Mathematical Sciences: Dynamical Modeling and Estimation ofMechanical Behavior of Elastomer Based Smart Materials

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9508617 Banks The University-Industry Cooperative Research Programs in the Mathematical Sciences are programs designed to establish a mechanism for exchange of mathematical scientists between academia and industry at different stages of their careers. These programs will strengthen the links between industry and academia and identify and encourage new avenues of research in the mathematical sciences. The University-Industry Postdoctoral Research Fellowships provide two years of support for recent recipients of doctoral degrees in the mathematical sciences. These awards are a means of contributing to the future vitality of the scientific effort of the nation. The postdoctoral fellow will work closely with scientific advisors from both academia and industry. In collaboration with polymer scientists at the Lord Corporation, the postdoctoral fellow will use material independent force and moment balance derivations combined with a material dependent finite strain elasticity theory to develop and validate nonlinear dynamic models for rubber based filled elastomers undergoing large deformations. The resulting nonlinear partial differential equation models, to be used in design of controllable or "smart material" elastomers, will be modified and validated using specially designed experiments performed in Lord Corporation labs along with inverse problem algorithms that are developed. These algorithms and associated computational packages will be developed in the context of a mathematical framework for wellposedness and approximation that will be developed by the applied mathematicians in this multidisciplinary team.