Modeling of Deformable Thermoelastic Thread-Like Inclusions in Isotropic Media

• Published in: Journal of mathematical sciences (New York, N.Y.) Vol. 274; no. 5; pp. 660 - 677
• Main Authors: Sulym, H. T., Pasternak, Ia. M., Tretiak, T. V.
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 09.08.2023; Springer; Springer Nature B.V
• Subjects: Analysis; Deformation; Electric properties; Formability; Functions (mathematics); Heat conductivity; Heat transfer; Inclusions; Inhomogeneity; Integral equations; Isotropic media; Mathematical analysis; Mathematical models; Mathematics; Mathematics and Statistics; Modulus of elasticity; Numerical analysis; Polynomials; Thermal conductivity; Thermal expansion; mathematical model; thread-like deformable inclusions; thermoelasticity; numerical analysis
• ISSN: 1072-3374; 1573-8795
• DOI: 10.1007/s10958-023-06629-1

By using the principle of coupling of continua of different dimensions, we propose an approach to the mathematical modeling of deformable thread-like inhomogeneities. The proposed approach is based on the conditional partition of the analyzed problem into three partially coupled subproblems: a) external for a medium with conditionally given ( a priori unknown) functions of influence on the space curves L ; b) intermediate in the form of the conditions of contact interaction of the medium with inhomogeneities, and c) internal , which is reduced to the construction of a mathematical model of inhomogeneity, which relates the function of influence directly on the surface of the inclusion with the distribution of physical and mechanical fields inside this inclusion. In the case of perfect thermomechanical interaction between the inhomogeneity and the medium, we construct integral relations for the external problem and mathematical models of thread-like inhomogeneities taking into account their thermal conductivity and deformation. In the case of rectilinear inhomogeneities, we propose a method for the solution of the constructed systems of integral equations based on the use of truncated series in Legendre polynomials for the required functions of influence of thread-like inclusions. The results of numerical analysis clarify the influence of relative thermal conductivity, relative elastic compliance, and linear thermal expansion of the material of inhomogeneity on the functions of influence and thermomechanical fields near the tip of the inclusion.