Issue 47

M.F. Funari et alii, Frattura ed Integrità Strutturale, 47 (2019) 277-293; DOI: 10.3221/IGF-ESIS.47.21 278 I NTRODUCTION omposites materials are widely utilized in several applications ranging from aerospace to civil engineering fields [1, 2]. Sandwich structures are a particular class of composites consisting of two thin face sheets made of stiff and strong materials such as metal or fiber reinforced composites bonded to a thick and deformable core with low density [3]. They are able to ensure a good resistance under bending/shear loading, offering a great variety of lightweight structural systems. Unfortunately, sandwich panels are affected by both macroscopic and microscopic damage phenomena, mainly produced by the heterogeneity of the layered systems, which reduce the integrity of the composite structure, leading to catastrophic failure mechanisms [4]. From physical and mathematical viewpoints, two main issues are demanding a detailed understanding of the mechanical behavior of sandwich panels: the propagation of internal macro-cracks in the core [5] and the delamination at face/core interfaces [6]. These problems have been addressed by mean of different numerical approaches, mostly developed in the framework of the Finite Element Method (FEM) due to its versatility to model complex structures. Specific modelling techniques are required to predict crack tip motion of internal material discontinuities. Interface elements based on Cohesive Zone Model (CZM) or Linear Elastic Fracture Mechanics (LEFM) are frequently used to predict crack tip evolution. Discrete or distributed interface elements can be easily incorporated into FEMs, by introducing constitutive traction forces between adherent internal surfaces [7]. These methodologies are frequently used in sandwich structures to predict the crack evolution at the core/skin interfaces, since the crack motion is expressed as a function of a linear positional variable coinciding typically with the interface coordinate. However, such modeling is affected by numerical problems due to mesh dependence, computing inefficiency, and sensitivity to the element aspect ratio. These issues may be partially addressed by adopting a very fine discretization at the crack tip front, but numerical complexity remains, due to the high number of computational points requested. Sandwich structures are also affected also by macro-cracks in the core. Quite complex scenarios are observed in presence of kinking phenomena of the crack, starting from the interfaces. In these cases, the crack growth requires more advanced numerical modeling techniques, since it needs to be expressed both in terms of angle of propagation and tip displacement. The use of CZM is quite cumbersome, since a very large number of interface elements need to be introduced, at least along the path where the crack growth is expected. Alternatively, crack propagation in 2D continuum elements can be achieved by using adaptive mesh refinement methods, in which the element boundaries are coincident with moving internal discontinuities [8]. However, an accurate description in terms of field variable interpolation is needed to describe the updated set of nodes at each mesh adaptation step and the corresponding quadrature points. Moreover, computational errors are introduced due to the projection procedures required by the re-meshing process [9]. Another possibility is to tackle the problem through the Boundary Element Method (BEM). In this case, only the structures boundaries (and not the internal domains) are represented by means of a proper mesh discretization [10]. Although such hypothesis reduces the computational costs required to generate new elements, computational complexity due to the need to define singular integrals remains. Previous formulations are classified in the literature as geometrical representation approaches [11], since an explicit definition of the cracked surfaces is required by the numerical models in order to evaluate the fracture variables and the subsequent crack propagation. Among the formulations in which an implicit crack definition is achieved, Extended Finite Element Method (XFEM) is currently used with success in many practical applications. The basic idea is to use nonconforming elements to model macro-cracks by enriching shape functions of the mesh elements by discontinuity properties. However, a further extension is required to predict fracture variables for nonlinear problems, especially in presence of frictional effects [12]. Moreover, the methodology needs a different number of kinematic variables for each node and thus the total number of mesh points may vary with the crack growth. Others methodologies based on Discrete Element Method (DEM) [13] or MeshFree Methods (MFMs) [14] have been formulated in the last decade, providing valid alternatives to study such problems. Methods based on Moving Mesh technique (MM) provide a feasible and sensible way to predict crack growth mechanisms in continuum media. Early studies were developed in [15], where MM was employed to predict energy release rate by using a virtual crack extension. The Arbitrary Lagrangian-Eulerian Formulation (ALE) was only recently implemented in Fracture Mechanics in [16, 17]. A generalization of the ALE approach was also proposed in the framework of weak based moving cohesive forces, where the interlaminar debonding phenomena are predicted without modifying the formulation of the structural problem [18]. The extension to a generalized crack path is quite rare in the literature, especially in those cases in which a proper prediction of crack angle variability is required. To the authors’ knowledge, only in [19] a generalized mesh refitting procedure applied to a continuum media is developed. The main goal of this paper is to generalize the numerical implementation proposed in [20-22] in the framework of sandwich structures, with the purpose to describe delamination phenomena along the interfaces and macrocracks evolution in the C