A coupled interface-multilayer approach for mixed mode delamination and contact analysis in laminated composites Domenico Bruno * , Fabrizio Greco, Paolo Lonetti Department of Structural Engineering, University of Calabria, Via P. Bucci, Cubo 39C, 87030 Rende Cosenza, Italy Received 2 September 2003; received in revised form 2 September 2003 Abstract An accurate laminate model developed by using multilayer shear deformable plate modeling and interface elements, based on fracture mechanics and contact mechanics, is proposed to analyze mixed mode delamination in composite laminates. Perfect adhesion along the undelaminated portion of the delamination plane is simulated by treating in- terface stiffnesses as penalty parameters, whereas to enforce interface displacement continuity between plate elements constituting each sub-laminate above or below the delamination plane, the Lagrange multiplier method is used. The governing differential equations are derived through a variational procedure by using a modified total potential energy functional. Results are obtained by numerical integration of the non-linear three-point boundary value problem modeling mixed-mode delamination of the laminate plate subjected to end loading, which accounts also for the fric- tionless contact condition. The coupling of a penalty procedure with the Lagrange multiplier method, results in an accurate and direct energy release rate evaluation. Comparisons with results available from the literature obtained with a local continuum ap- proach, show that mode partition may be performed to the desired accuracy by refining multilayer plate models for each sub-laminate. In addition, original analytical formulas for mode partition are obtained by coupling the interface approach and fracture mechanics concepts, evidencing the effectiveness of the proposed approach and gaining a better insight into the influence of shear effects on mode decomposition. Numerical computations for practical problems, evidence both the relative simplicity and the efficiency of the proposed model to represent mixed mode interlaminar fracturing as well as crack–face interaction. Ó 2003 Elsevier Ltd. All rights reserved. Keywords: Laminates; Delamination; Multilayer; Interface; Mode partition; Contact 1. Introduction Classic delamination models based on plate theories, which are frequently adopted in the literature, are very useful to obtain an accurate estimate of total energy release rate. According to these models, del- amination analysis is carried out by considering the laminate as composed of two plate elements in the * Corresponding author. Tel.: +39-984-496914; fax: +39-984-494045. E-mail address: d.bruno@unical.it (D. Bruno). 0020-7683/$ - see front matter Ó 2003 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijsolstr.2003.09.006 International Journal of Solids and Structures 40 (2003) 7245–7268 www.elsevier.com/locate/ijsolstr