Mesh sensitivity in stress based failure criterion

Hi,

 I want to simulate filaure in cement mortar. I am using Rankine criterion for detecting failure. For propagating damage i want to soften element. Here can I suddenly reduce the stiffness of the element to a negligible value as soon as it reaches specified failure criterion. I read in some book about mesh sensitivity in stress based failure criterion but i could not understand.Can some body expalin what is its consequence of suddenly reducing stiffness of element to a negligible value. How mesh will effect.

With Best Regards

Gouse