Saint-Venants principle and the plane elastic wedge

The stress field due to self-equilibrating loading on the inner or outer arc of a plane strain elastic wedge sector is affected by two agencies: a geometric effect of increasing or decreasing area, and decay as anticipated by Saint-Venants principle (SVP) . When the load is applied to the inner arc the two effects act in concert ; however, when the load is applied to the outer arc the two effects act in opposition and for a wedge angle in excess of the half-space, 2α > π, for the symmetric case, and for 2α > 1.43π for the asymmetric case, the geometric effect is dominant over Saint-Venant decay and stress level increases as one moves away from the outer arc, confirming the inapplicability of SVP. This is additional to previously reported difficulties at these angle when a self-equilibrated load on the inner arc decays at the same rate as does a concentrated moment, and is explained in terms of the interaction of a near-field geometric effect and a far-field stress interference effect at a traction-free edge. For wedge angle 2α = 2π the unique Modes I and II inverse square root stress singularities at the crack tip, which are at the heart of Linear Elastic Fracture Mechanics (LEFM) , can be attributed to this inapplicability for just one symmetric and one asymmetric eigenmode.