Issue 17

E. Benvenuti et alii, Frattura ed Integrità Strutturale, 17 (2011) 23-31; DOI: 10.3221/IGF-ESIS.17.03 30 For an opening angle 2 20 deg   , Fig. 11 displays the map of the total stress component yy  in a deformed configuration, which was obtained by using a magnification factor equal to 100. In Figs. 12 and 13, respectively, the total stress map and the profiles of the relevant stress components are reported. In particular, the black cross markers indicate the values of the total stress component at the Gauss points placed along the crack line, while the regularized stress c   are marked with red dots. It can be noted that the total strain attains its maximum value 105 MPa at the notch tip. Because, the enrichment extends over a length of 3 mm beyond the notch tip, a new stress singularity is there detected. An extension of the present approach to other non-linear constitutive laws is possible. However, in XFEM based approaches, in general, a crack tracking criterion has to be adopted in order to avoid that secondary multiple cracks open. This is a requirement common to embedded discrete-crack approaches. In the implicit gradient approach, instead, no hypotheses on the position of the critical points are necessary, because the effective stress is computed by post-processing the results, which are obtained by means of any standard finite element formulation of a continuum model. An advantage of the present approach over existing cohesive models is that, here, the bulk constitutive law of the material can be directly assumed, because the process zone behavior is not modeled by means of a traction-separation law. Instead, the stress and strain fields c  σ and c  ε are introduced, which can be modeled with same constitutive law of the bulk. Figure 11 : Stress map in the deformed mesh for 2  =20 obtained with a magnification factor 100. Figure12 : Total stress map for 2  =20. C ONCLUSIONS n the present note, a new approach based on a length-enriched eXtended Finite Element Method (XFEM) has been applied to the evaluation of the failure loads of tensile PMMA specimens. In particular, a comparison with the experimental results presented by Seweryn [2] has been performed. The present analysis shows that the proposed I