197 / 2019-08-21 14:45:41

An Elastoplastic Contact Solving Method for Two Spheres

Elastoplastic contact; Hertz contact theory; Contact stress distribution; Contact patch size; Finite element simulation

计算力学新方法，新理论 > 高性能算法的理论与实现

ABSTRACT: The traditional Hertz contact theory has been widely used in solving contact problems. However, the Hertz contact theory is only applicable to the elastic contact condition, and cannot truly reflect the contact stress distribution and contact radius in the elastoplastic contact condition. In this work, based on the Hertz contact theory, a fast solving method is proposed to calculate the contact stress distribution and contact radius in the elastoplastic contact condition between two spheres. It is assumed that the elastic contact only occurs at the outer edge of contact patch and its contact stress distribution satisfies the Hertz contact theory, the contact stress distribution at the inner edge of contact patch can be superimposed by a constant contact stress and several small ellipsoidal contact stress distributions. Moreover, based on the equivalent relation between the resultant force of contact stress and the normal external load, the contact radius in the elastoplastic contact condition can be solved. Finally, an elastoplastic contact example of two spheres is given based on the power hardening material model, and the influences of material parameters, contact radii and normal external loads on the accuracy of the proposed method are discussed by comparing the differences between numerical results by finite element simulations and predicted results by the proposed method. The results show that the proposed method can accurately calculate the maximum contact stress and contact radius in the elastoplastic contact condition, the relative errors of both maximum contact stress and contact radius are within ±5%. To sum up, the proposed fast solving method can be applied to perform elastoplastic contact analysis in engineering practices.
KEY WORDS Elastoplastic contact; Hertz contact theory; Contact stress distribution; Contact radius; Finite element simulation