Issue 29

M. Marino et alii, Frattura ed Integrità Strutturale, 29 (2014) 241-250; DOI: 10.3221/IGF-ESIS.29.21 246 The finite-element mesh has been obtained by triangular elements, based on a pure displacement formulation with quadratic displacement shape functions. Resulting from a numerical convergence analysis, computational mesh consisted in about 150.000 elements. In order to deal with convergence issues related to contact non-linearities, a mesh refinement around the pin-plate interface, characterized by an average mesh size of about 0.1 D , has been employed. As reported in Tab. 1, stiffness properties for fiber and matrix constituents are taken from [10]. In Tab. 1, strength properties for composite constituents (needed for Huang’s criterion and chose from [10]) are also reported. For the sake of simplicity, proposed results are based on the assumption of symmetric tensile/compressive strength of all constituents. Moreover, the undamaged CSM is treated as an isotropic linearly elastic material (with engineering constants CSM E and CSM  ) whose damage is predicted through the Von Mises criterion (with strengths / CSM S   ), [17]. Finally, the pin is assumed to comprise an isotropic linearly elastic material (with constants p E and p  ), and no damage is modeled for it. In Tab. 2, the mechanical strength of the GFRP Laminate (needed for the Rotem’s criterion), experimentally determined in [9], are also provided. Fibers: f f S S    2.5 GPa Matrix: m m S S    26 MPa A T f f E E  50 GPa m E 1.4 GPa m  0.4 A T f f    0.18 Pin: p E 210 GPa p  0.3 CSM: CSM CSM S S    250 MPa Others: q (Huang) 5 CSM E 12.41 GPa  100 CSM  0.4 N 20 Table 1 : Undamaged material properties of the layer constituents, CSM, pin and other model parameters [10,14,17,16]. Laminate: A S  222 MPa A S  201 MPa T S  71 MPa T S  81 MPa AT S 128.17 MPa Table 2 : Mechanical strength of the GFRP laminate [9]. The numerical model is based on an incremental displacement approach driven by the pin position. The plate damage has been evaluated with an iterative numerical procedure, summarized in the flowchart depicted in Fig. 3. In detail, after the geometric modeling, equivalent homogenized material properties are locally assigned for each element on the basis of the laminate theory [12] and by adopting the afore-mentioned homogenization technique. At each incremental step, FEM- based solution allows to compute the increment of the strain field d  representing an average measure along the laminate thickness for the overall laminate. By involving the constitutive relationships, the incremental field d  is used to compute the increment of the average stress field for the laminate, as well as (if necessary) the increment of the stress field in each layer and in its constituents. Accordingly, addressing the actual stress field, obtained by superimposing stress increments, a given failure criterion is employed in order to verify possible damage occurrence. If failure conditions are not detected for undamaged constituents, the geometry of the pin-plate system is updated, fibers packaging is updated on the basis of the computed strain field increment, and the value of pin displacement is increased to perform the analysis of a new incremental step. Otherwise, if damage locally occurs, material properties are locally altered by employing the degradation law previously introduced. In order to check if progressive material degradation occurs at that step, the actual incremental step is repeated with the same geometry and under the same boundary conditions until further material failure is no longer detected in the overall computational domain. If this iterative procedure is repeated for a number N of occurrences (see Tab. 1), the global failure condition is assumed to be reached and the numerical integral of the