Currently still under construction...
Hydrocodes are large computer programs that can be used to simulate highly dynamic events. These numerical routines can model the propagation of shock waves in a medium, and in turn compute stresses, strains, velocities, etc., as a function of time and position. Early formulations treated metal and rock as fluids, with no viscosity or strength, computing the approximate response of a body assuming that stresses were high enough to neglect material strength effects. Today, however, hydrodynamic computer codes (``hydrocodes'') can be more sophisticated in their material modeling. Hydrocodes employ classical continuum mechanics to describe the dynamics of a continuous medium through a set of differential equations derived from the principles of conservation of mass, momentum and energy. An equation of state relates changes in the density and internal energy of the material with pressure. The stress suffered by the material is related to the amount of strain (or distortion) required to produce that stress through the use of a constitutive relation.
We use a two-dimensional hydrocode (see Melosh et al., 1992) based on the Los Alamos SALE 2D program (Amsden et al. 1980) to model impact fragmentation. The hydrocode, which keeps track of stress wave propagation and interaction, includes a physical model for the formation and growth of cracks in brittle media, based on the work of Grady and Kipp (1980) on fragmentation in oil shale. The hydrocode program provides us with a means for calculating the outcome of a given impact event, and ultimately enables us to study problems outside the reach of laboratory investigation. Laboratory data permits us to gauge the success of the numerical calculations at small size scales.
Here is an example of a typical hydrocode grid. Laboratory impact modeling requires a grid resolution adequate to resolve the incoming stress wave and determine its accompanying modes of failure. Generally, we find a mesh of 12 X 24 cells (where 12 cells define the target radius) sufficient to produce highly accurate results for targets from 2 to 12 cm in diameter.
Final pressure (left) and damage (right) contours for the disruption of a 5.0 cm radius basalt target by a projectile travelling at 3.2 km/s. The undamaged region (inside the contour lines on the right) indicates the largest fragment post-impact.