Brittle failure in infinite domain??

Hi Everyone,

I am trying to understand what does "Brittle failure in infinite domain" means. Let me explain more:

Imagine that you have a configuration, here I choose a crack. My concern is not the crack tip. Imagine that for some reasons, somewhere along the crack, the displacemnt wants to become infinite (the solution from elasticity with considering full elastic behavior for material propose that). And we now that it is not possible, so the material will break, or goes to plastic deformation in that region. I understand that in brittle materials when the stress increases, the material will break with almost no plastic deformation. But what if the domain is infinite? what does failure mean here? it cannot break because it is infinite length. is there a plastic deformation? if there is what model will describe it best?

Thanks,

Navid Zolfaghari

P.S. My brittle material is rock.