The ballistic gelatin uses a compressible Neo-Hookean formulation for the deviatoric portion of the elastic stress contribution, with the Mie-Grunieson equation of state contributing the hydrostatic portion of the elastic stress tensor. When the material reaches the yield stress, the model uses a linear plasticity model to calculate the plastic strain of the gelatin. When a maximum principal strain of 0.7 is reached, the material is considered failed. In Uintah, when a material element has failed, it is considered to no longer be able to support stress, and is free to deform accordingly. Element deletion techniques are in place during this study, as the deformation of these failed elements can lead to negative Jacobians in our deformation gradients, causing the simulation to crash. While this simulation sees the deletion of a number of elements due to the magnitude of the element deformations, it is applied less liberally than in a finite element method, where the deletion method is required for any cavity to form. The constitutive model of the metal also uses the compressible Neo-Hookean formulation, although any model could be used for this structure. Due to the large difference in strength between the two materials, there is an insignificant amount of deformation seen in the projectile as long as the correct material properties have been used.
Mesh and Model Development:
\label{mesh-and-model-development}
Material Properties:
\label{material-properties}
The material properties used in developing the penetration model of the human leg are tabulated below: