Mathematical Sciences: Mathematical Problems from Materials Science

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The principal investigator will continue looking at the connection between variational models of coherent phase transitions, optimal bounds on the effective moduli of composites and the relaxation of nonconvex variational problems. In particular, he will attempt to predict the microstructure of two- phase coherent phase mixtures via bulk energy minimization, evaluate the role of surface energy in determining the microstructure of coherent phase mixtures, and derive nonlinear results geometrically from linear ones by means of a theory of deformations with uniformly small strain.