PSI - Issue 78

Francesco Bianco et al. / Procedia Structural Integrity 78 (2026) 41–48

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The interface springs are modeled as zero-length elements with nonlinear shear response. Their monotonic behavior follows a tri-linear backbone curve, a formulation widely used and recommended by design guidelines such as the Italian CNR-DT200 (2013). This backbone law defines both the interface status at the start of unloading and the response of regions not subjected to unloading or during reloading.

Fig. 1. Schematization of sample according to the proposed model.

2.1. Cyclic behavior model for interface springs The unloading behavior of interface springs is defined based on the slip value at which unloading starts. If unloading begins before the bond strength is reached, the behavior is elastic and follows the same trend as the initial loading phase. In contrast, if unloading starts after the peak strength but before complete detachment, the response involves a softening phase that reduces the shear stress progressively, eventually reaching zero. After this point, no stress is transferred during further unloading. If the slip is already beyond full detachment, the interface is considered fully debonded, and no shear stress is transmitted (Fig.2).

Fig. 2. Schematization of the unloading phase of shear springs.

The reloading phase depends on how unloading occurred. If the system had only undergone elastic unloading, reloading follows the same initial path. If it involved softening, the reloading follows a simplified rule based on the last reached slip value. If the interface was completely debonded, no shear stress is recovered during reloading (Fig.3).