Mathematical Sciences: Analysis of Cavitation

首席研究员将分析某些塑料和金属的数学模型，并制定标准来预测这些材料在外力作用下的失效。我们感兴趣的失效类型是那些由于微观孔洞的形成而引起的，这些孔洞的大小不断增大，并结合在一起在材料中形成裂纹。将讨论的具体问题是孤立孔的起始和动态生长，以及孤立孔表面上二次裂纹的形成。在数学上，所提出的问题涉及拟线性椭圆型系统奇异解的存在性分析，双曲型系统奇异解的存在性和可容许准则，以及变分问题中具有奇异性的极小解的存在性。

The Principal Investigator will analyze mathematical models for certain plastics and metals and will develop criteria to predict the failure of such materials under external forces. The types of failures of interest are those due to the formation of microscopic holes which grow in size and combine to form cracks in the material. Particular problems that will be addressed are the initiation and dynamic growth of a solitary hole, and the formation of secondary cracks upon the surface of a solitary hole. Mathematically, the proposed problems involve the analysis of existence of singular solutions to quasilinear elliptic systems, the existence of, and admissibility criterion for, singular solutions to hyperbolic systems, and the existence of minimizers with singularities for problems in the calculus of variations.