PSI - Issue 33

Umberto De Maio et al. / Procedia Structural Integrity 33 (2021) 954–965 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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behavior is simulated by means of the cohesive zone method, assuming that the cohesive traction vector coh t , acting along the crack faces, is parallel to the displacement jump vector and characterized by the following cohesive expression: ( ) ( )    = = with max coh history f t   (6) where ( )  f is a classical softening function for pure mode I (see Fig. 2b), and  is the maximum value attained by the effective displacement jump over the entire deformation history. Finally, the stress field of the cracked finite element must satisfy the following equilibrium condition with the cohesive tractions at the crack faces: ( )   +   = −    s c s f   C u b n  (7) Moreover, unlike for alternative models based on the strong discontinuity approach which use crack tracking procedures to avoid crack locking phenomena due to a bad prediction of the maximum principal stress direction in the element, the ECM incorporates an adapting crack approach which allows the crack to adapt itself to the later variations in principal stress direction, computing the vector + b and n at each simulation step until a threshold value of the crack opening is reached (Sancho et al., 2007). 3. Numerical results This section provides the numerical results of the cracking analyses performed by the adopted fracture models. In particular, it starts with the simulation of a plain concrete specimen under mode-I loading conditions, in which the crack path is a priori known, then move to a mixed-mode one. Suitable comparisons with available experimental and numerical results are reported and discussed. 3.1. Mode-I crack propagation analysis The effectiveness of the DIM and ECM models in predicting cracking behavior in quasi brittle materials, has been here demonstrated by performing a wedge splitting test, already experimentally analyzed by (Xiao et al., 2004), involving a ultra-high strength concrete (UHSC) specimen, whose geometric configuration and boundary conditions are illustrated in Fig.3.

Fig. 3. Wedge splitting test: (a) geometric configuration and boundary conditions (all dimensions are expressed in mm); (b) the unstructured and (c) structured tessellations performed in the damage zone for the DIM and ECM simulations, respectively.