Stress state of a transversally isotropic medium with a spheroidal inclusion under imperfect contact conditions

Abstract

Spatial problems related to the theory of elasticity and thermoelasticity play a significant role in the modern mechanics of deformable solids. Their importance arises from the numerous applications of this field in addressing critical technical and technological challenges across various industries. Research in this area is primarily driven by the need to understand the strength of materials and structural components. Typically, extreme stresses occur at the phase interface zones, as nearly all structural materials exhibit heterogeneity in their composition. Modeling the properties of interphase boundaries while considering their actual structural features is a crucial task. To obtain reliable and comprehensive information about stress distribution in structural elements, effective analytical and numerical methods must be employed to tackle spatial problems within the theory of elasticity. In spatial problems pertaining to the theory of elasticity and thermoelasticity for transversely isotropic bodies, solutions are expressed through potential functions that are harmonic in specifically chosen coordinate systems. This approach significantly alleviates the mathematical challenges typically encountered when solving particular boundary value problems. Recent publications from both domestic and international researchers have addressed issues related to the theory of elasticity and thermoelasticity for isotropic materials, particularly under conditions of imperfect mechanical and thermal contact. For instance, the works of A. T. Ulitko, Yu. M. Nemish, and N. E. Kachalovska explore axiometric problems. However, there are limited solutions available for transversely isotropic bodies with inclusions of canonical forms. Unlike the analyzed problems involving perfect contact, the latter cannot be solved in a closed form but instead requires the resolution of infinite systems of linear algebraic equations. Notable advancements in this field have been achieved by researchers such as Ya. S. Pidstryhach and Yu. M. Podilchuk, who have constructed exact solutions for spatial problems related to elasticity and static thermoelasticity across various coordinate systems, including spherical, cylindrical, spheroidal, and parabolic configurations. The current study addresses the distribution of normal, meridional, and circular stresses in a transversely isotropic medium that contains an anisotropic inclusion shaped like a compressed spheroid, subjected to uniform all-around compression. This analysis depends on the geometry of the inclusion. Building on the solutions derived from spatial problems of elasticity and thermoelasticity involving a transversely isotropic medium with a compressed spheroidal inclusion, investigations were conducted into the thermal stress distribution within both the medium and the inclusion. This was done under the influence of arbitrary linear temperature and force fields. Engineering formulas were developed to calculate stress concentrations in both the surrounding medium and the inclusion under various mechanical loads, including compression, tension, shear, bending, and torsion.