Damage as a function of distance to a point

Hi all, I am trying to start a convection-diffusion process in a simple geometry. I want it to start after "damage" is applied. Damage is only present in some parts of the geometry so I want it to initialize as a function of distance to a point of the geometry. So in the regions where damage is present the process starts and if damage is not presence there is no change.

How can I do that?

Thank you