Stable numerical simulations of propagations of complex damages in composite structures under transverse loads N. Hu a,b, * , Y. Zemba b , H. Fukunaga b , H.H. Wang c , A.M. Elmarakbi b a Department of Engineering Mechanics, Chongqing University, Chongqing 400011, PR China b Department of Aerospace Engineering, Tohoku University, 6-6-01 Aramaki-Aza-Aoba, Aoba-ku, Sendai 980-8579, Japan c School of Mechanical and Power Engineering, East China University of Science and Technology, Shanghai 200237, PR China Received 8 February 2006; received in revised form 25 April 2006; accepted 27 April 2006 Available online 27 June 2006 Abstract In this paper, to deal with complex damage propagations in various composite structures under quasi-static transverse loads, a numer- ical simulation methodology based on the three-dimensional (3D) finite element method (FEM) is proposed. In this numerical model, two categories of damage patterns existing in composite structures under transverse loads are tackled independently. First, a kind of stress-based criteria is adopted to deal with the first category, which includes various in-plane damages, such as fiber breakage, transverse matrix cracking, matrix crushing, etc. Second, a bi-linear cohesive interface model is employed to deal with the second category, i.e., interface damages, such as delaminations. Also, to overcome the numerical instability problem when using the cohesive model, a simple and useful technique is proposed. In this technique, the move-limit in the cohesive zone is built up to restrict the displacement increments of nodes in the cohesive zone of laminates after delaminations occurred. The effectiveness of this method is illustrated using a DCB exam- ple and its characteristic is discussed in detail. This numerical model is further applied to various composite structures, such as 2D lam- inated plates and 3D laminated shells under transverse loads. The results of the numerical simulations are compared with the experimental results and good agreements are observed. The obtained information is helpful for understanding the propagation mech- anisms of various damages in composite structures. Ó 2006 Elsevier Ltd. All rights reserved. Keywords: Cohesive interface model; C. Laminate; C. Delamination; C. Finite element analysis; Move-limit 1. Introduction It is well known that very complicated damage phenom- ena occur in composite laminated structures under the transverse loads. Understanding the mechanisms of the happening and propagation of these damages is crucial for properly designing this kind of composite structures. Generally, there are two main categories of various dam- ages in composite laminates under the transverse loads. The first category consists of various kinds of in-plane damages, such as fiber failure and transverse matrix crack- ing, etc. The second category includes the interface dam- ages, i.e., delaminations between multiple laminae. Clearly understanding the damage mechanism of only one damage pattern in composites mentioned above is a tough task. Moreover, the interaction between the different types of damages makes it more difficult. So far, a lot of research has been conducted to experimentally or numeri- cally investigate the damage phenomena of composite lam- inates under the transverse loads. In this paper, only the work in the field of theoretical models and numerical sim- ulations is briefly reviewed. First, for various damages, such as in-plane damages and delaminations, some authors have proposed various stress-based criteria. For example, Chang and Chang [1] 0266-3538/$ - see front matter Ó 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.compscitech.2006.04.014 * Corresponding author. Address: Department of Aerospace Engineer- ing, Tohoku University, 6-6-01 Aramaki-Aza-Aoba, Aoba-ku, Sendai 980-8579, Japan. Tel.: +81 22 217 4109/6994; fax: +81 22 217 6995. E-mail address: hu@ssl.mech.tohoku.ac.jp (N. Hu). www.elsevier.com/locate/compscitech Composites Science and Technology 67 (2007) 752–765 COMPOSITES SCIENCE AND TECHNOLOGY