The EXOS computer program numerically simulates impacts of orbital debris on spacecraft. EXOS can be used to simulate meteoroid- and orbital-debris-impact damage to commercial satellites, and to simulate effects of weapons on personal and vehicular protection systems. With further development, the simulation technique employed in the EXOS package could be adapted for use in structural applications; for example, to simulate crashes in evaluating designs of vehicles.

These Images Are Results of a Computational Simulation of hypervelocity impact of an aluminum sphere on an aluminum plate.

EXOS includes a preprocessor subprogram, an analysis code, and a simple rezoner subprogram, for use in simulating large-strain thermoelastic-plastic continuum dynamics, including contact-impact effects. Commercial graphics codes are used to postprocess simulation data. EXOS implements a hybrid particle/finite-element method and is an alternative to prior Lagrangian, Eulerian, and particle-based impact codes.

In the present method, Hamilton's equations are applied to a system of translating, deforming, and thermomechanically interacting physical particles, to obtain a three-dimensional hydrodynamical model for shock-physics simulations. The method is energy-based and, hence, simple to formulate, with no need to consider continuum balance laws, interpolation functions, or weighted-residual solution techniques. Inasmuch as equations of particle kinematics, energy functions, and constraints are fully Lagrangian in form, the method makes it possible to avoid the diffusion problems typically associated with interpolation on space-fixed meshes and the stability problems observed in some moving interpolations.

Although previous methods have involved limited use of entropy states, total-entropy variables appear in this method as generalized coordinates for the particles, subject to nonholonomic thermal constraints that describe conduction of heat and dissipation of energy. Additional nonholonomic constraints on the particle coordinates and deformation gradients are introduced to represent mechanical interaction of the particles; this approach makes it possible to avoid the introduction of essentially Eulerian potential-energy functions or the remapping of data between the particles and a grid to quantify collision forces. Finally, the use of a fully Lagrangian frame of reference means that no mixing or partial pressures are needed to represent the multimaterial case.

EXOS is a three-dimensional implementation of the aforementioned particle method with an extension to include a finite-element-based description of material-strength effects, suitable for use in the simulation of hypervelocity impacts. In comparison with conventional continuum hydrocodes that have been used previously to solve orbital-debris-impact problems, EXOS is faster and more robust. Although numerous codes have been used in the past to simulate impacts of meteoroids and debris on spacecraft shields, in general they have proven very difficult to apply to three-dimensional simulations.

The figure presents selected results from an EXOS simulation of the impact of an aluminum sphere of diameter 0.953 cm on an aluminum plate of thickness 0.1143 cm at a speed of 6.56 km/s and an angle of 45°. The first image depicts the situation immediately before impact, the second image shows the situation 6.6 µs after impact, and the third image shows the resulting hole in the plate. The color contours depict accumulated plastic strain. The results of simulation have been found to be in substantial agreement with a radiograph taken in an experiment that corresponds to the simulation and that was reported in NASA Contractor Report 4707 (by A. J. Piekutowski, dated February 1996).

Johnson Space Center is working closely with the University of Texas to validate the use of EXOS in predicting the results of hypervelocity impacts on spacecraft shields. In the course of this verification process, EXOS has been modified and improved. The verification process was continuing at the time of reporting the information for this article.

Johnson Space Center is taking advantage of the stability and speed of EXOS to perform shield-impact simulations at its Hypervelocity Impact Technology Facility. Other agencies and companies involved in effects of hypervelocity impacts and protection of spacecraft could benefit from this code. With further development, its range of applications could be expanded.

This work was done by Eric P. Fahrenthold of the University of Texas at Austin for Johnson Space Center. Further information is available in the article, "Hamiltonian Particle Hydrodynamics," by E. P. Fahrenthold and J. C. Koo, published in the journal Computer Methods in Applied Mechanics and Engineering, Volume 146 (1997), pp. 43-52.

In accordance with Public Law 96-517, the contractor has elected to retain title to this invention. Inquiries concerning rights for its commercial use should be addressed to

Eric P. Fahrenthold, Professor
Dept. of Mechanical Engineering
University of Texas
Mail Code C2200
26th Street and San Jacinto
Austin, TX 78712

Refer to MSC-22979, volume and number of this NASA Tech Briefs issue, and the page number.