Issue 17

E. Benvenuti et alii, Frattura ed Integrità Strutturale, 17 (2011) 23-31 ; DOI: 10.3221/IGF-ESIS.17.03 28 Figure 6 : Tensile specimen geometry after Seweryn (1994). The limit tensile stress which was indicated by Seweryn is 105 MPa. As soon as the bulk reaches the critical damage 0.01 cr D  , the continuous-discontinuous transition is activated. Figure 7 : Constitutive law of the PPMA which has been adopted in the numerical tests. The meshes which were adopted are refined in the central zone as shown in Fig. 8. A minimal value of the finite element size h=0.1 mm was used for all opening angles (semi-opening angle  = 10, 20, 30, 40, 50, 60, 70 degrees). In the case of a tensile plate made of a softening materials, it was shown in Benvenuti [19], that the optimal value of the parameter  which leads to optimal convergence is  = 1/13.33 h which in the present case leads to  = 0.0075 mm . In order to check the ability of the method to effectively approximate the experimental failure loads, a unique value of the ratio between the minimal mesh size h and the parameter  was adopted for all meshes. In order to identify the optimal value of the regularization length  , the following values have been adopted:  = 0.0 001, 0.002, 0.0075, 0.01 mm . The critical failure load versus half the opening angle of the notch are displayed in Fig. 8. In particular, the value of  = 0.0001 mm leads to divergent results, while the value  = 0.0075 mm leads to the best approximation. Fig. 10 shows the computed failure loads for various opening angles and the experimental values from Seweryn [2] by using  = 0.0075 mm.