Issue 47

M.F. Funari et alii, Frattura ed Integrità Strutturale, 47 (2019) 277-293; DOI: 10.3221/IGF-ESIS.47.21 281 where r is the parameter used to describe fracture in different material and   , IC IIC G G are the total area under the traction separation law. Moreover,   , I II G G are the individual ERRs, which correspond to the integral function of the TSL defined in terms of the maximum opening/axial stresses and displacements. For the sake of simplicity, classical bilinear relationships of the TSL are assumed in the present paper, whilst the generalization to more complex cases can be implemented straightforward. Boundary and initial conditions at the crack tip front are verified by enforcing a rigid displacement of the process zone on a specific length, namely  , at the extremities of the computational nodes. This choice ensures that the NL involved in the debonding mechanisms are constrained to a small portion containing the process zone, reducing the total complexities of the model. Consequently, the following boundary conditions should be considered in the analysis:     1 j j j j X X X X      with   0 j j f g X  and   0 j f g X    (5) where + or – refer to the Right or Left debonding crack fronts, respectively, and   , j j X X   correspond to the coordinates of the extremities of the debonding region (Fig.2). It is worth noting that the conditions in Eqs.(5) are prescribed by means of a simple procedure, which consists, at first, to predict the values of the fracture function at the extremities of the debonding region and, subsequently, to enforce that each step of the crack growth corresponds to a null value of the fracture energy. Therefore, by using a linear approximation function along the debonding region, the current nominal crack tip displacements can be expressed by means of the following relationships:       0 0, 0 j f j j j j f f j j j j f f g X toll X g X g g X toll g X             (6) Figure 3 : Moving and referential coordinate systems for core domain. Core debonding crack growth The evolution of preexisting cracks in the core is simulated by the generalization of the formulation developed in previous subsection to a two-dimensional domain. Two configurations are introduced to describe the mesh motion defined as referential or material ones. The latter is modified by the geometry variations produced by the crack advance, whereas the