Mesh convergence of gradient-enhanced plasticity models in explicit dynamics

Blast experiments on reinforced concrete structures are often limited to small structures and therefore simple shock waves. Complex load scenarios that occur because 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. To address this issue, we incorporate a gradient-enhanced damage formulation into a representative concrete model. This enhancement adds an inertia term to the additional partial differential equation to allow the use of explicit solvers. We further investigate the flow rule and its effect on mesh convergence. Many widely used models employ the radial return algorithm, which assumes a purely deviatoric flow rule. We compare implementations using both the radial return algorithm and an associated flow rule, demonstrating that the radial return algorithm leads to mesh-dependent results even when the damage formulation is omitted. Conversely, using an associated flow rule improves numerical stability and yields converging results.