Scaling Model Parameters Research Articles

Optimal estimation of gradient damage parameters from localization phenomena in quasi‐brittle materials

Non-local and gradient enhanced damage models are able to properly model localization phenomena in quasi-brittle materials. By the introduction of an internal length scale they avoid mesh-size sensitivity in finite element calculations and are capable of describing size effects. To experimentally determine the internal length scale and other damage model parameters, indirect identification methods have to be used. The method presented is based on the Markov estimation procedure, which also permits to evaluate the accuracy and the well-posedness of the identification problem, characterized by the uniqueness and identifiability of the estimated values. This information offers the possibility to compare and optimize the designs of laboratory tests in order to minimize the effect of errors on the estimated values. The indirect determination of the gradient damage parameters based on global response measurements far from the crack on one-size specimens is sensitive to the problem of ill-posedness due the high correlation between the gradient damage parameters, which dominate the localization process. The size effect method can be used as an accurate identification method for the gradient damage parameters, when information on the tensile behaviour is included and a sufficient size range is considered. Local displacement analysis close to the crack provides sufficient information with respect to the identification problem independent of the size of the specimen and gives the most accurate parameter estimations. Copyright © 1999 John Wiley & Sons, Ltd.

Relation between Feynman's variable and the fractional energy of gamma-family constituents

Monte-Carlo calculations on gamma families at mountain altitude (4500 m) have been carried out for appropriate scaling model parameters which are currently used in high-energy cosmic-ray phenomenology. There are no correlations between Feyman's variable x and the fractional energy f' taken by the gamma rays. The rejuvenated an non-rejuvenated families select secondaries with average x values 0.14 and 0.12, respectively. The so called pionisation region also contributes to family formation (40% secondaries at x<0.1). The model involving an increase in the interaction cross section due to scaling violation in the x<0.1 region is not in agreement with the experimental multiplicity distribution.