Ciavarella M, Tricarico M, Papangelo A
Department of Mechanics Mathematics and Management, TriboDynamics Lab, Politecnico di Bari, Via Orabona 4, 70125, Bari, Italy.
Eur Phys J E Soft Matter. 2025 Apr 29;48(4-5):20. doi: 10.1140/epje/s10189-025-00484-5.
We investigate the 2D contact problem of sliding a non-cylindrical punch on a viscoelastic halfplane, assuming a power law shape with . We find with a full boundary element numerical solution that the Persson analytical solution for friction, which works well for the cylindrical punch case assuming the pressure remains identical in form to the elastic case, in this case leads to significant qualitative errors. However, we find that the friction coefficient follows a much simpler trend; namely, we can use as a first approximation the solution for the cylinder, provided we normalize friction coefficient with the modulus and mean pressure at zero speed, despite that we show the complex behaviour of the pressure distribution in the viscoelastic regime. We are unable to numerically solve satisfactorily the ill-defined limit of sharp flat punch, for which Persson's solution predicts finite friction even at zero speed.
我们研究了在粘弹性半平面上滑动非圆柱形冲头的二维接触问题，假设其形状为幂律形状 。通过全边界元数值解，我们发现对于摩擦的佩尔松解析解，在假设压力形式与弹性情况相同的圆柱形冲头情形下效果良好，但在此情况下会导致显著的定性误差。然而，我们发现摩擦系数遵循一个简单得多的趋势；也就是说，尽管我们展示了粘弹性区域中压力分布的复杂行为，但只要我们用零速度下的模量和平均压力对摩擦系数进行归一化，就可以将圆柱体的解作为一阶近似。对于尖锐扁平冲头的定义不明确的极限情况，我们无法通过数值方法令人满意地求解，佩尔松的解预测即使在零速度下也存在有限摩擦。
