tesi A. Caggiano.pdf - EleA@UniSA - Università degli Studi di Salerno

1.2. Theoretical proposals for concrete-like materialsthe smeared crack approach suffer a strong FE-size dependence of the localizationband width [Oliver, 1989, Rots et al., 1985]. Different regularization procedures havebeen proposed to avoid this severe deficiency of the smeared-crack approach [Willamet al., 1984]. On the one hand, several continuum models are based on fracture mechanicsconcepts leading to fracture energy release regularization, but still sufferingfrom loss of objectivity of the deformation pattern [Etse and Willam, 1994]. In this field,fracture energy-based concrete models are, among others, due to Bazant and Oh [1983],Shah [1990], Carpinteri et al. [1997], Comi and Perego [2001], Duan et al. [2007] andMeschke and Dumstorff [2007]. On the other hand, more sophisticated constitutivetheories have been proposed to solve the strong mesh dependency which appearswhen the governing equations turn ill posed [Carosio et al., 2000]. They are based onrate dependency, higher strain gradients, micropolar theory, etc. Among others, it canbe here referred the contributions by Vardoulakis and Aifantis [1991], de Borst et al.[1995], Peerlings et al. [2004], Lee and Fenves [1998] and Etse et al. [2003].Figure 1.4: Numerical specimens based on the Element-Free Galerkin method by Belytschkoet al. [1995] for near-tip crack problems.Discrete Crack Approaches (DCAs) aimed at incorporating strain or, moreover, displacementdiscontinuities into standard FE procedures have progressively became anattractive and effective alternative to the smeared-crack approach. Several proposalsare currently available in literature to introduce crack discontinuities within FEdomains and are outlined in the following paragraphs.Element-Free Galerkin (EFG) method: this represents an attractive tool to model thecrack propagation in brittle materials. The EFG approach differs from the classicalFinite Element Method (FEM) because the discretization is achieved by only nodal data11