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

9508617银行数学科学校企合作研究项目旨在建立学术界与产业界在数学科学家职业生涯不同阶段的交流机制。这些项目将加强工业界和学术界之间的联系，并确定和鼓励数学科学研究的新途径。大学-行业博士后研究奖学金为最近获得数学科学博士学位的人提供两年的支持。这些奖项是为国家科学事业的未来活力作出贡献的一种手段。该博士后将与来自学术界和工业界的科学顾问密切合作。博士后将与Lord公司的聚合物科学家合作，利用材料独立的力和力矩平衡推导，结合材料依赖的有限应变弹性理论，开发和验证橡胶基填充弹性体在大变形下的非线性动态模型。由此产生的非线性偏微分方程模型将用于可控或“智能材料”弹性体的设计，将通过在Lord公司实验室进行的专门设计的实验以及开发的逆问题算法进行修改和验证。这些算法和相关的计算包将在适位性和近似的数学框架的背景下开发，该框架将由这个多学科团队中的应用数学家开发。

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.