Effective Properties of Multi-phase Materials by Stochastic Reduced Order Models (SROMs)

该项目将开发一种概率方法，用于计算多相和其他随机非均匀材料的宏观特性。多相材料在实践中被广泛使用，因为它们的性质可以通过改变其组分的体积分数、几何形状和物理性质来调整到特定的应用。例如，不需要空中加油就能不间断地环游世界的旅行者号飞机的结构部件是由石墨纤维制成的;波特兰和沥青水泥混凝土被广泛用作结构和铺路材料;碳纤维水泥基复合材料已成功地应用于电子产品。随机降阶模型将用于表征小尺度下随机非均匀材料的性质，并计算这些材料的宏观性质。该项目将有一个显着的理论影响，制定和解决广泛的问题，在科学和工程，因为这些问题可以描述的方程与随机系数/输入，随机降阶模型提供了一个有效的工具来解决这些方程。预计所提出的研究将产生重大的实际影响，因为它可以应用于解决土木和机械工程中的大规模问题。该项目还将促进研究生和本科生教育。 例如，一名本科生将参与拟议研究的各个方面，并将在一门关于连续介质力学的热门本科课程中讲述他/她的工作，以获得教学经验，并激励本科生进行研究并考虑研究生课程。

The project will develop a probabilistic method for calculating macroscopic properties of multi-phase and other random heterogeneous materials. Multi-phase materials are used extensively in practice since their properties can be tuned to particular applications by altering the volume fraction, geometry, and physical properties of their constituents. For example, the structural members of the Voyager aircraft, that has flown nonstop around the world without midair refueling, were made of graphite fibers; portland and asphaltic cement concretes are used extensively as structural and paving materials; and carbon fiber cement matrix composites have been applied successfully in electronics. Stochastic reduced order models will be used to characterize properties of random heterogeneous materials at small scale and calculate macroscopic properties of these materials. The project will have a notable theoretical impact on both the formulation and solution of a broad range of problems in science and engineering since these problems can be described by equations with random coefficients/input, and stochastic reduced order models provide an efficient tool for solving these equations. The proposed research is expected to have a significant practical impact since it can be applied to solve large scale problems in civil and mechanical engineering. The project will also contribute to both graduate and undergraduate education. For example, an undergraduate student will be involved in all aspects of the proposed research and will lecture on his/her work in a popular undergraduate course on continuum mechanics to gain teaching experience and motivate undergraduates to do research and consider graduate studies.