Linear elastic fracture mechanics, abbreviated LEFM, is an approach to
fracture mechanics ("how shit breaks" in layman's terms) that assumes the material in question behaves according to
Hooke's Law. LEFM is used to model the very complex behavior of materials under stress, especially those with preexisting cracks, voids or other imperfections & anomalies. Many materials have linear elastic behavior over a small range of stress. LEFM assumes a much simplified model of how the material behaves over most ranges of stress, which is
good enough and conservative enough to be used safely.
LEFM is one of the assumptions used to define the stress intensity factor, K. This factor is important, as when it rises above a critical value, Kc, brittle fracture can occur. In other words, all hell breaks loose. No bending (aka plastic deformation), no creaking, no crack propogation, no slip, just instant catastrophic failure.
LEFM is also used to determine the stresses caused by a crack in a material. Contrary to popular belief, cracking isn't always such a bad thing. As long as the stresses at the crack tip (which are characterized by K) are low enough, the plastic zone (in metals) or craze zone (in ceramics) will prevent the crack from propagating.
Node what you know. Node your homework. Thank you Georgia Tech and ME3201.