I am modelling concrete cylinders loaded in uniaxial compression. In FEM, the characteristic length is an important material property to obtain meshfree solution. Since in Bazant's(1984) famous paper on size effect assumes width of the crack band is three times max. aggregate size, a constant for a particular concrete, is the characteristic length while modelling in concrete can be taken same as crack band width?
In a paper Bazant defines the characteristc length of the concrete as 2.7 times the maximum aggregate size. But he writes "Thus, the characteristic length is essentially the same as the width of the strain- softening zone" and "The value of the characteristic length obtained in Eq. 6 for the presentexperiments is consistent with previous estimates obtained when the crackband model was proposed by Bazant and Oh (1983). At that time, the characteristic length was inferred indirectly, by using only the fracture test resultsand optimizing their fits for specimens of various geometries and sizes, madefrom different concretes. In that study, the optimum fit was obtained approximately for I = 3do"
In the same paper Bazant writes that in concrete the name "characteristic length" is not appropriate. It should be called "length of the fracture process zone" or similar.
I don't know if Bazant adopted other names in his later work.
http://www.civil.northwestern.edu/people/bazant/PDFs/Papers/249.pdf
Following up on this question, is this length the same for loading in compression as compared with that obtained for loading in tension?
Dear Luca Sgambi,
Thank you for your valuable suggestion.
In "Crack band theory" by Bazant and Oh (1983) concluded that the length of fracture process zone is about twelve times the maximum aggregate size(eq 23).
However in the paper whose link you have attached, Bazant found that the characteristic length or length of crack band is 8.65*max. aggregate size. So I am a bit confused which one to consider as characteristic length.
Dear Rimen Jamatia and dear Mahendra Gattu, fracture mechanics is not really my area, but I read the two articles mentioned above.
In Bazant and Cabot (1989) the equation 8.65*max. aggregate size is not from Bazant but from Irwin's (1958) with "presently measured values".
In Bazant and Oh (1983) before equation 23, Bazant wrote: "the characteristic length is generally between 2*Wc and 6*Wc", the twelve times the maximum aggregate size is only a typical value.
In addition in the same article Bazant wrote: "Wc to the size of aggregate ranged from 1.5 to 4 for various concretes" (page 166).
So (using the two definitions) the characteristic length range from 3*max. aggregate size to 24*max. aggregate size... depending on the type of concrete. You can see... 8.65*max. aggregate size or 12*max. aggregate size are both in the middle (typical values).
I believe that this parameter can not be a certain value. Maybe you need to do a sensitivity analysis of your FEM model to change this parameter. If in your structure there are also steel reinforcement, and you looking for a "global behavior" of the structure, this parameter should not affect much the results. I found the problem of mesh free solution analyzing bridge piers, I used both regularization based on fracture energy and non-local approach and this is from my experience.
Instead if your problem is on fracture mechanics field (micro-level behavior) you need further investigation and studies (sensitivity analysis can be a good starting point).
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