Blast experiments on reinforced concrete structures are often limited to small structures and therefore simple shock waves. Complex load scenarios that occur as a result of shock wave reflection in larger structures are difficult to realize in practice. Consequently, numerical simulations of shock wave propagation and structural response offer a promising alternative for investigating blast loads on complex structures. Concrete damage models in commercial hydrocodes such as LS-Dyna, Autodyn, and Abaqus are commonly formulated as plasticity models, with damage represented by a reduction of the yield surface as plastic strain accumulates. However, these models are typically local, which can result in mesh-dependent outcomes and undermine the reliability of simulation results. This shortcoming has been mitigated by a gradient-enhanced formulation, that also includes inertia effects to use in an explicit dynamics framework [1]. Nevertheless, the convergence behavior reported in previous work is still not fully satisfactory. In this contribution, we examine the conditions under which the coupled system of PDEs in the gradient‑enhanced model remains strongly elliptic, a requirement for mesh‑objective results. We find that plasticity models with associated flow rules generally retain strong ellipticity, whereas the use of non‑associated flow rules -- common in modeling concrete and particularly in explicit dynamics -- can still lead to non‑converging results even when softening is regularized by a gradient-enhanced formulation. We confirm these theoretical findings through dynamic numerical test cases, showing that associated flow rules yield converging solutions, while purely deviatoric flow rules result in strain localization and mesh‑dependent, non‑converging solutions. [1] Rosenbusch S.M., Balzani D., Unger J.F., Regularization of softening plasticity models for explicit dynamics using a gradient-enhanced modified Johnson–Holmquist model, International Journal of Impact Engineering, 198, 105209, 2025.