Origins of Stress in Elastic Membranes

9528957维滕软材料，如橡胶，泡沫，凝胶和生物组织将是这个理论项目的主题。 该项目将开发新的方法来描述和预测这种软定量使用数学，统计物理和计算机模拟。 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片，如一叠纸，扭曲的红细胞或皱巴巴的挡泥板。 通过利用最近发现的关于变形能如何分布在变形片材中的洞察力来预测使这些弹性片材变形的力的量。 这项研究的结果将有助于工程师设计以受控方式起皱的材料片材。 第二类待研究的材料是附着在表面的聚合物分子的微观层。 这些层用于保持微小的固体颗粒悬浮在许多广泛使用的流体中，如机油或墨水。 这些层抵抗变形，因为柔性聚合物保持尽可能随机的趋势。 这种最大化随机性的驱动力导致聚合物集体而不是单独地扭曲。 该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种类型的材料。 首先，将研究弹性材料（如橡胶）的片材，以确定它们在应力下起皱时的行为。 这些结果对于预测大量不同材料在起皱时的行为非常重要。 其次，将研究附着在表面上的聚合物层的行为。 这些材料用于悬浮小颗粒，例如用于机油中。 这项研究将研究这些材料在变形时的行为。 ***

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. ***