Stress tensor and gradient of hydrostatic pressure in the contact plane of axisymmetric bodies under normal and tangential loading,ZAMM - Journal of Applied Mathematics and Mechanics

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Stress tensor and gradient of hydrostatic pressure in the contact plane of axisymmetric bodies under normal and tangential loading
ZAMM - Journal of Applied Mathematics and Mechanics ( IF 2.3 ) Pub Date : 2020-05-14 , DOI: 10.1002/zamm.201900223
Emanuel Willert ₁ , Fabian Forsbach ₁ , Valentin L. Popov _{1,

2}

Affiliation

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.

中文翻译：

法向和切向载荷下轴对称物体接触面的应力张量和静水压力梯度

赫兹接触理论以及法向和切向接触的大多数其他经典理论直接在接触表面中提供了法向和切向应力分量的位移和分布。但是，材料中全应力张量的其他成分可能会实质上影响材料在接触时的行为。特别令人关注的是主应力和等效的冯·米塞斯（von Mises）应力，以及静水压力的梯度。对于许多工程和生物力学问题，重要的是至少在接触平面中找到这些应力特征。在本文中，我们表明，在非常普遍的假设下，对于轴对称接触，可以轻松地在接触平面中找到完整的应力状态。

更新日期：2020-05-14

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