Modeling imperfect interfaces in layered beams through multi- and single-variable zigzag kinematics

Multiscale structural models based on the coupling of a zigzag kinematics and a cohesive crack approach have been recently formulated to analyze the response of shear deformable layered structures with imperfect interfaces and describe progressive delamination fracture (Massabò, in Handbook of Damage Mechanics, Springer, 2022, pp.665-698). The zigzag kinematics accounts for zigzag effects associated to the elastic mismatch of the layers and displacement jumps due to interfacial imperfections, using a limited number of variables, which is independent of the number of layers. The effects of imperfect interfaces on the response of structures subjected to thermo-mechanical loading and on wave propagation and dispersion have been studied analytically and the advantages of this approach over discrete layer models and layerwise theories have been highlighted and discussed. In the presentation we review and discuss these models and present preliminary results on novel single-variable formulations, which have been inspired by a technique developed for homogeneous Timoshenko beams in (Kiendl et al., Comput Methods Appl Mech Eng, 284, (2015), 988-1004). An isogeometric collocation scheme is developed for the numerical solution of the problem. The formulation is locking free and satisfies high continuity requirements for the approximating functions.