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Title of the article NUMERICAL AND ANALYTICAL MODELING OF DAMAGE ACCUMULATION PROCESSES AND EVOLUTION OF STRESS-STRAIN STATE AT THE CRACK TIP IN CREEP MODE
Authors

STEPANOVA Larisa V., D. Sc. in Phys. and Math., Prof., Head of the Department of Mathematical Modeling in Mechanics, Samara National Research University, Samara, Russian Federation, This email address is being protected from spambots. You need JavaScript enabled to view it.">This email address is being protected from spambots. You need JavaScript enabled to view it.

CHAPLIY Dmitry V., Postgraduate Student of the Department of Mathematical Modeling in Mechanics, Samara National Research University, Samara, Russian Federation, This email address is being protected from spambots. You need JavaScript enabled to view it.">This email address is being protected from spambots. You need JavaScript enabled to view it.

BELOVA Oksana N., Associate Professor of the Department of Mathematical Modeling in Mechanics, Samara National Research University, Samara, Russian Federation, This email address is being protected from spambots. You need JavaScript enabled to view it.">This email address is being protected from spambots. You need JavaScript enabled to view it. 
In the section DYNAMICS, DURABILITY OF VEHICLES AND STRUCTURES
Year 2026
Issue 1(74)
Pages 56–65
Type of article RAR
Index UDK 539
DOI https://doi.org/10.46864/1995-0470-2026-1-74-56-65
Abstract The work is devoted to the study and analysis of finite element (FE) calculations performed by a large cycle of computational experiments of plate deformation with a section under steady-state creep conditions, which revealed a power-law self-similar distribution of the continuity function (damage) and stress components in the immediate vicinity of the tip of the section at the second and third stages of creep in a damaged medium in a related formulation of the problem, when the continuity parameter is included in the constitutional relations. The FE computations of stress fields and continuity near the tip of the defect were carried out using the powerful SIMULIA Abaqus platform using the UMAT utility, which integrates the process of damage development into the computational scenario of the finite element method (FEM). The paper implements computer modeling of uniaxial stretching of a plate weakened by a central horizontal section or an inclined section in creep mode, in which computational algorithms include damage growth that progresses over time according to the classical mechanical model of damage growth by Kachanov–Rabotnov according to a power law for various values of exponents of the kinetic equation and the power determining equation with the concept of true tension in a related formulation. Numerical study and analysis of the obtained FE representations of stress and continuity fields in the vicinity of the crack tip for a number of material constants clearly reveals a self-similar distribution of stress fields and damage near the tip of a power-type defect. The structure of the solution is revealed and the values of the exponents in the self-similar variable and the self-similar representation of the solution are found, which can be interpreted as an intermediate self-similar solution of the second type according to the classification of G.I. Barenblatt. It is shown that the discovered self-similar property of the solution can be interpreted as self-similar asymptotics of the far field of continuity and stresses. Also, the stress dependences extracted from FEM calculations on the distance from the tip of the incision, reproduced in double logarithmic coordinates, clearly demonstrate the asymptotic behavior corresponding to the near-field stress, characterized by the complete absence of a singularity in the immediate vicinity of the tip of the incision.
Keywords damage, continuity, Kachanov–Rabotnov model, fields at the crack tip, UMAT, stress field asymptotics, self-similarity
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