DEVELOPMENT OF A SEMI-ANALYTICAL MODEL FOR SUBSURFACE STRESS IN ELASTIC CONTACT
Abstract
The paper presents the development of a semi-analytical model to describe subsurface stress distribution in linear elastic contact problems. The model is constructed based on the Hertzian pressure distribution on the contact surface combined with a depth attenuation function derived from the Padé approximation of the Green’s function solution in an elastic half-space. By analyzing fundamental physical conditions of the problem, including boundedness at the surface, force equilibrium, and the asymptotic behavior of the Boussinesq solution, the study demonstrates that a cubic-order attenuation function provides a reasonable representation of the stress field with depth. The proposed model is capable of reproducing the three-dimensional stress distribution with small deviations compared to the classical Hertz–Boussinesq solution, while maintaining a compact analytical form suitable for efficient computation. The results indicate that the model has potential applications in contact mechanics, subsurface stress analysis, and preliminary evaluation of contact fatigue phenomena in elastic materials.
Tóm tắt
The paper presents the development of a semi-analytical model to describe subsurface stress distribution in linear elastic contact problems. The model is constructed based on the Hertzian pressure distribution on the contact surface combined with a depth attenuation function derived from the Padé approximation of the Green’s function solution in an elastic half-space. By analyzing fundamental physical conditions of the problem, including boundedness at the surface, force equilibrium, and the asymptotic behavior of the Boussinesq solution, the study demonstrates that a cubic-order attenuation function provides a reasonable representation of the stress field with depth. The proposed model is capable of reproducing the three-dimensional stress distribution with small deviations compared to the classical Hertz–Boussinesq solution, while maintaining a compact analytical form suitable for efficient computation. The results indicate that the model has potential applications in contact mechanics, subsurface stress analysis, and preliminary evaluation of contact fatigue phenomena in elastic materials.
Tài liệu tham khảo
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