J. Carmeliet, Optimal estimation of gradient damage parameters from localization phenomena in quasi-brittle materials, MECH C-F M, 4(1), 1999, pp. 1-16
Non-local and gradient enhanced damage models are able to properly model lo
calization phenomena in quasi-brittle materials. By the introduction of an
internal length scale they avoid mesh-size sensitivity in finite element ca
lculations and are capable of describing size effects. To experimentally de
termine the internal length scale and other damage model parameters, indire
ct identification methods have to be used. The method presented is based on
the Markov estimation procedure, which also permits to evaluate the accura
cy and the well-posedness of the identification problem, characterized by t
he uniqueness and identifiability of the estimated values. This information
offers the possibility to compare and optimize the designs of laboratory t
ests in order to minimize the effect of errors on the estimated values. The
indirect determination of the gradient damage parameters based on global r
esponse measurements far from the crack on one-size specimens is sensitive
to the problem of ill-posedness due the high correlation between the gradie
nt damage parameters, which dominate the localization process. The size eff
ect method can be used as an accurate identification method for the gradien
t damage parameters, when information on the tensile behaviour is included
and a sufficient size range is considered. Local displacement analysis clos
e to the crack provides sufficient information with respect to the identifi
cation problem independent of the size of the specimen and gives the most a
ccurate parameter estimations. Copyright (C) 1999 John Wiley & Sons, Ltd.