Issue 45

L.M. Viespoli et alii, Frattura ed Integrità Strutturale, 45 (2018) 121-134; DOI: 10.3221/IGF-ESIS.45.10 126 A mean SED exceeding a critical value leads the material to failure. The condition of resistance results to be:  C W W In the hypothesis the material is characterised by an ideally brittle behaviour and adopting Beltrami’s failure criterion, the critical value of mean SED is a function of the ultimate stress, that is:   C R W E 2 / 2 The critical radius on which to compute the averaged SED is a property typical to the material and depends on its toughness. Considering a notch of zero opening angle and a null Mode II contribution due to symmetry of geometry and loading conditions, the N-SIF can be correlated to the mean SED:           E K W R I 1 1 1 1 1 4 which, at the critical conditions, becomes:                     R R K R f R I 1 1 1 1 1 1 1 1 2   2 being f 1 a function of the opening angle. Noting that, when the V-shaped notch opening angle is null, the notch constitutes a crack and the N-SIF coincides with the toughness of the material for LEFM.          C IC R K K f R 0.5 1 1 0 0 So, the critical radius of the volume on which to compute the mean SED results:            IC R K R f 2 1 0 R APID SED COMPUTATION IN VIRTUE OF MESH REFINEMENT INSENSITIVITY n order to give a mathematical explanation to the Strain Energy Density mesh-refinement insensitivity, it is necessary to recall some of the fundamentals of the Finite Element Method [21] in linear elastic analysis. Starting from the fundamental laws in the finite element method, it is possible, with some passages [10], to express the SED stored in an element as:        t t E d K d 1 2 where:   d is the nodal displacements vector and   K is the elemental stiffness matrix. I