Mathematical model for diagnosing a nonlinear elastic medium

Alexander V. Lomazov; Vadim A. Lomazov; Alexei G. Stupakov; Vladislav L. Anichin; Dmitry Yu. Evsyukov

doi:10.1117/12.3025210

20 February 2024 Mathematical model for diagnosing a nonlinear elastic medium

Alexander V. Lomazov, Vadim A. Lomazov, Alexei G. Stupakov, Vladislav L. Anichin, Dmitry Yu. Evsyukov

Proceedings Volume 13065, Third International Conference on Optics, Computer Applications, and Materials Science (CMSD-III 2023); 1306516 (2024) https://doi.org/10.1117/12.3025210
Event: Third International Conference on Optics, Computer Applications, and Materials Science (CMSD-III 2023), 2023, Dushanbe, Tajikistan

Abstract

The article deals with the problem of mathematical modeling of physical processes when conducting diagnostic tests within the framework of non-destructive testing of materials. The consideration of elastic processes is due to the fact that elasticity is characterized by the return of the body to its original state after removal of force loads (thereby ensuring the non-destructive nature of the tests). It is assumed that the material under study has weakly expressed spatially distributed anisotropic and nonlinear properties due to the uneven accumulation of microdamage during the operation of the product. The purpose of the work is to formulate and solve the problem of diagnosing a nonlinear elastic inhomogeneous anisotropic half-space within the framework of mathematical modeling of non-destructive testing of massive bodies. In mathematical terms, the problem belongs to the class of coefficient inverse problems for dynamic elasticity equations. An approach to determining density and elastic moduli (coefficients of equations) depending on spatial variables is proposed, based on the use of the perturbation method.

(2024) Published by SPIE. Downloading of the abstract is permitted for personal use only.

Citation Download Citation

Alexander V. Lomazov, Vadim A. Lomazov, Alexei G. Stupakov, Vladislav L. Anichin, and Dmitry Yu. Evsyukov "Mathematical model for diagnosing a nonlinear elastic medium", Proc. SPIE 13065, Third International Conference on Optics, Computer Applications, and Materials Science (CMSD-III 2023), 1306516 (20 February 2024); https://doi.org/10.1117/12.3025210

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