Mathematical Sciences: Nonlinear Problems of Solid Mechanics

主要研究者将使用非线性本构方程的几何精确理论研究由各种弹性、塑性和粘性材料组成的杆、壳和固体，以处理新的非线性效应、阈值和不稳定性。他还将研究固体材料的耗散机制，如冲击波和接触不连续面。二维和三维固体是由弹性或塑性材料构成的复杂物体。原因是这些物体在受到载荷或压力时往往表现得与直觉相反。为了帮助理解这些材料并预测它们对施加的力的反应，重要的是要有现实的数学模型，同时也要易于解决。本建议将制定几个这样的模型，并试图找到有意义的解决办法。

The principal investigator will study rods, shells and solid bodies composed of various elastic, plastic and viscous materials using geometrically exact theories for nonlinear constitutive equations, in order to treat new nonlinear effects, thresholds and instabilities. He will study also dissipative mechanisms in solid materials such as shock waves and contact discontinuities. Two-and three-dimensional solid bodies are complicated objects to study when they are composed of elastic or plastic material. The reason is that such objects often behave counter- intuitively when subjected to loading or stress. In order to help understand these materials and predict their responses to applied forces it is important to have mathematical models that are realistic and at the same time amenable to solution. This proposal will formulate several such models and attempt to find meaningful solutions.