Mathematical Sciences: Analysis of Cavitation

首席调查员将分析某些塑料和金属的数学模型，并将制定标准来预测这些材料在外力下的失效。令人感兴趣的失效类型是那些由于形成微观孔洞而引起的失效，这些微观孔洞的尺寸增大并结合在一起形成材料中的裂纹。将解决的具体问题是孤立孔的萌生和动态生长，以及在孤立孔表面形成二次裂纹。在数学上，所提出的问题包括分析拟线性椭圆组奇异解的存在性，双曲组奇异解的存在性和可容许性准则，以及变分中问题的奇性极小元的存在性。

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.