Comparison between thick level set (TLS) and cohesive zone models

Abstract

Background: Two main families of methods exist to model failure of quasi-brittle structures. The first one consists on crack based models, like cohesive zone models. The second one is a continuum damage approach that leads to a local loss of stiffness. Local damage models need some regularization in order to avoid spurious localization. A recent one, the thick level set damage model, bridges both families by using level-sets. Cohesive and TLS models are presented. The cohesive one represents quasi-brittle behaviors with good accuracy but requires extra equations to determine the crack path. The TLS has proved its capability to model complex crack paths while easily representing cracks (i.e. displacement jumps); contrary to most damage models. Methods: A one-dimensional analytical relationship is exhibited between TLS and cohesive models. The local damage behavior needed to obtain the same global behavior of a bar than with cohesive model is derived. It depends on the choice of some TLS parameters, notably the characteristic length ℓc. This local behavior is applied to bi-dimensional simulations of three point bending as well as mixed-mode single edge notched specimens are performed. Results are compared to cohesive simulations, regarding both crack paths and force-CMOD curves. Results: Force-CMOD curves obtained are very similar with both models. Theoretical analysis in 1D and numerical results in 2D indicates that, as ℓc goes to zero, TLS results tend to CZM ones. Conclusions: The TLS model yields very similar results to the cohesive one, without the need for extra equations to determine the crack path.