We present a general energy approach to study the unsteady adhesive contact of viscoelastic materials. Under the assumption of infinitely short-range adhesive interactions, we exploit the principle of virtual work to generalize Griffith’s local energy balance at contact edges to the case of a non-conservative (viscoelastic) material, subjected to a generic contact time–history. We apply the proposed energy balance criterion to study the approach–retraction motion of a rigid sphere in contact with a viscoelastic half-space. A strong interplay between adhesion and viscoelastic hysteretic losses is reported which can lead to strongly increased adhesion strength, depending on the loading history. Specifically, two different mechanisms are found to govern the increase of pull-off force during either approach–retraction cycles and approach – full relaxation – retraction tests. In the former case, hysteretic losses occurring close to the circular perimeter of the contact play a major role, significantly enhancing the energy release rate. In the latter case, instead, the pull-off enhancement mostly depends on the glassy response of the whole (bulk) material which, triggered by the fast retraction after relaxation, leads to a sort of ‘frozen’ state and results in a flat-punch-like detachment mechanism (i.e., constant contact area). In this case, the JKR theory of adhesive contact cannot be invoked to relate the observed pull-off force to the effective adhesion energy, i.e. the energy release rate , and strongly overestimates it. Therefore, a rigorous mathematical procedure is also proposed to correctly calculate the energy release rate in viscoelastic dissipative contacts.

中文翻译：

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粘弹性非稳态接触中粘合强度的增强


我们提出了一种通用能量方法来研究粘弹性材料的不稳定粘合接触。在无限短程粘合相互作用的假设下，我们利用虚功原理将接触边缘处的格里菲斯局部能量平衡推广到非保守（粘弹性）材料的情况，并受到通用接触时程的影响。我们应用所提出的能量平衡准则来研究与粘弹性半空间接触的刚性球体的接近-回缩运动。据报道，粘附力和粘弹性滞后损失之间存在强烈的相互作用，这可能导致粘附强度大幅增加，具体取决于加载历史。具体来说，发现两种不同的机制在接近-回缩循环和接近-完全松弛-回缩测试期间控制拉脱力的增加。在前一种情况下，靠近接触圆周边发生的磁滞损耗起着主要作用，显着提高了能量释放率。相反，在后一种情况下，拉脱增强主要取决于整个（块状）材料的玻璃响应，该响应由松弛后的快速回缩触发，导致某种“冻结”状态并导致平坦-类似冲头的分离机制（即恒定的接触面积）。在这种情况下，不能援引粘着接触的 JKR 理论将观察到的拉脱力与有效粘着能（即能量释放率）联系起来，并且严重高估了它。因此，还提出了严格的数学程序来正确计算粘弹性耗散接触中的能量释放率。