Mixed‐mode delamination in 2D layered beam finite elements

Abstract

SummaryIn this work, a 2D finite element (FE) formulation for a multi‐layer beam with arbitrary number of layers with interconnection that allows for mixed‐mode delamination is presented. The layers are modelled as linear beams, while interface elements with embedded cohesive‐zone model are used for the interconnection. Because the interface elements are sandwiched between beam FEs and attached to their nodes, the only basic unknown functions of the system are two components of the displacement vector and a cross‐sectional rotation per layer. Damage in the interface is modelled via a bi‐linear constitutive law for a single delamination mode and a mixed‐mode damage evolution law. Because in a numerical integration procedure, the damage occurs only in discrete integration points (i.e. not continuously), the solution procedure experiences sharp snap backs in the force‐displacements diagram. A modified arc‐length method is used to solve this problem. The present model is verified against commonly used models, which use 2D plane‐strain FEs for the bulk material. Various numerical examples show that the multi‐layer beam model presented gives accurate results using significantly less degrees of freedom in comparison with standard models from the literature. Copyright © 2015 John Wiley & Sons, Ltd.