Emergence of New Properties at the Large-Scale on Elastic Surfaces due to Small-Scale Adhesion and Waviness

该奖项支持使用数学建模和实验研究摩擦的物理机制。摩擦力是两个机械接触的固体表面之间的滑动阻力。这些机制在亚微米长度尺度下操作，并且涉及由表面的粘附力和粗糙度决定的复杂的机械相互作用。然而，这些机制的具体细节仍然知之甚少。新的知识将导致新的战略，可以减少能源浪费，例如在发动机中，由于摩擦。此外，新知识与微制造技术的结合将使工程师能够创建具有定制或可调表面特性的表面。具体而言，它将告知他们应该使用哪些尺寸，形状和表面特征的布置，以产生所需的摩擦效果。这种“结构表面工程”有可能激发许多学科的科学和技术突破。例如，它可以推动假肢的发展，使假肢具有人类的触觉，新的知识将通过调查假设得出，涉及弹性材料表面的摩擦的很大一部分是由发生在小范围内的机械不稳定性所消耗的能量引起的，由于附着力和表面粗糙度而产生的水垢。通过研究基于连续介质力学的接触问题的模型族来研究该假设。将推导出将平均横向接触力与净法向接触力、附着力和粗糙度参数联系起来的方程。通过对这些方程进行渐近分析，可以确定平均横向力是否仍然是有限的，也就是说，当问题中的粗糙度长度尺度无限小时，是否会出现摩擦型行为。将开发新的粘着接触模拟技术和实验，并用于指导和验证理论工作。目前，表面力学现象，如摩擦，被认为是内在的属性，并与唯象模型描述。人们对表面现象如何与小尺度机制和参数相联系的理解非常有限。该项目旨在推导出一个基于微观力学的摩擦数学理论。它将导致创建一个通用的理论方法所需的根本性进展，用于理解表面特性如何在大尺度上出现，作为隐藏在小尺度上的复杂相互作用的模糊效应。

This award supports the study of the physical mechanisms that underlie friction using mathematical modeling and experiments. Friction is the resistance to sliding between two solid surfaces that are in mechanical contact. These mechanisms operate at sub-micrometer length scales and involve complex mechanical interactions that are dictated by the surfaces' adhesion and roughness. The specifics of these mechanisms, however, remain poorly understood. The new knowledge will lead to new strategies that can reduce energy wastage, for example in engines, due to friction. Additionally, the new knowledge in alliance with micro-fabrication techniques will allow engineers to create surfaces with tailored or tunable surface properties. Specifically, it will inform them which sizes, shapes and arrangements of surface features should be used in order to produce the desired frictional effects. Such "structural surface engineering" has the potential to galvanize scientific and technological breakthroughs in many disciplines. For example, it can drive the development of prosthetics that are capable of the human sense of touch, and increase the agility of the next generation of climbing robots for search and rescue missions.The new knowledge will be derived by investigating the hypothesis that a significant fraction of friction involving elastomeric material surfaces is caused by the energy dissipated by mechanical instabilities that take place at the small-scale due to adhesion and surface roughness. The hypothesis will be investigated by studying a model family of continuum mechanics-based contact problems. Equations that connect the mean transverse contact force to the net normal contact force, adhesion and roughness parameters will be derived. By performing an asymptotic analysis of these equations it will be determined whether the mean transverse force remains finite, that is, whether friction type behavior emerges at the large-scale, as the roughness length scale in the problem is made infinitesimally small. New adhesive contact simulation techniques and experiments will be developed and used to guide and verify the theoretical work. Currently, surface mechanical phenomena, such as friction, are considered intrinsic properties and are described with phenomenological models. There is a very limited understanding of how surface phenomena are connected to small-scale mechanisms and parameters. The project aims to derive a micro-mechanics based, mathematical theory of friction. It will lead to fundamental advances required for creating a general, theoretical methodology for understanding how surface properties emerge at the large-scale as the smeared out effects of complex interactions that are hidden at the small-scale.