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.
