PSI - Issue 79

310 America Califano et al. / Procedia Structural Integrity 79 (2026) 306–312 sphere and the fibril are in contact, therefore they move simultaneously: ( ) , the blue curve, and ( ) , the red dashed curve, are overlapped. As the fibril is pulled by the sphere, it starts to elongate and, thus, the ( ) increases (black dashed curve). As soon as the detachment criterion is met ( i.e. , = ), the time instant of first detachment ( 0 ) is identified and ( ) becomes zero.

Fig. 2. Sphere’s displacement ( ( ) , blue curve), fibril’s displacement ( ( ) , red dashed curve) and the stress on the fibril ( ( ) , black dashed curve) At this point, the fibril starts to relax (the red dashed curve decreases along a negative exponential curve), while the sphere goes on with its harmonic motion. There is, then, a time instant in which the sphere and fibril re-attach, 1 , and move together again. The cycles of detachment/re-attachment are clearly visible in Fig. 2. In addition, it can be highlighted that from the second cycle on the detachment/re-attachment phenomenon stabilizes, namely the fibril’s stress curve keeps a given behavior for the analysed number of cycles. Considering, now, a carpet of one hundred fibrils, the ( ) is reported in Fig. 3 for the innermost fibril (blue curve), the outermost fibril (yellow curve) and the mid one (red curve), respectively. In particular, the total force is plotted versus the displacement of the sphere’s centre. Such total force is computed as the integral sum of the stress of the fibrils over the circular area of interest, namely = ∫ ( , ) 2 (9) In addition, Fig. 4 shows, in agreement with Fig. 2 and Fig. 3, that the phenomenon stabilizes quickly. The preliminary results shown here highlight that the proposed methodological approach, despite being quite simple in its present form, provides promising results, which are physically reasonable. It is clear that, in order to model the dynamic contact behaviour between viscoelastic and rigid bodies, the approach needs to be refined by introducing, step by step, the aspects of the actual problem (frequency effect, degradation of material properties over time, friction).