According to the Hertz's contact theory (HCT) and considering the strain hardening of materials, an effective calculation method is proposed for solving the elasto-plastic contact pressure and the contact patch size under arbitrary smooth and continuous contact conditions. Firstly, it is assumed that the outer and inner edges of the contact patch are elastic and elasto-plastic contact zones, respectively, the contact pressure in the elastic contact zone satisfies the HCT, while the contact pressure in the elasto-plastic contact zone is the superposition of a constant contact pressure and several small ellipsoidal distribution contact pressures. Then, the explicit expressions of contact patch size and contact pressure under the elasto-plastic elliptical, circular and line contact conditions are derived, respectively. Subsequently, the accuracy and applicability of the proposed method are evaluated by comparing the predicted results with the finite element simulations. Finally, the accuracy of the proposed method is further verified by comparing the predicted results with the typical results in literature. It is shown that the proposed method has high calculation accuracy, and the maximum relative errors are 9.32% for the elliptical contact, 4.61% for the circular contact and 11.84% for the line contact, respectively. Meanwhile, the proposed method can effectively predict the contact pressure distribution under the elasto-plastic elliptical, circular and line contacts, and shows a general applicability for different contact materials, contact-body's sizes and normal external loads, as well as for the elasto-plastic wheel-rail contact analysis.

根据赫兹接触理论（HCT），考虑材料的应变硬化，提出了一种有效的计算方法，用于求解任意光滑连续接触条件下的弹塑性接触压力和接触斑大小。首先，假设接触贴片的外边缘和内边缘分别是弹性接触区和弹塑性接触区，弹性接触区中的接触压力满足HCT，而弹塑性接触区中的接触压力为HCT。恒定的接触压力和几个小的椭圆形分布接触压力的叠加。然后，分别导出了弹塑性椭圆形，圆形和线形接触条件下接触斑大小和接触压力的显式表达式。随后，通过将预测结果与有限元仿真结果进行比较，评估了所提方法的准确性和适用性。最后，通过将预测结果与文献中的典型结果进行比较，进一步验证了所提方法的准确性。结果表明，该方法具有较高的计算精度，椭圆接触的最大相对误差为9.32％，圆形接触的最大相对误差为4.61％，线接触的最大相对误差为11.84％。同时，所提出的方法可以有效地预测弹塑性椭圆，圆形和线形接触下的接触压力分布，并显示出对不同接触材料，接触体的尺寸和正常外部载荷以及弹塑性的普遍适用性。塑料轮轨接触分析。