Stress rate for Johnson-Cook material model

I am using Johnson-Cook material model to simulate foam response, but am confused about which stress rate definition the material model uses. The manual mentions that Abaqus/Explicit uses Green-Naghdi stress rate for viscoelastic materials, but the Johnson-Cook model definition shows viscoplastic behavior, while the elasticity limi depends on the strain rate. Thus I am confuesd if Abaqus/Explicit uses Jaumann or Green-Naghdi stress rate for Johnson-Cook material model. Can someone please guide me,