Mesh-size independent rigid-body spring network for simulation of the dynamic fracture behavior of concrete

In this study, a numerical approach is developed for simulating the rate-dependent behaviors of concrete without mesh sensitivity. The rheological units (e.g., dashpot) are integrated with the six directional springs in the rigid-body spring network (RBSN) elements to reflect the rate-dependent behavior of concrete. Previously, the viscoplastic damage model was associated with the elemental degrees of freedom. However, in the present approach, a viscoelastic constitutive law is newly defined for the normal direction as a function of the strain rate, from which the internal forces can be updated from the regularized elemental stresses. Such improvements are validated through the numerical simulations of the direct tensile test and spalling test using the modified split-Hopkinson pressure bar (SHPB). The simulated results show consistent structural responses without mesh dependence on the strain rate. In addition, the influences of the softening curve shapes on the crack localizations are examined. It is shown that the rheological parameters can be optimized and determined for consistent applications through virtual experiments. The proposed numerical approach enables the mesh construction procedure without concerning the mesh-size sensitivity due to the strain rate, and various applications are expected for the simulations of detailed numerical models of concrete materials and structures under high loading rates.