Issue 47

M.F. Funari et alii, Frattura ed Integrità Strutturale, 47 (2019) 277-293; DOI: 10.3221/IGF-ESIS.47.21 279 core. The proposed strategy explores the possibility to combine different crack growth phenomena. In detail, interface debonding phenomena at core/skin interfaces are simulated by using a weak-based moving interface strategy. Moreover, the evolution of internal cracks in the core is predicted by using a strong-based ALE strategy, in which the governing equations are expressed in the moving ALE coordinates by means of transformation rules between moving and fixed referential configurations and proper crack growth functions to identify the crack tip motion. The model is implemented numerically by using a finite element approximation. This allows the development of a series of numerical results demonstrating the effectiveness of the method to simulate both the interfacial debonding and the crack propagation in the sandwich core. Experimental tests are also performed in order to analyze the fracture parameter of a commercially available foam that are commonly used as core material in real applications. The actual material properties experimentally obtained are employed to inform the numerical simulations. T HEORETICAL FORMULATION he proposed model is formulated in the framework of a two-dimensional idealization of a sandwich structure. It consists of an internal core, modelled by means of a plane stress formulation, and two external skins, following a Timoshenko beam kinematic. The formulation is able to predict crack growth of material discontinuities, which may affect the skin/core interfaces and the core. At interface level, this is achieved by the use of moving interface elements, which ensure an accurate description of the fracture variables in the process zone in terms cohesive Traction Separation Laws (TSL). For the core region, a generalization of the above interface model is proposed, since the crack tip may evolve in the two-dimensional domain. A synoptic representation of the model is reported in Fig. 1, where, without loss of generality, an initial crack length is assumed in both interface and core. Figure 1 : Schematic representation of the sandwich structure: interfacial and core macrocracks. Interface/core debonding phenomena ALE strategy is implemented in the interface regions to accurately describe the evolution of debonding phenomena. In particular, moving cohesive interface elements simulate the traction forces produced by the evolution of material discontinuities. Cohesive constitutive laws are parametrized in terms of a moving interface coordinate system in order to simulate the motion of the process zone acting at the skin/core interfaces. From the mathematical point of view, the parametrization of positional variables is expressed as a function of two configurations, i.e. Referential Configuration (RC) or Moving Configuration (MC). The relationship between RC and MC coordinates of each particle is descripted by the mapping operator  (Fig.2), as follows:   , : X t with RC MC      (1) where  and X are the referential and moving coordinates, respectively. The mesh motion is expressed, by introducing the regularization or rezoning equations, defined in terms of the mesh displacement function X  of the computational nodes. T