A survey of numerical methods for shock physics applications Page: 4 of 22
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ble, limited only by the availability of computer memory and time.
If we can assume valid material models, numerical simulations can explore material response in
pressure and temperature regimes that are beyond available experimental or diagnostic capabili-
ties to investigate. Hypervelocity impacts can be studied in velocity regimes that exceed present
projectile launcher capabilities, and detailed investigation of material response can be made where
temperatures would preclude use of diagnostic apparatus in any experimental study, e.g., in mate-
rials subjected to intense x-ray energy deposition or in expanding products of chemical explo-
Furthermore, in many cases, numerical studies can be done in less time and at lower cost than ex-
perimental studies. In general, small changes in problem parameters, such as material thicknesses,
impact conditions, or material properties, merely involve changes to the problem input file. These
changes in a numerical study can often be made in a matter of minutes; whereas, corresponding
changes in an experimental configuration may require additional machining and assembly of
hardware and can, therefore, be quite time-consuming.
Simulations are only useful, however, insofar as there is some reason to have confidence in the ac-
curacy of the solution method and material response models used in the calculations. Presently,
accurate material response models exist for only a small part of the spectrum of materials and
loading regimes of interest in shock compression studies. One notable shortcoming of present
modeling techniques is the lack of capability to predict failure and post-failure response for most
materials of practical interest. Also, the response of many materials is strongly influenced by mi-
cro-mechanical factors which cannot be modeled explicitly and are not sufficiently well-under-
stood to be incorporated in macroscopic models. Composites, which are of great and increasing
importance in engineering applications, are an example of a class of materials where fidelity is
lacking in numerical simulations of dynamic response in shock compression processes.
Numerical simulations are designed to solve, for the material body in question, the system of
equations expressing the fundamental laws of physics to which the dynamic response of the body
must conform. The detail provided by such "first-principles" solutions can often be used to devel-
op simplified methods for predicting the outcome of physical processes. These simplified analytic
techniques have the virtue of numerical efficiency and are, therefore, preferable to numerical sim-
ulations for parameter sensitivity studies. Typically, rather restrictive assumptions are made on the
bounds of material response in order to simplify the problem and make it tractable to analytic
methods of solution. Thus, analytic methods lack the generality of numerical simulations and care
must be taken to apply them only to problems where the assumptions on which they are based will
be valid. This can apply also to hydrocodes, particularly with respect to material models and their
The problems solved by large deformation hydrocodes are quite challenging for several reasons.
The geometry can be very complex, such as would be the case in modeling bridges, space vehi-
cles, or missiles. The phenomena can be highly nonlinear, including for example nonlinear mate-
rial models, fracture, or buckling. The codes must be minimally capable of resolving gross
behavior of the discontinuous fields without undue expense. The material models may be very
complex, encompassing strain history dependent plasticity, internal voids, or anisotropic re-
sponse. Tremendous progress has been made over the last forty years, but much remains to be
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Hertel, E.S. Jr. A survey of numerical methods for shock physics applications, article, October 1, 1997; Albuquerque, New Mexico. (digital.library.unt.edu/ark:/67531/metadc697116/m1/4/: accessed September 23, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.