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，则表面具有粘性或“粘性”。在原子尺度上，所有表面都通过普遍存在的范德华相互作用相互作用，每单位面积产生的力比大气压力大几个数量级。这导致小物体（例如壁虎刚毛和工程模仿物）具有很强的粘附力。这些相互作用的强度通常用粘附的内在功来描述，即通过紧密接触的每个表面积的微观相互作用获得的能量。虽然对于硬质基材来说，粗糙度将该区域限制为最高的突出部分，但软固体具有粘性，因为它们可以变形以接触大部分粗糙的地形。在这种顺应接触的热力学观点中，破坏粘合接触成为断裂机械问题。从软接触中观察到的一个常见现象是，断开接触所需的力通常远高于压痕期间测得的力。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，表面粗糙度将粘附问题归入“wiggly 类”而不是“Serfaty 类”——简而言之，采用能量均质化极限并不意味着解决相关的梯度流演化问题。这导致快速振荡的势能景观和粘性演化之间的相互作用而出现与速率无关的接触线滞后。该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，其中包括用于描述材料中弹性相互作用的分数阶拉普拉斯算子。这使得这些模型既适合分析又适合高效的数值处理。下一步是将这些模型扩展到更高阶。在这里，需要证明比较原理，既使这些高阶展开式适合钉扎和脱钉效应的严格数学研究，又证明有效的数值方法的合理性。最后，我们将通过边界元方法对完全非线性模型进行数值检验。获得的钉扎结果将再次与构建的子解决方案和超级解决方案进行比较，这些解决方案对新出现的接触线磁滞给出确定性估计。