Methods:

\label{methods}

Validation of MPM:

\label{validation-of-mpm}
To validate the accuracy of the Material Point Method in a penetration and damage experiment on soft materials, it was chosen to investigate the method against a problem with existing physical and computational studies. For this purpose, the method is validated against the impact and penetration of a spherical steel projectile into a ballistic gelatin sample. In addition to being a thoroughly investigated problem in both the physical and computational domains, the underlying mechanics behind the problem are generally suited towards an MPM study. Primarily, this revolves around the formation of the cavity seen in a sample after the impact occurs. The formation of the cavity in the sample after impact is a complex relationship of the strength of the gelatin coupled with a pressure buildup within the cavity itself. Since the MPM grid stores this pressure information in this void space, it could potentially serve as a more accurate methodology for such a problem.
The geometries and most material properties for this validation study were done using the findings of Y. Wen, et al [ref#]. In this study, a spherical steel projectile of varying radii and initial velocities are impacted into a rectangular ballistic gelatin sample. This validation uses the results of one of the studies, specifically using a projectile of radius 4.2 mm, with an initial velocity of 729 m/s. The rectangular block takes the dimensions of 250 x 200 x 330 mm, with the projectile oriented to impact the x-y face at its center, travelling along the z-direction. The projectile is initialized a distance of 10 mm from the sample at the initial timestep, as initializing a stationary object in the same grid cell of a initially moving object can potentially cause initialization errors with certain contact definitions. A image of the created particle mesh for this study can be seen in the image below.