Issue 17

E. Benvenuti et alii, Frattura ed Integrità Strutturale, 17 (2011) 23-31; DOI: 10.3221/IGF-ESIS.17.03 27 The damage is calculated as   0 ( ) ,1 ( , ( ) ) [0, )            c cr eff q r D max D r max r max σ t t r (9) where q is an internal variable defined as 0 0 0 0 ( ) ( 2 )     s r r q r r exp H r r r (10) and 0 r is an initial threshold, which is set equal to the maximum tensile stress, which can be deduced from the experiments. The variational formulation which has been adopted makes it possible to recover standard cohesive model for vanishing regularization length. Moreover, the ductility of the computed structural paths turns out being proportional to  itself. Details can be found in previous References [17-19]. Figura 5 : Thin process zone enrichment. The enrichment strategy is general: it can be applied to both the cases of thin and thick process zone. More precisely, the width of the enrichment layer can be larger than a single layer of finite elements. In this case, the model can be seen as an XFEM with cohesive crack. Alternatively, the width of the enriched volume can be larger than a single layer of finite elements, similarly to what happens in a non-local integral model. The enrichment strategy has been thoroughly discussed in a previous Reference [17]. In the present preliminary analysis, the analysis is applied to very brittle materials such as the PMMA. To this purpose, only one layer of finite elements has been enriched, as shown in Fig. 4, where represents the width of the truncated support of function    In the present analyses contributions of Gauss points placed at distances larger than 20  were neglected. Moreover, the nodes marked with a red square indicate the enriched nodes, while the nodes which are not enriched are indicated by a green circle. The enriched elements have been indicated in light gray. N UMERICAL RESULTS he PMMA tensile specimen experimentally tested by Seweryn [2] has been considered (Fig. 6).The width W is 109 mm, while the thickness is equal to 4 mm. The notch depth a = 27 mm. In view of the symmetry of both geometry and loading, only one half of the specimen was studied. A plane stress two-dimensional analysis was performed. The constitutive law for the PMMA, which is shown in Fig. 7 for the one-dimensional case, has been adopted according to the material parameters given in Seweryn (1994). In particular, Young modulus E=3200 MPa, Poisson coefficient equal to 0.4 and a maximum effective stress 105 MPa have been taken. T