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Cohesive Zone Models are elasticity
I have always, and I believe correctly, considered cohesize/bridging models linear elasticity. This is because whether we apply them to holes or cracks, we are solving the equations of ELASTICITY, with nonlinear boundary conditions along the part(s) of the crack along which a traction-separation law is applied. So the material model is totally elastic. All we did was to augment the elasticity theory with an ad hoc physical condition (inspired by experiments such as Dugdale).
So if I take that point of view, the ratio of crack length to plastic zone size enters the elasticity model, and can predict the behavior of small and long cracks (or small and large holes).
By the way, for 25 years I always correct people when they say cohesive models are “nonlinear fracture mechanics”. I call them “linear elastic fracture mechanics with nonlinear boundary conditions.”
- Roberto Ballarini's blog
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partially agreed
I agree with you on your first part of statement. That is why I cover CZ model next to LEFM, stressing on the removal of stress singularity by CZ model, and then EPFM.
However, CZ model IS nonlinear FM, FM with nonlinear effect taken into account somewhere, though on the crack surfaces. If you do computational FM, you may soon realize it because you have to solve it iteratively.
If someone called it nonlinear elastic FM or nonlinear plastic FM, I would join you to correct it.
I think this is just like elastic contact problem
the nonlinearity comes from the boundary condition.
We call it a nonlinear problem since superposition principle is not valid in this case and
at the same time, the P-\Delta relationship is not linear anymore.
the ratio of crack length
the ratio of crack length to plastic zone size enters the elasticity model, and can predict the behavior of small and long cracks (or small and large holes).
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I am very interested in that is there someone has introduce yielding into cohesive zone models. In my opinion, it will be too complicated to be widely applied, because so many unknown criterion will involove
Study 5 minutes at least every day
what is linear in cohesive models?
It is funny to see how some weird arguments and doctrines show up from time to time again. One is Roberto Balarini’s statement “cohesive models are elasticity”. I do not even understand the meaning of it. No model can ever be a constitutive theory like elasticity, we may just have models of a certain structural or constitutive behaviour. Roberto states that for 25 years he has always corrected people addressing cohesive models as “nonlinear fracture mechanics”. Actually, I had a PhD student some 25 years ago who modelled crack extension in an elastic panel by node release along a symmetry line governed by some LEFM criterion. This indeed was elasticity with a nonlinear boundary condition.
However, cohesive modelling has advanced ever since! I recommend reading volume 3 on “Numerical and Computational Methods” of Elsevier’s encyclopaedia on “Comprehensive Structural Integrity”, for example. Cohesive models have been developed for numerous separation mechanisms in the context of various types of material behaviour. Cohesive elements describe the nonlinear decohesion process of continuum elements obeying any kind of constitutive equations, for instance plasticity and visco-plasticity. What else than “nonlinear fracture mechanics” is this? A statement like Roberto’s is meaningless and starts a needless discussion, in my eyes. Or is this really an actual problem in Civil Engineering?
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