Mathematical Sciences: Material Instabilities in Solids

本研究将对数学模型进行分析， 聚合物和韧性材料，以预测故障， 这些材料在外力作用下。 使用的模型是 非线性弹性和粘弹性。 从数学上讲， 问题涉及奇异解的存在性， 拟线性椭圆型和双曲型方程组， 微积分中的奇异极小化问题 变化. 这项工作的应用，以材料故障相关联 随着材料中空腔的形成以及由于 涉及材料表面的抛光。

This research will analyze mathematical models for certain polymers and ductile materials in order to predict the failure of such materials under external forces. The models to be used are nonlinear elasticity and viscoelasticity. Mathematically, the problems involve the existence of singular solutions to quasilinear elliptic and hyperbolic systems, and the existence of minimizers with singularities for problems in the calculus of variations. This work has applications to material failures associated with the formation of cavities in the material and failures due to wrinkling of the material surface.