High Damping Natural Rubber (HDNR) bearings are characterized by stiffness and damping capacity that significantly depend on the shear deformation amplitude. More in details, at low deformations stiffness and damping increase, whereas at large deformations the stiffness remarkably increase but the damping capacity decreases. Additionally, this kind of bearings show a loading hysteresis dependence, due to the internal damage of the rubber occurring as the deformation history progresses. This effect, also known as stress-softening, becomes significant for large deformation amplitudes and represents a source of uncertainty, which has recently caused a limitation of the use of this kind of isolators. However, consequences of this nonlinear beha...