Modeling and Analysis of Adhesion Hysteresis Between Rough Surfaces

粗糙表面之间的粘附滞后的建模与分析

• 批准号: 523956128
• 负责人: Professor Dr. Patrick Dondl
• 金额: --
• 依托单位: Abteilung für Angewandte Mathematik
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/523956128?language=en
• 关键词: Modeling; Analysis; Adhesion; Hysteresis; Between

Surfaces are adhesive or "sticky" if breaking contact requires a finite force. At atomic scales, all surface interact via ubiquitous van-der-Waals interactions, that produce forces per unit area that are orders of magnitude larger than atmospheric pressure. This leads to strong adhesion of small objects, such as Gecko setae and engineered mimics. The strength of these interactions is commonly described by the intrinsic work of adhesion, i.e., the energy that is gained by microscopic interactions per surface area of intimate contact. While for hard substrates roughness limits this area to the highest protrusions, soft solids are sticky because they can deform to come into contact over a large portion of the rough topography. In this thermodynamic view of conforming contact, breaking adhesive contact becomes a fracture-mechanical problem. A common observation from soft contact is that the force needed to break the contact is typically much higher than the force measured during indentation. This observation contradicts expectations from theories that assume the contact follows thermodynamic equilibrium. Indeed, the surface roughness puts the adhesion problem in the "wiggly class" instead of the "Serfaty class" - in short, taking the energetic homogenization limit does not commute with solving the associated gradient flow evolution problem. This leads to a rate-independent contact-line hysteresis emerging from the interplay between a rapidly oscillating potential energy landscape and a viscous evolution. The main objectives in this project are as follows. We will study crack-front pinning and depinning effects on rough surfaces, starting with first-order approximate models, which include a fractional-order Laplacian to describe the elastic interaction in the material. This makes those models amenable to both analytic as well as efficient numerical treatment. The next step is then to extend these models to higher order. Here, comparison principles need to be proved, both to make these higher-order expansions amenable to rigorous mathematical study of pinning and depinning effects, but also to justify efficient numerical methods. Finally, we will examine the fully nonlinear models numerically by means of boundary-element methods. The pinning results obtained will be again compared to constructed sub- and super-solutions which give deterministic estimates on the emerging contact line hysteresis.

如果断开接触需要有限的力，则表面是粘性的或“粘性的”。在原子尺度上，所有表面都通过无处不在的范德华相互作用来相互作用，这种相互作用产生的单位面积的力比大气压力大几个数量级。这导致小型物体(如壁虎刚毛和工程仿制品)具有很强的粘附性。这些相互作用的强度通常用粘着的内功来描述，即每一亲密接触表面的微观相互作用所获得的能量。对于坚硬的衬底，粗糙度将这一区域限制在最高的突起处，而软固体是粘性的，因为它们可以变形，在粗糙的地形的很大一部分上接触。在协调接触的热力学观点中，破坏粘性接触成为一个断裂力学问题。软接触的一个常见观察结果是，断开接触所需的力通常比在压痕过程中测得的力大得多。这一观察结果与假设接触遵循热力学平衡的理论的预期相矛盾。事实上，表面粗糙度将附着力问题归入“摇摆类”而不是“伺服类”--简而言之，采用能量均化极限并不等同于解决相关的梯度流演化问题。这导致了由于快速振荡的势能格局和粘性演化之间的相互作用而出现的与速率无关的接触线滞后。本项目的主要目标如下。我们将从一阶近似模型开始研究粗糙表面上的裂纹前沿钉扎和脱钉效应，其中包括一个分数阶拉普拉斯函数来描述材料中的弹性相互作用。这使得这些模型既可以进行解析处理，也可以进行有效的数值处理。下一步是将这些模型扩展到更高的阶数。在这里，需要证明比较原理，既要使这些高阶展开符合钉扎和去钉扎效应的严格数学研究，也要证明有效的数值方法是正确的。最后，我们将利用边界元方法对完全非线性模型进行数值分析。所得到的钉扎结果将再次与所构造的子解和超解进行比较，所构造的子解和超解对出现的接触线滞后给出确定性的估计。