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Dynamic earthquake rupture simulations are used to understand earthquake mechanics and the ground shaking that earthquakes produce. These simulations can help diagnose past earthquake behavior and are also used to generate scenarios of possible future earthquakes. Traditional dynamic rupture models generally assume elastic rock response, but this can lead to peak on‐fault slip rates and ground shaking that are higher than those inferred from seismological observations. Some have approached this challenge using inelastic off‐fault rock behavior to dissipate energy, but the addition of inelasticity can make it difficult to select parameters and establish suitable initial conditions, and increases the model’s complexity and computational cost. We propose a new method that works by adding a nonlinear radiation damping term to the friction law, with the surrounding rocks remaining linear elastic. Our new method results in lower peak slip rates, reduced seismic radiation, and an increasing slip‐weakening critical distance with increasing rupture propagation distance, all within a linear elastic model. In addition, it is easy to implement. more...