PSI - Issue 44

Amparo de la Peña et al. / Procedia Structural Integrity 44 (2023) 2144–2151 Author name / Structural Integrity Procedia 00 (2022) 000–000

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(Figure 4) . This variation can also be explained by the increase of density during the progressive squashing phenomena. The design of the damper presented in section 3 has been carried out by considering the properties determined in the four-layer AFM test. In particular, the values considered are derived from a pre-squash procedure aimed at increasing both the yield stress of the material and the elastic modulus. The pre-hardening procedure consists of the following steps: i) Pre-loading of the AFM up to a strain level of about 30%. The stress corresponding to that strain level ( i.e. , 7.1 MPa) is the yield stress of the foam; ii) Unloading up to a strength value equal to zero. This point will be subsequently considered the new origin of the stress-strain diagram; iii) Reloading of the specimen up to a total strain equal to 60%. The stress corresponding to that strain level ( i.e. , 10.8 MPa), represents the maximum stress the AFM can be subjected to. Through this procedure, the rise of the elastic module of the AFM reaches a value about ten times higher than the initial one, providing the device with sufficient stiffness. 4.3. ABAQUS simulation In order to evaluate the behaviour of the device, a Finite Element Model has been developed in Abaqus code. The set-up of the FE model consists of a series of steps: defining the geometry of the elements, modelling the material properties, defining the boundary conditions and choosing the element type and mesh size. The objective is to define a solid three-dimensional model constituted by seven elements: the external tube, the endplates, the bearing plate, the AFM layers, the top and bottom wedges and the springs (Figure 5) . The geometry of such parts has been generated by means of the modelling tools available in ABAQUS. In particular, the plates have been defined through extrusion of their cross-section, while the external tube and the AFM layers have been defined by re-volving half their vertical section around its axis. The material properties were subsequently introduced. The AFM layers have been defined though inelastic properties considering the experimental test carried out and detailed in section 4.2, whereas the external tube, the wedges and the plates have been defined as elastic ones. The springs are characterized by a stiffness of 2kN/mm and are pre-elongated 70 mm before the analysis. The interaction among the various elements has been defined according to a surface-to-surface formulation with finite sliding. In the normal direction a “hard contact” has been used, while in the tangential direction a friction coefficient equal to 0.6 has been adopted for the contact between the top and bottom wedges and 0.2 has been assumed for the rest of the surfaces in contact.

Figure 5. Finite element model The FE model has been analysed by applying a boundary condition to the top wedge with a cyclical history characterized by a constant amplitude of 5 mm, leading to a total stroke of 50 mm in the AFM layers. the movement of the bottom wedge increases progressively until the last cycle, in which the movement is evident. Figure 6 (a) shows the analysis results in terms of force-displacement curves regarding the bearing plate, whereas Figure 6 (b) represents the curve corresponding to the top wedge. The results shown in (a) illustrate the displacement accumulation during the cycles up to 50 mm, which represents the maximum stroke of the AFM. The progressive displacement of the bearing plate is the one expected, as the plastic deformations are absorbed by the wedge system in each cycle. In fact, the curve in (b) demonstrates the correct activation of the wedge system. Once the gap between the top and bottom wedge is generated, due to the plastic deformation, the pre-elongated springs pull the bottom wedge