A CAREER award supports research and education in mathematical modeling of materials processing and properties. The research work will examine the influence of random microstructure on the development of thermo-mechanical stresses and stress concentrations in metal matrix composites during cooling after consolidation processing. In order to investigate the effect of randomness in microstructure on the development of stresses during processing this work will employ the Moving Window-GMC technique. It uses the micromechanics model, known as the generalized method of cells (GMC), in a moving window procedure to generate material property fields for a given material microstructure. Statistical methods are then used to develop probability density, auto- and cross correlation functions associated with the fields. These functions will be used with Monte Carlo techniques to generate additional material property fields with the same statistics as the original. Standard finite element methods, used to model consolidation cool down, will use the original and simulated properties as input. The analysis of the output from these models, e.g. residual stress states, will be used to improve predictions of the effective pre-use properties of the composite material.
The educational plan associated with this project has several focus areas. The development of two new courses is planned. The first is an advanced undergraduate class in Numerical Methods. The emphasis of this class would be on problem solving techniques; problem definition through identification with classic engineering problems, choice of solution technique and implementation of the method via appropriate technological platforms. The second class is an undergraduate class in mathematical modeling. It will improve the ability of undergraduate engineers to set up and define problems. Also planned are short courses for undergraduates on special topics, in the format of seminars or interdisciplinary classes, as well as development of competitive undergraduate research projects integrated with the research work under this award. ***
