A non-local fractional-order interface mechanical model

Recently, cohesive zone models (CZMs) have been used to describe the failure and the debonding phenomena of materials and interfaces [1, 2]. In this work a CZM is enriched introducing in the inter- facial constitutive law a displacement-based non-local elastic interaction. In this way, the debonding process is described taking into account the non-linear elastic local force and the long-range inter- actions depending on the relative displacements. In order to model the non-locality effects, elastic interaction forces depending on the relative displacements and distance-decaying functions ruling the amount of interactions are introduced in the constitutive equation of the interface. In several works from the literature a power-law is adopted as distance-decaying function [3, 4, 5]. Such choice leads to fractional order operators in the non-local constitutive law. In the present study, a structural element composed by two beams partly bonded together by a non-local elastic interface is considered. For this case, a numerical solution is achieved by a finite element analysis introducing the proposed non-local constitutive law of the interface element.