Finite cavity expansion method for near-surface effects and layering during earth penetration Page: 4 of 9
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Finite Cavity Expansion Method for Near-Surface Effects and Layering
During Earth Penetration
Richard W. Macek, Thomas Duffey
Group ESA-EA MS P946
Los Alamos National Laboratory
Los Alamos, NM 87544, USA
A finite spherical cavity expansion technique is developed to simulate the loading on projectiles
penetrating geologic media. Damaged Mohr-Coulomb plasticity models and general pressure-dependent
damaged plasticity models are used with incompressible kinematics to approximate a wide range of targets.
The finite cavity expansion approximation together with directional sampling reasonably captures near
surface and layering effects without resort to ad hoc or empirical correction factors. The Mohr-Coulomb
models are integrated exactly to provide a very efficient loading algorithm for use with conventional implicit
or explicit finite element structural analysis. The more general constitutive model requires numerical
integration and leads to a more computationally intensive procedure. However, subcycling is easily
implemented with the numerical integration and thus an efficient loading method is readily achieved even for
large complex simulations using explicit finite element analysis. The utility of the finite cavity expansion
approach is demonstrated by comparison of simulations to measured test data from projectiles penetrating
rock and soil targets.
The general subject of the penetration of various media by projectiles has recently been surveyed by
Backman and Goldsmith , Corbett, Reid, and Johnson , and Heuzd . Typically penetration problems
are solved by either empirical, analytical, or numerical methods. In general empirical methods are most often
employed when the depth of penetration and the trajectory of the projectile in the target are desired.
Furthermore, the empirical methods are the most successful when the penetrator can be approximated as a
rigid body. If the structural response of the projectile during penetration is the main concern, then analytical
or numerical approaches have shown more success.
Full numerical approaches to penetration have the most firm theoretical basis. With these both the
target and the projectile are discretized and integrated numerically in both space and time. Lagrangian,
Eulerian, and coupled Lagrangian-Eulerian methods have been successfully used. Any of these methods
provide generality in both the geometrical and constitutive representation of the target. However, they are
very computationally intensive and the strictly Lagrangian approaches often suffer from mesh entanglement
in the target which can prematurely terminate the analysis.
One of the more popular analytical techniques is cavity expansion coupled to a flexible body projectile
model . With this approach the pressure on the projectile is typically computed analytically by assuming
that the penetrator is uniformly (one dimensionally) expanding either a spherical or cylindrical cavity in an
infinite medium at a constant velocity (the velocity normal to the projectile's outer surface). The projectile,
itself, is usually modeled with conventional finite elements. While this method is very computationally
efficient and accurately predicts the axial response of the penetrator, it often errs significantly in predicting the
lateral response. This deficiency is presumed to be due to inadequate geometrical representation of the target
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Macek, R.W. & Duffey, T. Finite cavity expansion method for near-surface effects and layering during earth penetration, article, September 1, 1998; New Mexico. (digital.library.unt.edu/ark:/67531/metadc710622/m1/4/: accessed June 22, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.