Abstract
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. 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 $$\ell _c$$ . 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. Force-CMOD curves obtained are very similar with both models. Theoretical analysis in 1D and numerical results in 2D indicates that, as $$\ell _c$$ goes to zero, TLS results tend to CZM ones. The TLS model yields very similar results to the cohesive one, without the need for extra equations to determine the crack path.
Highlights
Two main families of methods exist to model failure of quasi-brittle structures
The goal of this paper is to establish a one-dimensional equivalence between the cohesive zone model and a damage model with thick level set (TLS) regularization
We look for h by only using the stress-opening function f and the opening w, instead of fully describing gCZM and Ac and α [see (6)]
Summary
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 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 representing cracks (i.e. displacement jumps); contrary to most damage models. Modeling the failure of quasi-brittle structures is an important aim of numerical simulations. Two main kind of models have been developed [1]: crack based ones, as the cohesive zone model, and damage based ones. Quasi-brittle structures are characterized by the existence of a non-negligible fracture process zone. Linear elasticity fracture mechanics (LEFM) does not apply as it requires this zone to be negligible. In cohesive zone models (CZM), it is assumed that the process zone is concentrated over a line (2D problems) or a surface (3D), that defines the crack
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