PSI - Issue 8

A. De Luca et al. / Procedia Structural Integrity 8 (2018) 288–296 A. De Luca/ Structural Integrity Procedia 00 (2017) 000 – 000

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characterized by an average mesh size equals to 0.3 mm, (27336 nodes and 27334 elements). The penalty contact formulation has been considered for the contact definition between the impactor and the laminate. The impact location is in the center of the plate.

Fig. 1. (a) FE model; (b) composite layup.

All impact simulations are characterized by a drop mass of 2 kg. In particular, five different initial velocities of the drop mass have been considered, by changing the initial velocity of the drop mass, in order to achieve the impact energy levels of 5 J, 10 J, 15 J, 20 J and 25 J, respectively. Intra-laminar failures, such as fibre and matrix failures, have been modelled according to Hashin criteria. Inter-laminar damages have not been considered within such model. Before updating the stress-strain, it is need to damp-out all vibrations produced by the impact. In fact, since the LVI is simulated by means of an explicit analysis, if no-damping factor is introduced in the material properties, the laminate will keep vibrating without reaching own equilibrium and the Lamb wave propagation will be performed on to a vibrating plate, which vibration amplitudes are bigger than the ones produced by the actuator. Considering damping properties of the material increases the computational costs of the LVI simulation. For such reason, in this section, a different technique is proposed to damp-out such vibrations. The damping-out of vibrations can be also performed by introducing a load step after the LVI one, characterized by the application of a viscous pressure (Equation 1) on to the plate allowing the plate to reach quasi-static equilibrium in a minimal number of increments. = − (1) where p is the pressure applied to the body; cv is the viscosity; v is the velocity vector of the point on the surface where the viscous pressure is being applied and n is the unit outward normal vector to the surface at the same point. The choice of viscous pressure coefficient (cv) is critical for using the technique effectively. Typically it is set equal to a small percentage (1% or 2%) of ρcd (Equation 2): = √ (1− ) (1+ )(1−2 ) (2) So when the velocity is equal to 0, the applied pressure is equal to 0.

2.2. PZT sensor modelling

An important aspect of the numerical simulation consists of the PZT sensors modelling. According to piezo electric definition, PZT sensors convert the electrical field in the deformation field, imposing a vibration in the plate. Consequently, the actuation signal has been modeled by introducing the displacement produced by the applied