Premium
Stress tensor and gradient of hydrostatic pressure in the contact plane of axisymmetric bodies under normal and tangential loading
Author(s) -
Willert Emanuel,
Forsbach Fabian,
Popov Valentin L.
Publication year - 2020
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201900223
Subject(s) - axial symmetry , cauchy stress tensor , hydrostatic pressure , von mises yield criterion , contact mechanics , hydrostatic stress , rotational symmetry , plane (geometry) , stress (linguistics) , hydrostatic equilibrium , mechanics , tensor (intrinsic definition) , plane stress , classical mechanics , viscous stress tensor , normal , contact force , materials science , geometry , mathematics , surface (topology) , physics , finite element method , thermodynamics , linguistics , philosophy , quantum mechanics
The Hertzian contact theory, as well as most of the other classical theories of normal and tangential contact, provides displacements and the distribution of normal and tangential stress components directly in the contact surface. However, other components of the full stress tensor in the material may essentially influence the material behaviour in contact. Of particular interest are principal stresses and the equivalent von Mises stress, as well as the gradient of the hydrostatic pressure. For many engineering and biomechanical problems, it would be important to find these stress characteristics at least in the contact plane. In the present paper, we show that the complete stress state in the contact plane can be easily found for axially symmetric contacts under very general assumptions. We provide simple explicit equations for all stress components and the normal component of the gradient of hydrostatic pressure in the form of one‐dimensional integrals.