Application of harmonic mean values of energy quantities of elastic deformation in fracture criteria (Q2760646)

It is known that, in a neighborhood of a crack vertex, the stress fields have singularities of type \(r^{-1/2}\), where \(r\) is the distance to the crack vertex. Hence, the fields of energy variables have singularities of type \(r^{-1}\), and their mean values cannot be found in terms of the usual integration. The author proposes to calculate the harmonic mean values of energy variables, and use them in formulating fracture criteria.