have developed a robust algorithm for this purpose based on the Hugoniot jump condition for the energy. The algorithm utilizes the time dependence of density, pressure and energy within each cell. The method is independent of the numerical dissipation used for shock capturing. It is local and can be used in one or more space dimensions. The burn model has a small number of parameters which can be calibrated to fit velocity gauge data from shock initiation experiments.

HERMES (High Explosive Response to MEchanical Stimulus) was developed to fill the need for a model to describe an explosive response of the type described as BVR (Burn to Violent Response) or HEVR (High Explosive Violent Response). Characteristically this response leaves a substantial amount of explosive unconsumed, the time to reaction is long, and the peak pressure developed is low. In contrast, detonations characteristically consume all explosive present, the time to reaction is short, and peak pressures are high. However, most of the previous models to describe explosive response were models for detonation. The earliest models to describe the response of explosives to mechanical stimulus in computer simulations were applied to intentional detonation (performance) of nearly ideal explosives. In this case, an ideal explosive is one with a vanishingly small reaction zone. A detonation is supersonic with respect to the undetonated explosive (reactant). The reactant cannot respond to the pressure of the detonation before the detonation front arrives, so the precise compressibility of the reactant does not matter. Further, the mesh sizes that were practical for the computer resources then available were large with respect to the reaction zone. As a result, methods then used to model detonations, known as [beta]-burn or program burn, were not intended to resolve the structure of the reaction zone. Instead, these methods spread the detonation front over a few finite-difference zones, in the same spirit that artificial viscosity is used to spread the shock front in inert materials over a few finite-difference zones. These methods are still widely used when the structure of the reaction zone and the build-up to detonation are unimportant. Later detonation models resolved the reaction zone. These models were applied both to performance, particularly as it is affected by the size of the charge, and to situations in which the stimulus was less than that needed for reliable performance, whether as a result of accident, hazard, or a fault in the detonation train. These models describe the build-up of detonation from a shock stimulus. They are generally consistent with the mesoscale picture of ignition at many small defects in the plane of the shock front and the growth of the resulting hot-spots, leading to detonation in heterogeneous explosives such as plastic-bonded explosives (PBX). The models included terms for ignition, and also for the growth of reaction as tracked by the local mass fraction of product gas, [lambda]. The growth of reaction in such models incorporates a form factor that describes the change of surface area per unit volume (specific surface area) as the reaction progresses. For unimolecular crystalline-based explosives, the form factor is consistent with the mesoscale picture of a galaxy of hot spots burning outward and eventually interacting with each other. For composite explosives and propellants, where the fuel and oxidizer are segregated, the diffusion flame at the fuel-oxidizer interface can be interpreted with a different form factor that corresponds to grains burning inward from their surfaces. The form factor influences the energy release rate, and the amount of energy released in the reaction zone. Since the 19th century, gun and cannon propellants have used perforated geometric shapes that produce an increasing surface area as the propellant burns. This helps maintain the pressure as burning continues while the projectile travels down the barrel, which thereby increases the volume of the hot gas. Interior ballistics calculations use a geometric form factor to describe the changing surface area precisely. As a result, with a suitably modified form factor, detonation models can represent burning and explosion in damaged and broken reactant. The disadvantage of such models in application to accidents is that the ignition term does not distinguish between a value of pressure that results from a shock, and the same pressure that results from a more gradual increase. This disagrees with experiments, where explosives were subjected to a gradual rise in pressure and did not exhibit reaction. More recent models do distinguish between slow pressure rises and shocks, and have had some success in the describing the response of explosives to single and multiple shocks, and the increase of shock sensitivity with porosity, at least over a limited range. The original formulation is appropriate for sustained shocks, but further work is ongoing to describe the response to short pulses. The HERMES model combines features from these prior models. It describes burning and explosion in damaged reactant, and also will develop a detonation if the gradual rise in pressure from burning steepens into a strong-enough shock. The shock strength needed for detonation in a fixed run distance decreases with increasing porosity.

Recently, interest has been shown concerning the mechanical response of plastic-bonded explosives (PBX) and propellants to enable the development of predictive materials models describing the mechanical behavior of these composites. Accordingly, detailed information about the constitutive response is crucial. Compression measurements were conducted on two explosive formulation binders, extruded Estane{trademark} 5703 (hereafter referred to as Estane) and plasticized Estane as a function of temperature from -60 C to +23 C using a specially-designed split Hopkinson pressure bar (strain rate of (almost equal to) 2800 s−1) and quasi-stattically (strain rates from (almost equal to) 0.001 to 1 s−1) using a hydraulic load frame. The mechanical response of the Estane was found to exhibit a stronger dependency on strain rate and temperature and higher flow strength for similar test conditions of the materials tested. Plasticized Estane was less sensitively dependent on strain rate and temperature. The visco-elastic recovery of both binders is seen to dominate the mechanical behavior at temperatures above the glass transition temperature (T{sub g}). The binders exhibited increasing elastic loading moduli, E, with increasing strain rate or decreasing temperature, which is similar to other polymeric materials. There is a pronounced shift in the apparent T{sub g} to higher temperatures as the strain rate is increased. At low strain rates the binders exhibit a yield behavior followed by a drop in the flow stress which may or may not recover. At high strain rates the load drop does not occur and the flow stresses level out. A discussion of the Hopkinson bar technique as applied to polymeric or low impedance materials is described in detail.

Providing a complete overview of the rapidly emerging field of modeling for explosives and propellants, this updated text imparts a thorough understanding of new computational methods and experimental measuring techniques. The CD-ROM contains FORTRAN and executable computer codes.