This problem considers the linear elastic response of a center crack in a planar "test specimen" to an imposed tensile loading. From symmetry of the geometry and loading, we consider just one quarter of the domain: a half-crack of length μ1 in a slab of half-thickness unity and of half-length (hence aspect ratio) μ2. Our intermediate output is the compliance — displacement-stress product over the loaded boundary — which is equivalent to the total strain energy (per unit depth); our "final" output — the square root of the derivative of the compliance with respect to the crack length — is the Stress Intensity Factor (SIF). The SIF is crucial in the analysis of cracks and failure.
From the physical point of view, this Worked Problem emphasizes the scaling of the Stress Intensity Factor with geometric parameters; the connections between the total strain energy (or compliance), the Energy Release Rate (ERR), and the Stress Intensity Factor (SIF); and the application of the Energy Release Rate and Stress Intensity Factor to the prediction of (i) brittle failure by Griffith's criterion, and (ii) fatigue-induced crack growth by Paris's law.