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Study On Fractal Damage Constitutive Laws Of Concrete Based On Najar Energy Method

Posted on:2014-02-02Degree:MasterType:Thesis
Country:ChinaCandidate:M N RenFull Text:PDF
GTID:2252330422454861Subject:Disaster Prevention
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The concrete material is a multiphase composite material. The disordered fracturesurface and disorganized crack will emerge after the concrete damaged. There is a largenumber of mechanical mechanism about damage and fracture of concrete material in themacroscopic breakage. In this paper, the extent irregularities of fracture surface isachieved quantitative description of continuity by the concept of fractal dimension andmulti-fractal spectrum. Accordingly, it could provide theoretical foundation through themacroscopic damage phenomena of concrete to study the failure mechanism. Theconcept of fractal stress and multi-fractal strain are proposed on the basis of thecontinuity expressed quantitatively of fractal characteristics of concrete. And fractaldamage constitutive is derived by means of Najar energy principle. The studies of thispaper are as follows:1. In this paper, the geometric characteristics of multi-fractal spectrum of fracturesurfaces of different strength grade of concrete are carefully observed and analyzed.And the multi-fractal spectrum of fracture surfaces of concrete is concluded to be asimilar parabola bell curve as a left hook or right hook. Based on the above judgment,the method of the minimum squares is applied to the quadratic fitting of multi-fractalspectrum of fracture surface. Thus the multi-fractal spectrums composed of discretepoints are continuously expressed by the analytic function. Then the quantitativedescription of anomalistic fracture surfaces of concrete is realized by the simplefunction. By the way of quantitative representation of fractal fracture surface of theconcrete, quadratic fitting will provide a theoretical foundation which could study the macro-mechanical properties of the concrete in macro-level.2. Based on the study of the fractal characteristics of concrete, this paper modifiesthe inadequacies of fractal stress-fractal strain proposed by Carpinteri. And the conceptof fractal stress and multi-fractal strain is put forward. The improved fractal stress andmulti-fractal strain can achieve three-dimensional quantitative representation of therandom distribution of internal defects and damage.3. Based on the concept of fractal stress and multi-fractal strain, a fractal damageconstitutive model which can reflect the random distribution of the internal defects anddamage in the internal of concrete is derived by the use of Najar energy principle.Because this fractal damage constitutive model could consider the distribution of thefractal characteristics of internal defects, damage along the loading axis and thecross-section. The fractal damage constitutive model can simulate the randomness,discrete and nonlinear of the mechanical properties of concrete. The improved damageevolution equation of probability distribution of Weibull is used to give expression tothe fractal characteristics of deformation in the loading process.The research of fractal damage constitutive model and fractal characteristics ofconcrete could help the researchers deeply recognize and understand interactionmechanism of inside the component of concrete. And this paper could provide areference for further to study on macroscopic fractal damage fracture characteristics ofconcrete and fractal damage mechanics mechanism.
Keywords/Search Tags:Concrete, Fractal fracture surface, Multi-fractal spectrum, Quadratic fitting, Fractal stress, Multi-fractal strain, Fractal damage constitutive, Fractaldamage evolution
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