Validity of linear elasticity in the crack-tip region of ideal brittle solids

It is a well known that, according to classical elasticity, the stress in the crack-tip region is singular, which has led to a debate over the validity of linear elasticity in this region. In this work, comparisons of finite and small strain theories have been made in the crack-tip region of a brittle crystal to comment on the validity of linear elasticity in the crack tip region. We find that linear elasticity is capable of accurately defining the state of stress very close (~1 nm) to a static crack tip.