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

小行星9508617 数学领域的产学研合作研究 科学是旨在建立数学交流机制的计划。 学术界和工业界之间的科学家在他们职业生涯的不同阶段。这些 计划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。大学与产业 博士后研究奖学金为最近的获奖者提供两年的支持， 数学科学博士学位。这些奖项是一种贡献的手段 国家未来的科学活力。博士后将 与学术界和工业界的科学顾问密切合作。 与Lord公司的聚合物科学家合作， 研究员将使用与材料无关的力和力矩平衡推导， 材料相关的有限应变弹性理论，以开发和验证非线性 橡胶基填充弹性体承受大变形的动态模型。的 所得到的非线性偏微分方程模型，可用于可控的设计， 或“智能材料”弹性体，将修改和验证使用专门设计的 在Lord Corporation实验室沿着使用逆问题算法进行的实验 是发达的。这些算法和相关的计算软件包将 在适定性的数学框架的背景下发展起来， 应用数学家们将在这一领域开发的近似 多学科团队。

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.