Origins of Stress in Elastic Membranes

9528957 Witten橡胶、泡沫、凝胶和生物组织等软材料将是本理论项目的主题。该项目将开发新的方法，用数学、统计物理和计算机模拟来定量地描述和预测这种柔软性。这项研究将集中在两种有望改善预测的材料上。第一种是变形的弹性薄片，如一团纸、一个扭曲的红细胞或一个皱巴巴的挡泥板。扭曲这些弹性薄片的力的大小将通过利用最近发现的关于变形能量如何在变形薄片中分布的见解来预测。这项研究的结果将有助于工程师们设计出能以可控方式折叠的材料片。要研究的第二种材料是附着在表面的聚合物分子的微观层。这种层被用来保持微小的固体颗粒悬浮在许多广泛使用的液体中，如机油或墨水。这些层抵抗变形，因为柔性聚合物倾向于保持尽可能随机。这种最大化随机性的驱动导致聚合物集体扭曲，而不是单独扭曲。这项研究将预测这些层在各种情况下如何扭曲。这个理论研究项目将涉及两类材料。首先，研究人员将研究橡胶等弹性材料的薄片，以确定它们在压力作用下发生皱缩时的行为。这些结果对于预测大量不同材料的皱缩行为将是重要的。其次，将研究附着在表面的聚合物层的行为。这些材料用于悬浮小颗粒，例如用于机油。该研究将研究这些材料在扭曲时的行为。* * *

9528957 Witten Soft materials such as rubbers, foams, gels and biological tissues will be the subject of this theoretical project. The project will develop new ways to describe and predict this softness quantitatively using mathematics, statistical physics and computer simulations. The research will focus on two materials that show promise for improved prediction. The first type are deformed elastic sheets, such as a wad of paper, a distorted red blood cell or a crumpled fender. The amount of force to distort these elastic sheets will be predicted by utilizing a recently discovered insight about how the deformation energy is distributed in a deformed sheet. The results of this research will assist engineers in designing sheets of materials which crumple in controlled ways. The second type of material to be studied will be microscopic layers of polymer molecules attached to surfaces. Such layers are used to keep tiny solid particles suspended in many widely-used fluids such as motor oil or ink. These layers resist deformation because of the tendency for the flexible polymers to remain as random as possible. This drive to maximize randomness leads the polymers to distort collectively rather than individually. The research will predict how these layers distort in various situations. %%% This theoretical research project will deal with two types of materials. First, sheets of elastic materials, such as rubber, will be studied in order to determine how they behave as they crumple under stress. These results will be important for predicting the behavior of a large number of different materials as they crumple. Second, the behavior of polymer layers attached to surfaces will be studied. These materials are used to suspend small particles, such as used in motor oils. The research will study the behavior of these materials as they are distorted. ***