Mathematical Sciences: Analysis of Cavitation

有了这个建议，首席研究员将继续分析某些聚合物和金属的数学模型，以预测这些材料在外力作用下的失效。数学模型来源于非线性弹性和粘弹性理论，其分析涉及双曲和椭圆系统奇异解的研究以及变分法技术的使用。测试聚合物或金属在外力作用下何时会失效的最常用方法是使实际材料承受载荷，直到其断裂或变形。如果一个人只对材料的总体特性感兴趣，这是很好的，但是如果一个人想要理解为什么材料在给定的载荷下失效，那么他必须求助于材料的数学模型。在这项资助中，首席研究员将通过检查粘弹性理论中的偏微分方程系统，利用高等数学来揭示聚合物和金属的失效和断裂机制。

With this proposal the principal investigator will continue his analysis of mathematical models of certain polymers and metals in order to predict the failure of these materials when external forces are applied. The mathematical models come from the theories of nonlinear elasticity and viscoelasticity, and their analysis involves the study of singular solutions of hyperbolic and elliptic systems and the use of techniques from the calculus of variations. The most common way of testing when a polymer or metal will fail under the influence of an external force is to subject the actual material to loading until it breaks or deforms. This is fine if one is interested only in the gross properties of the material, but if one wants to understand why the material fails at a given load then one must have recourse to mathematical models of the material. In this grant the principal investigator will use advanced mathematics to uncover the mechanisms of failure and fracture in polymers and metals by examining systems of partial differential equations from the theory of viscoelasticity.