The contact between a rigid Hertzian indenter and an adhesive broad-band viscoelastic substrate is considered. The material behavior is described by a modified power law model, which is characterized by only four parameters, the glassy and rubbery elastic moduli, a characteristic exponent n and a timescale τ0. The maximum adherence force that can be reached while unloading the rigid indenter from a relaxed viscoelastic half-space is studied by means of a numerical implementation based on the boundary element method, as a function of the unloading velocity, preload and by varying the broadness of the viscoelastic material spectrum. Through a comprehensive numerical analysis we have determined the minimum contact radius that is needed to achieve the maximum amplification of the pull-off force at a specified unloading rate and for different material exponents n. The numerical results are then compared with the prediction of Persson and Brener viscoelastic crack propagation theory, providing excellent agreement. However, comparison against experimental tests for a glass lens indenting a PDMS substrate shows data can be fitted with the linear theory only up to an unloading rate of about 100μm/s showing the fracture process zone rate-dependent contribution to the energy enhancement is of the same order of the bulk dissipation contribution. Hence, the limitations of the current numerical and theoretical models for viscoelastic adhesion are discussed in light of the most recent literature results.

中文翻译：

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体和断裂过程区对粘弹性宽带材料中速率依赖性粘附放大的贡献


考虑了刚性赫兹压头和粘合剂宽带粘弹性基材之间的接触。材料行为由改进的幂律模型描述，该模型仅由四个参数表征，玻璃弹性模量和橡胶弹性模量、特征指数 n 和时间尺度 τ0。通过基于边界元法的数值实现来研究从松弛的粘弹性半空间卸载刚性压头时可以达到的最大粘附力，作为卸载速度、预载荷和改变粘弹性材料光谱的广度的函数。通过全面的数值分析，我们确定了在指定的卸载速率和不同材料指数 n 下实现拉断力的最大放大所需的最小接触半径。然后将数值结果与 Persson 和 Brener 粘弹性裂纹扩展理论的预测结果进行比较，得出了极好的一致性。然而，与压痕 PDMS 基板的玻璃透镜的实验测试进行比较表明，只有在卸载速率约为 100μm/s 的情况下，数据才能用线性理论拟合，这表明断裂过程区速率依赖性对能量增强的贡献与整体耗散贡献相同。因此，根据最新的文献结果讨论了当前粘弹性粘附的数值和理论模型的局限性。