Mathematical Sciences: Bounds and Estimates for the Effective Behavior of Inhomogeneous Materials: The Roles of Anisotrophy and Nonlinear Behavior

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9510513 Olson This work is supported by a Research Planning Grant for Women Scientists and Engineers Award. The purpose of the proposed research is to shed light on the behavior of mixtures of materials, particularly in cases where anisotropy or nonlinear behavior plays an important role. Effective medium theories and the self-consistent approximations have been successfully used to pridict behavior of mixtures in linear and isotropic situations. New approximations are proposed which circumvent some of the drawbacks of the effective medium theories. An average energy approach rather than an average stress approach will be used. The National Science Foundations mandate to ensure the vitality of the Nations scientific enterprise includes concern for the quality, composition, distribution and effectiveness of the human resource base in science and engineering. Within this context, the Foundation is committed to enhancing the current rate of participation of women in science and engineering careers, in general, and as active participants in all of its programs. Research Planning Grant awards are made: (1) to help increase the number of new women investigators participating in NSFs research programs; and, (2) to facilitate preliminary studies and other activities related to the development of competitive research projeats and proposals by women who have not previously had independent Federal research funding. Research Planning Grants are one-time awards that may be used for preliminary work to determine the feasibility of a proposed line of inquiry, and/or for other activities that will facilitate proposal development.