Abstract—

The indentation of a rigid cylinder with a flat base into a viscoelastic layer situated without friction on a rigid base is considered. The interaction process consists of two stages: indentation of a cylinder at a constant speed to a certain depth and its further holding in this depth. The mechanical behavior of a viscoelastic layer is described by equations of linear viscoelasticity with relaxation functions of two types: exponential and power. The solution of the problem is based on the application of the Volterra principle and the use of an elastic solution constructed by the asymptotic “methods of large and small λ” that were developed by I. I. Vorovich and his students. On the basis of the solution obtained, the nature of the time variation in contact stresses and loads during the indentation of the cylinder has been studied for both relatively small and relatively large layer thicknesses. A comparison of the time variation of the studied quantities for two different relaxation functions and with the results of calculations based on a simplified one-dimensional model used to describe the behavior of a viscoelastic layer during indentation is performed.

中文翻译：

---

圆柱压痕到粘弹性层的建模

摘要-

考虑了将具有平坦基底的刚性圆柱体压入粘弹性层中，该粘弹性层在没有摩擦的情况下位于刚性基底上。相互作用过程包括两个阶段：以恒定速度将圆柱体压入一定深度，并将圆柱体进一步保持在该深度。粘弹性层的机械性能由具有两种松弛函数的线性粘弹性方程描述：指数和幂。该问题的解决是基于沃尔泰拉原理的应用以及由II沃罗维奇和他的学生们开发的渐近“大和小λ方法”构造的弹性解的使用。根据获得的解决方案，对于相对较小和相对较大的层厚，已经研究了圆柱压痕过程中接触应力和载荷随时间变化的性质。对两个不同松弛函数的研究量的时间变化进行了比较，并与基于简化的一维模型的计算结果进行了比较，该模型用于描述压痕过程中粘弹性层的行为。