## 1 Introduction  
The highly specific stiffness and strength of carbon fiber reinforced plastic (CFRP) materials have led to a progressive increase of their use in the aerospace industry. However, their integration in aeronautical components has been delayed by their high manufacturing costs and their damage mechanisms, which can be hard to predict. As a matter of fact, CFRP structures have been found to be highly sensitive to delaminations, induced by manufacturing defects [1; 2], or resulting from low energy impacts [3; 4]. Indeed, global and local instabilities can result in the growth of a pre-existing delamination, leading to a premature collapse of the structure [5; 6; 7]. Therefore, the development of innovative numerical tools, able to consider the effects of the delamination onset and propagation in complex composite components, has become mandatory. In this scenario, newer and faster methodologies, able to study the delamination growth in a preliminary design stage, are needed to develop less conservative damage tolerant structures. The mechanisms governing the delamination growth in composite structures, mostly under compressive loading condition, have been widely investigated by several authors, from an experimental [8; 9; 10; 11; 12], analytical [13; 14], and numerical [15; 16; 17; 18; 19; 20] perspective. In particular, the compressive behavior of delaminated panels has been simulated, adopting geometrically non-linear analyses, while the onset of the delamination growth has been simulated based on energy release rate (ERR) considerations. In [21], the post-buckling behavior of composite panel with embedded delaminations, subjected to compressive load has been investigated by adopting an analytical procedure based on the Rayleigh-Ritz formulation. The study demonstrated the correlation between the post-buckling response and the delamination growth phenomenon. The compressive behavior of CFRP laminates characterized by multiple delaminations has been investigated both analytically and experimentally in [22]. In particular, the influence of the delaminations on the strength and on the residual stiffness of the structure has been assessed. Finally, the influence of the delaminations location, size, and distribution on the compressive behavior of the laminate has been investigated by means of numerical simulations. In [23], an experimental and numerical investigation on the inter-laminar damage behavior of CFRP stiffened structures is presented. The delamination has been numerically simulated by means of a virtual crack closure technique (VCCT) [24] and the numerical results have been correlated with experiments. A numerical investigation of delaminated CFRP panels has been performed in [25], where an in-house numerical code was used to assess the influence of the delamination growth on the load carrying capability of the laminates. 2D and 3D parametric numerical analyses have been performed on CFRP flat laminates, subjected to compressive load, with two through-the-width delaminations. The delamination growth has been simulated by means of VCCT, and the effect of multiple delaminations on the post-buckling behavior has been analyzed. In [26; 27], an accurate 3D model able to predict inter-laminar crack onset and propagation by means of a cohesive zone model (CZM) was introduced. In [28; 29], experimental/numerical studies focused on the effects of reinforcements to delay the skin-stringer debonding in CFRP components under flexural loading conditions have been presented. In particular, in [28] the effect of the selective stitching on the onset and the propagation of delamination has been assessed, while in [29] a novel numerical procedure able to account the \"Fibre-Bridging\" effect was introduced. In [30], the tensile behavior of notched composite laminates was investigated both experimentally and numerically, assessing the effects of the mutual interaction between inter-laminar and intra-laminar damages.