A Single-Variable Zigzag Approach to Model Imperfect Interfaces in Layered Beams

The flexibility of the bonds between the adjacent layers of multi-layered systems and their degradation or the presence of delaminations strongly affect mechanical response and final collapse. The formulation of accurate and efficient models able to capture the complex local distributions of stresses and displacements, which arise due to the layered structure and imperfect bonding, is of great importance for the design and verification of the systems. In this paper a novel and effective “single-variable zigzag” theory is formulated to analyze beams with homogeneous layers made of the same material and imperfect interfaces, which allow sliding between the layers. The primal variable is a fictitious bending displacement, which is derived in order to define all other kinematic and static quantities in terms of it. The “zigzag” technique describes multilayer systems with imperfect interfaces as equivalent single-layers, so that the problem is governed by equations similar to those of the classical theories for homogeneous beams; the “single-variable” formulation facilitates the implementation into numerical schemes and eliminates well-known numerical problems. Explicit solutions are straightforwardly derived for simply supported beams subjected to uniform and sinusoidal transverse loads. The results for some exemplary structural elements confirm the accuracy and efficiency of the approach. The study is preliminary to the single-variable reformulation and numerical implementation of the zigzag models for laminates with elastic mismatch between the layers.