Innovation science and technologiy 1-jild 11-son (2025)
MATHEMATICAL MODEL FOR PREDICTING THE DYNAMIC EVOLUTION OF CRACKS IN URBAN CONSTRUCTION STRUCTURES
Sh. A. Anarova, M. N. Samidov
Annotatsiya
In this study, a new mathematical model based on fractal theory has been developed to predict the servicelife of cracks. The model covers the entire life cycle of a crack, from its initiation to its critical length. A mathematicalmodel grounded in kinetic theory has been formulated and expressed as a differential equation, and its integral form hasbeen solved. The main innovation of the model is the introduction of the fractal dimension parameter Dₛ, which makesit possible to account for the complex geometry of the crack surface. The accuracy of the model has been confirmedthrough computer experiments, showing R² = 0.96. The proposed model is an effective tool for assessing the long-termbehavior of construction materials.
fractal, criterion, strength, mathematical model, crack, critical stress
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