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Determination of the Fractal Dimension of the Irregular, Compressive Stress‐Strain Relationships of brittle, crumbly particulates
Author(s) -
Peleg Micha,
Normand Mark D.
Publication year - 1993
Publication title -
particle and particle systems characterization
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.877
H-Index - 56
eISSN - 1521-4117
pISSN - 0934-0866
DOI - 10.1002/ppsc.19930100603
Subject(s) - fractal dimension , fractal , brittleness , measure (data warehouse) , dimension (graph theory) , deformation (meteorology) , a priori and a posteriori , mathematics , geometry , constant (computer programming) , fractal dimension on networks , materials science , mathematical analysis , fractal analysis , composite material , computer science , pure mathematics , data mining , philosophy , epistemology , programming language
The apparent fractal dimension of normalized rugged compressive force‐deformation curves of two types of brittle particulates was determined using the blanket algorithm. Although the shape of the original force‐deformation relationships of the individual specimens was irreproducible, the apparent fractal dimension of the normalized data was fairly constant and characteristic of the material. The applicability of the algorithm and the validity of the results were tested with computer simulated relationships generated with a set of Weierstrass functions whose fractal dimension was known a‐priori. It is demonstrated that as long as the resolution along the two axes is the same, the fractal dimension so calculated provides an absolute rather than a relative measure of the relationship's jaggedness.