Analysis of Compatibility with Experimental Data of Fractal Descriptions of the Fracture Parameters

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Abstract

In order to check if the Fractal theory could be a useful tool for some quantitative descriptions of the fracture parameters, the present work studied different theoretical models (e.g. the Bazant’s Size Effect Law (SEL) [1], the Modified Size Effect Law [2,3] and the Carpinteri’s MultiFractal Scaling Law (MFSL) [4] of the fracture parameters of concrete specimen, and the compatibility of some of the above studied theoretical models relative to the experimental data, using certain recent procedures to study the global and local compatibility. The fracture parameters can be considered as main quantities for computational procedures for modeling the fracture of a certain ensemble (a suddenly emerging phenomena). In the next phase, the thermoelastic generation of ultrasonic perturbations in semitransparent solids was analyzed (using computer simulation) so as to find similarities with material properties as fractal dimensions, when the heat source is a laser radiation. The algorithm, the numerical analysis has taken into account three main physical phenomena: the absorption of electromagnetic energy in substance with heat generation; thermal diffusion with electromagnetic energy based heat source and elastodynamic wave generation by thermoelastic expansion.