Viscoelastic materials are receiving increasing attention in soft robots and pressure sensitive adhesives design, but also in passive damping techniques in automotive and aerospace industry. Here, by using the correspondence principle originally developed by Lee and Radok and further extended by Ting and Greenwood, we transform the elastic solutions of Persson for contact of nominally flat but randomly rough surfaces to viscoelastic indentation. As an example, the cases of step loading and of the response to a single cycle of harmonic loading are studied. For the latter, the effect of the loading frequency, of the ratio between the rubbery and the glassy moduli of the material, and of the mean normal load on the dissipated energy per cycle is studied in detail for a standard viscoelastic material. The results shown are significant for the engineering applications involving cyclic indentation of soft materials, such as in tire-road contact, seals, pick-and-place manipulators and grippers

粘弹性材料在软机器人和压敏粘合剂设计以及汽车和航空航天工业的被动阻尼技术中受到越来越多的关注。在这里，通过使用最初由 Lee 和 Radok 开发并由 Ting 和 Greenwood 进一步扩展的对应原理，我们将 Persson 的弹性解转换为名义上平坦但随机粗糙的表面接触到粘弹性压痕。作为一个例子，研究了阶跃加载和对单个谐波加载周期的响应的情况。对于后者，详细研究了标准粘弹性材料的加载频率、材料的橡胶状和玻璃状模量之间的比率以及平均法向载荷对每个循环耗散能量的影响。