Issue 51

R. Massabò et alii, Frattura ed Integrità Strutturale, 51 (2020) 275-287; DOI: 10.3221/IGF-ESIS.51.22 275 Focussed on IGF25 – Fracture and Structural Integrity International Conference 2019 Local zigzag effects and brittle delamination fracture of n -layered beams using a structural theory with three displacement variables Roberta Massabò, Ilaria Monetto Department of Civil, Chemical and Environmental Engineering, University of Genova, Italy Roberta.massabo@unige.it, http://orcid.org/0000-0002-9746-1801 A BSTRACT . Equivalent single layer theories for layered beams effectively and accurately predict global displacements and internal force and moment resultants using a limited number of displacement variables. However, they cannot reproduce local effects due to material architecture or weak/imperfect bonding of the layers, such as zigzag displacement fields, displacement jumps at the layer interfaces and complex transverse stress fields, nor can they simulate delamination damage growth. In this work we will present some applications and discuss advantages and limitations of a recently formulated zigzag model. The model, through a modification of the equilibrium equations of an equivalent single layer theory, which maintains the same number of variables, reproduces local effects and delamination fracture under mode II dominant conditions. The approach is based on a local enrichment of the displacement field of first order shear deformation theory, the introduction of cohesive interfaces and homogenization. K EYWORDS . Structural theory; Zigzag; Homogenization; Cohesive zone model; Brittle fracture; Laminate. Citation: Massabò, R., Monetto, I., Local zigzag effects and brittle delamination fracture of n-layered beams using a structural theory with three displacement variables, Frattura ed Integrità Strutturale, 51 (2020) 275-287. Received: 13.11.2019 Accepted: 27.11.2019 Published: 01.01.2020 Copyright: © 2020 This is an open access article under the terms of the CC-BY 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. I NTRODUCTION he mechanical response of layered structures, such as laminates, sandwich composites, laminated glass, and laminated wood, is controlled by local effects due to the elastic mismatch of the layers, the presence of thin interlayers (adhesives, resin rich regions, polymeric layers), and interfacial imperfections, defects and delaminations, which are typical consequences of manufacturing processes. Zigzag displacement fields and complex transverse stress distributions, which are due to the multilayer architecture, and displacement discontinuities, due to the presence of interlayers or interfacial damage/delaminations, are not captured by the widely used equivalent single layer theories (ESLT), such as first order shear deformation theory (FSDT). These theories assume a C 1 continuous displacement field through the thickness which introduces discontinuities in transverse stresses and the impossibility to satisfy local equilibrium. Modeling local effects requires the use of layerwise, discrete-layer or 2D/3D finite-element models, where layers and interfacial regions between layers are distinctly modelled and continuity of displacements, but not of their derivatives (slopes), is imposed at the interfaces [1]. Modeling delamination evolution using these techniques requires in addition a T