Brittle behavior of metal alloys is often critical to modeling ballistic impact and penetration. The ALEGRA multiphysics finite element software incorporates calibrated models for the equation of state, elasticity, yield stress, plasticity and fracture, but simulations do not always capture expected metal fracture. Here we report concerted efforts to do so for one important case where experiments clearly show shear fractures: a tungsten sphere impacting a steel plate at various angles. Our best simulations show fractures that are qualitatively similar to experiments, but there are significant differences in quantitative metrics. Specifically, velocities of tracers used to quantify simulated plug parameters consistently fall short of measured plug velocities. Also, simulated plugs break apart more than expected from experimental evidence. We attribute these shortfalls to the lack of an explicit shear fracture mechanism in the material models, leading to over-estimated resistance to plug formation and movement.
The spatial distribution of electric field due to an imposed electric charge density profile in an infinite slab of dielectric material is derived analytically by integrating Gauss's law. Various charge density distributions are considered, including exponential and power-law forms. The Maxwell stress tensor is used to compute a notional static stress in the material due to the charge density and its electric field. Characteristics of the electric field and stress distributions are computed for example cases in polyethylene, showing that field magnitudes exceeding the dielectric strength would be required in order to achieve a stress exceeding the ultimate tensile strength.
The Glassy Amorphous Polymer (GAP) model is a viscoelastic/plastic model developed at Los Alamos National Laboratory to accurately model a variety of polymers across a wide range of conditions and loading rates, including shock loading. In the present report we introduce and assess this model, newly implemented in the ALEGRA shock and multiphysics code, using a series of verification and application-related validation problems. We describe the mathematical and theoretical formulation of the model, as well as its implementation in ALEGRA, in detail. We provide verification results that assess the model implementation against published computational results, as well as validation results which we compare to existing experimental results when possible. These comparisons instill confidence in the implementation and indicate that the addition of the GAP model to the ALEGRA code provides users with a high-fidelity polymer modeling capability that is capable of recreating complex polymer phenomena.
Two complementary approximations for describing aspects of continuum electromagnetics in moving media are discussed: electroquasistatic and magnetoquasistatic. Each has been implemented in the finite element shock code ALEGRA for modeling dynamic electromechanical phenomena on typical engineering time scales, with fully integrated circuit coupling (Niederhaus et al. 2023). The approximations can be obtained by consistent asymptotic balancing of Maxwell's equations relative to timescales associated with magnetic diffusion, charge relaxation, and electromagnetic wave propagation. In ALEGRA, the electroquasistatic approximation is used for ferroelectric (FE) modeling, while the magnetoquasistatic approximation is used for magnetohydrodynamic (MHD) modeling. In this paper we introduce for the first time a detailed derivation of a useful quasi-steady “low-Rm” variant of the MHD approximation applicable for cases, such as with detonators, where the thermodynamic pressure arising from Joule heating dominates over magnetic forces. An additional purpose of this paper is to present a coupling mode using Multiple Program-Multiple Data (MPMD) message passing communication that allows the user to run 3D FE problems together with 2D and/or 3D MHD problems with the respective simulation domains coupled through a common circuit equation. The MPMD coupling capability is used here to model the dynamic coupling of a notional ferroelectric generator with an RP-87 exploding bridgewire detonator. The simulated bridgewire heats up and bursts under current generated by simulated depoling of the ferroelectric generator, as a demonstration of the MPMD capability.
Interpenetrating lattices consist of two or more interwoven but physically separate sub-lattices with unique behaviors derived from their multi-body construction. If the sublattices are constructed or coated with an electrically conducting material, the close proximity and high surface area of the electrically isolated conductors allow the two lattices to interact electromagnetically either across the initial dielectric filled gap or through physical contact. Changes in the size of the dielectric gap between the sub-lattices induced by deformation can be measured via capacitance or resistance, allowing a structurally competent lattice to operate as a force or deformation sensor. In addition to resistive and capacitive deformation sensing, this work explores capacitance as a fundamental metamaterial property and the environmental sensing behaviors of interpenetrating lattices.
While modeling a generic pulse transformer, we became interested in the possibility of electric sparks between winding layers in a solid encapsulant. We significantly modified a previously developed ALEGRA MHD model of a generic spark in lexan. The cumulative modifications are significant enough to report here. Possibly the most significant modification was a change in how the simulated spark is initiated from a thin initial channel. The change was from imposing an initial hot temperature to imposing a conductivity floor. The reasons and comparisons of results are included. The second significant change was to replace a fixed current rise rate with an external circuit model. We built a model specifically mimicking the distributed inductance and stray capacitance between the coil turns closest to the modeled spark. Excursions from nominal values examine the sensitivity of resulting behaviors to extreme capacitance and inductance values.
ALEGRA is a multiphysics finite-element shock hydrodynamics code, under development at Sandia National Laboratories since 1990. Fully coupled multiphysics capabilities include transient magnetics, magnetohydrodynamics, electromechanics, and radiation transport. Importantly, ALEGRA is used to study hypervelocity impact, pulsed power devices, and radiation effects. The breadth of physics represented in ALEGRA is outlined here, along with simulated results for a selected hypervelocity impact experiment.
This is an extension of work described by Rodriguez et al. (2021). It continues analyses of a generic transformer design by Wes Greenwood. In this report, we summarize that work and add comparable results using the ANSYS Maxwell software (henceforward, “ANSYS”), and with COMSOL . We found the ANSYS and COMSOL calculations of inductance agreed well with previous results for simplified coils in air, and with a ferromagnetic core. We then describe the ANSYS and COMSOL approach and show results for a full transformer model based on magnetic field analyses. Finally, we present electrostatic analyses of E field enhancement, once again resolving individual wires. The purpose is to assess the electrostatic fields in order to locate where electric breakdown is likely to originate. We found the maximum enhancement between the secondary and either the primary or the tertiary at the end of the windings with a large potential difference.
We report progress on a task to model transformers in ALEGRA using the “Transient Magnetics” option. We specifically evaluate limits of the approach resolving individual coil wires. There are practical limits to the number of turns in a coil that can be numerically modeled, but calculated inductance can be scaled to the correct number of turns in a simple way. Our testing essentially confirmed this “turns scaling” hypothesis. We developed a conceptual transformer design, representative of practical designs of interest, and that focused our analysis. That design includes three coils wrapped around a rectangular ferromagnetic core. The secondary and tertiary coils have multiple layers. The tertiary has three layers of 13 turns each; the secondary has five layers of 44 turns; the primary has one layer of 20 turns. We validated the turns scaling of inductance for simple (one-layer) coils in air (no core) by comparison to available independent calculations for simple rectangular coils. These comparisons quantified the errors versus reduced number of turns modeled. For more than 3 turns, the errors are <5%. The magnetic field solver failed to converge (within 5000 iterations) for >10 turns. Including the core introduced some complications. It was necessary to capture the core surfaces in thin grid sheaths to minimize errors in computed magnetic energy. We do not yet have quantitative benchmarks with which to compare, but calculated results are qualitatively reasonable.
In this work we evaluated the effects that equations of state and strength models have on SCJ development using the Sandia National Laboratories multiphysics shock code, ALEGRA. Results were quantified using a Lagrangian tracer particle following liner collapse, passing through the compression zone, and flowing into the jet tip. We found consistent results among several EOS: 3320, 3331, and 3337. The 3325 EOS generated a measurable low density and hollow region near the jet tip which appears to be reflected in a lower internal energy of the jet. At this time, we cannot tell, experimentally, if such a hollow region exists. The 3337 EOS is recent, well documented [6], and produces results similar to 3320 [3]. The various strength models produced more noticeable differences. In terms of internal energy and temperature, SGL had the largest values followed by PTW, ZA, and finally JC and MTS, which were quite similar to each other. We looked at melt conditions in the SGL and JC models using the 3337 EOS. The SGL model reported a liquid region along the jet axis all the way to the tip-seemingly consistent with experiment-while the JC model does not indicate any phase transition. None of the other yield models indicated melt along the jet axis. For all EOS and strength models, we found similar results for the velocity history of the jet tip as measured against experiment using photon Dopper velocimetry.
A verification study is conducted for the ALEGRA software, using the problem of an electrified medium with a spherical inclusion, paying special attention to resistive heating. We do so by extending an existing analytic solution for this problem to include both conducting and insulating inclusions, and we examine the effects of mesh resolution and mesh topology, considering both body-fitted and rectangular meshes containing mixed cells. We present observed rates of convergence with respect to mesh refinement for four electromagnetic quantities: electric potential, electric field, current density and Joule power.
We show here that Sandia's ALEGRA software can be used to model a permanent magnet in 2D and 3D, with accuracy matching that of the open-source commercial software FEMM. This is done by conducting simulations and experimental measurements for a commercial-grade N42 neodymium alloy ring magnet with a measured magnetic field strength of approximately 0.4 T in its immediate vicinity. Transient simulations using ALEGRA and static simulations using FEMM are conducted. Comparisons are made between simulations and measurements, and amongst the simulations, for sample locations in the steady-state magnetic field. The comparisons show that all models capture the data to within 7%. The FEMM and ALEGRA results agree to within approximately 2%. The most accurate solutions in ALEGRA are obtained using quadrilateral or hexahedral elements. In the case where iron shielding disks are included in the magnetized space, ALEGRA simulations are considerably more expensive because of the increased magnetic diffusion time, but FEMM and ALEGRA results are still in agreement. The magnetic field data are portable to other software interfaces using the Exodus file format.
A preliminary finite-element model has been developed using the ALEGRA-FE code for explosive driven depoling of a PZT 95/5 ferroelectric generator. The ferroelectric material is characterized using hysteresis-loop and hydrostatic depoling tests. These characteristics are incorporated into ALEGRA-FE simulations that model the explosive drive mechanism and shock environment in the material leading to depoling, as well as the ferroelectric response and the behavior of a coupled circuit. The ferroelectric-to-antiferroelectric phase transition is captured, producing an output voltage pulse that matches experimental data to within 10% in rise time, and to within about 15% for the final voltage. Both experimental and modeled pulse magnitudes are less than the theoretical maximum output of the material. Observations from materials characterization suggest that unmodeled effects such as trapped charge in the stored FEG material may have influenced the experimentally observed output.
Use of insensitive high explosives (IHEs) has significantly improved ammunition safety because of their remarkable insensitivity to violent cook-off, shock and impact. Triamino-trinitrobenzene (TATB) is the IHE used in many modern munitions. Previously, lightning simulations in different test configurations have shown that the required detonation threshold for standard density TATB at ambient and elevated temperatures (250 C) has a sufficient margin over the shock caused by an arc from the most severe lightning. In this paper, the Braginskii model with Lee-More channel conductivity prescription is used to demonstrate how electrical arcs from lightning could cause detonation in TATB. The steep rise and slow decay in typical lightning pulse are used in demonstrating that the shock pressure from an electrical arc, after reaching the peak, falls off faster than the inverse of the arc radius. For detonation to occur, two necessary detonation conditions must be met: the Pop-Plot criterion and minimum spot size requirement. The relevant Pop-Plot for TATB at 250 C was converted into an empirical detonation criterion, which is applicable to explosives subject to shocks of variable pressure. The arc cross-section was required to meet the minimum detonation spot size reported in the literature. One caveat is that when the shock pressure exceeds the detonation pressure the Pop-Plot may not be applicable, and the minimum spot size requirement may be smaller.
This report introduces the concepts of Bayesian model selection, which provides a systematic means of calibrating and selecting an optimal model to represent a phenomenon. This has many potential applications, including for comparing constitutive models. The ideas described herein are applied to a model selection problem between different yield models for hardened steel under extreme loading conditions.
