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Previous efforts have modeled the Didymos system as two irregularly shaped rigid bodies, although it is likely that one or both components are in fact rubble piles. Here, we relax the rigid-body assumption to quantify how this affects the spin and orbital dynamics of the system following the DART impact. Given known fundamental differences between our simulation codes, we find that faster rigid-body simulations produce nearly the same result as rubble-pile models in scenarios with a moderate value for the momentum enhancement factor, $β$ ($β{\sim}3$) and an ellipsoidal secondary. This indicates that the rigid-body approach is likely adequate for propagating the post-impact dynamics necessary to meet DART Mission requirements. Although, if Dimorphos has a highly-irregular shape or structure, or if $β$ is unexpectedly large, then rubble-pile effects may become important. If Dimorphos's orbit and spin state are sufficiently excited, then surface particle motion is also possible. However, these simulations are limited in their resolution and range of material parameters, so they serve as a demonstration of principle, and Future work is required to fully understand the likelihood and magnitude of surface motion.