PSI - Issue 79

America Califano et al. / Procedia Structural Integrity 79 (2026) 306–312

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vibrations. Therefore, tuning such vibro-adhesion mechanisms may be fundamental for preserving (or, better, improving) the durability of the involved materials and enhancing the load-bearing capabilities. The physical principles behind such vibro-adhesion mechanisms can be rigorously described using classical adhesion contact models. The Johnson – Kendall – Roberts (JKR) (Johnson et al. (1971), Kendall (1971))theory, for example, provides a foundation by modeling elastic contact between deformable bodies where surface energy and deformation are strongly coupled, a framework highly relevant for compliant grippers. In contrast, the Derjaguin – Muller – Toporov (DMT) (Derjaguin et al. (1975)) theory better captures adhesion when dealing with stiffer contacts or smaller radii of curvature, situations that may occur at localized asperities in irregular surfaces. Extensions like the Gent – Schultz (GS) (Gent et al. (1972)) model enrich this understanding by accounting for viscoelastic energy dissipation at the contact interface, which becomes especially important in vibro-adhesion since micro-vibrations modulate the rate of contact formation and separation, thus influencing hysteresis and energy loss. Building further on viscoelasticity, Schapery’s (Schapery (1975)) model for viscoelastic fracture provides a rigorous framework to understand how time-dependent material behavior influences crack initiation and propagation in polymers and elastomers, which are central to many soft robotic grippers. Unlike purely elastic fracture mechanics, where the energy release rate is determined only by geometry and surface energy, Schapery’s theory incorporates the effects of viscoelastic relaxation and creep on the fracture process. The model builds on linear viscoelasticity and introduces a correspondence principle, allowing the elastic stress intensity factor solutions to be extended to viscoelastic cases by replacing elastic constants with time-dependent operators. A key outcome is that the apparent fracture toughness becomes a function of crack velocity, but the evolution of crack length over time can be given in a closed-form solution only for a couple of simplified cases. More recently, biological insights, such as the Shargott – Popov – Gorb (SPG) (Schargott et al. (2006)) model of fibrillar adhesion, have inspired soft robotic designs that mimic the hierarchical structures of insect pads and gecko feet; this perspective highlights how vibration can dynamically switch adhesion states, improving both load-bearing capacity and detachment control. Together, these theoretical frameworks suggest that tuning vibration frequency, amplitude, and waveform can optimize adhesion. From a purely practical point of view, embedding such model-driven tuning into soft robotic systems could dramatically improve durability of both the grippers and the handled objects while expanding the operational envelope of soft pick-and place robots into previously inaccessible domains such as electronics assembly, food handling, and biomedical applications. Within such framework, in this paper a methodology is proposed for modelling the dynamic fibrillar adhesion introduced above. The main aim is starting from a simple analytical model which could explain the mechanisms in object without, possibly, introducing strict hypotheses. The model is based on considering a system comprising a rigid sphere which moves onto a carpet of discrete viscoelastic springs (named fibrils) following an imposed law of motion. The logic behind the definition of the model is described in Section 2, while the main preliminary results and the conclusions are presented in Sections 3 and 4, respectively. Nomenclature amplitude of the harmonic component of the displacement 1 , 2 integration constants displacement of the single fibril ̇ first derivative of the displacement of the single fibril displacement of the sphere static component of the displacement phase of the harmonic component of the displacement F total force η damping coefficient K 0 relaxed modulus K 1 stiffness of spring 1 K 2 stiffness of spring 2 K ∞ instantaneous modulus angular velocity of the harmonic component of the displacement