Earthquake ruptures dynamically activate coseismic off-fault damage around fault cores.Systematic field observation efforts have shown the distribution of off-fault damage around main faults, while numerical modeling using elastic-plastic off-fault material models have demonstrated the evolution of coseismic off-fault damage during earthquake ruptures. Laboratory-scale microearthquake experiments have pointed out the enhanced high-frequency radiation due to the coseismic off-fault damage. However, the detailed off-fault fracturing mechanisms, subsequent radiation, and its contribution to the overall energy budget remain to be fully understood because of limitations of current observational techniques and model formulations. Here, we constructed a new physics-based dynamic earthquake rupture modeling framework, based on the combined finite-discrete element method, to investigate the fundamental mechanisms of coseismic off-fault damage, and its effect on the rupture dynamics, the radiation and the overall energy budget. We conducted a 2-D systematic case study with depth and showed the mechanisms of dynamic activation of the coseismic off-fault damage. We found the decrease in rupture velocity and the enhanced high-frequency radiation in near field due to the coseismic off-fault damage. We then evaluated the overall energy budget, which shows a significant contribution of the coseismic off-fault damage to the overall energy budget even at depth, where the damage zone width becomes narrower. The present numerical framework for the dynamic earthquake rupture modeling thus provides new insights into earthquake rupture dynamics with the coseismic off-fault damage. Plain Language SummaryThe medium surrounding fault cores can be damaged due to stress concentration caused by the dynamic earthquake ruptures propagating on the faults, which is called coseismic off-fault damage. Systematic field observation efforts have shown the distribution of off-fault damage around main faults, while numerical modeling has demonstrated the evolution of off-fault damage during earthquake ruptures. Laboratory-scale microearthquake experiments have pointed out the enhanced high-frequency radiation due to the off-fault damage. However, the detailed off-fault fracturing mechanisms, subsequent seismic wave radiation and its contribution to the overall energy budget remain to be fully understood. Here, we constructed a new physics-based dynamic earthquake rupture modeling framework to investigate the fundamental mechanisms of coseismic off-fault damage and its effect on the rupture dynamics, the radiation, and the overall energy budget. We found the enhanced high-frequency radiation in near field due to the coseismic off-fault damage. We then evaluated the overall energy budget, which shows a significant contribution of the coseismic off-fault damage to the overall energy budget even at depth. The present numerical framework for the dynamic earthquake rupture modeling thus provides the insight into the earthquake rupture dynamics with the cosei...