Int J Fract (2009) 159:21–41 DOI 10.1007/s10704-009-9380-1 ORIGINAL PAPER Modeling of cohesive crack growth using an adaptive mesh refinement via the modified-SPR technique A. R. Khoei · H. Moslemi · K. Majd Ardakany · O. R. Barani · H. Azadi Received: 27 January 2009 / Accepted: 1 July 2009 / Published online: 23 July 2009 © Springer Science+Business Media B.V. 2009 Abstract In this paper, an adaptive finite element procedure is presented in modeling of mixed-mode cohesive crack propagation via the modified supercon- vergent path recovery technique. The adaptive mesh refinement is performed based on the Zienkiewicz– Zhu error estimator. The weighted-SPR recovery tech- nique is employed to improve the accuracy of error estimation. The Espinosa–Zavattieri bilinear cohesive zone model is applied to implement the traction-sep- aration law. It is worth mentioning that no previous information is necessary for the path of crack growth and no region of the domain is necessary to be filled by the cohesive elements. The maximum principal stress criterion is employed for predicting the direction of extension of the cohesive crack in order to implement the cohesive elements. Several numerical examples are analyzed numerically to demonstrate the capability and efficiency of proposed computational algorithm. Keywords Cohesive crack model · Mixed-mode crack propagation · Adaptive remeshing · Weighted-SPR technique A. R. Khoei (B ) · H. Moslemi · K. Majd Ardakany · O. R. Barani · H. Azadi Center of Excellence in Structural and Earthquake Engineering, Department of Civil Engineering, Sharif University of Technology, P.O. Box. 11365-9313, Tehran, Iran e-mail: arkhoei@sharif.edu 1 Introduction Over the last decades several numerical methods have been developed to simulate the failure mechanism in materials. The finite element method provides an approach to predict the failure behavior of materials. After the earliest work of Griffith (1920) for an ideal elastic material, various alternative approaches have been proposed to simulate the failure in more appli- cable problems. One of the original techniques used to simulate the crack initiation and crack growth was based on the cohesive zone model (CZM) introduced by Barenblatt (1959, 1962) for brittle materials and by Dugdale (1960) for plastic materials. Hillerborg et al. (1976) proposed these models and developed the fictitious crack model (FCM) for Mode I fracture in quasi-brittle materials. The method was then extended into the mixed mode fracture and incorporated into the finite element codes by researchers (Reich et al. 1991, 1997; Cervenka 1994; Xie and Gerstle 1995). One dif- ficulty associated with such models is the evaluation of material properties, which needs usually to be fit- ted to experimental results. The cohesive zone models have been widely used to simulate the near crack tip stress field. There are a wide range of applications of cohesive zone models in various problems, including: the crack tip plasticity (Li and Chandra 2003), creep under static and fatigue loading (Zhang et al. 2005), adhesive bonded joints (Liljedahl et al. 2006, cohesive crack bridging (Wang 2007), and interface cracks in biomaterials (Freed and Banks-Sills 2008). 123