On using a penalty-based cohesive-zone finite element approach, Part I: Elastic solution benchmarks

This paper develops and demonstrates a novel penalty methodology for enhancing the use of the cohesive-zone method (CZM) in finite element models to analyze crack initiation and propagation of surface-bonded structures. For many industrial uses, the CZM finite element approach is troublesome because it is a 3-parameter model depending on critical energy release rate, critical limiting maximum stress and the shape of the traction-separation law. The penalty framework described in the current work maps the CZM approach to fit within the classic Griffith energy release method which is dependent solely on the single material parameter of critical energy release rate. This penalty approach is demonstrated for two generalized problems: double cantilever beam (DCB) analysis and single-arm peeling of very thin elastic substrates. Comparisons with several analytical and pseudo-analytical benchmarks demonstrates how to utilize this new technique as well as the accuracy of the resulting finite element analysis (FEA) solutions for these nonlinear crack propagation and peeling problems.