Mathematical Sciences: Nonlinear Problems of Solid Mechanics

小行星9623261 PI建议处理各种杆，壳和三维固体的动态和稳态非线性问题。 这些物体由非线性弹性、粘弹性、塑性、 粘塑性或磁弹性材料。 他还打算治疗 流体-固体相互作用在每种情况下，正确不变，几何 包含一般非线性本构方程的精确理论， 被利用 这些研究的目标是发现新的非线性效应， 定性分离本构方程阈值的确定 不同的反应，检查重要的不稳定性，有助于 冲击理论和固体中的耗散机制，并发展非线性分析和有效计算问题的新方法 固体力学。 %%% 研究人员建议研究各种固体经历大的动态变形的行为，包括固体与流体相互作用的情况，如飞机和船舶。 通过将现代数学方法应用于可变形固体理论， 他以极大的概括性和精确性来阐述问题， 一次可以处理大量的材料。 这项工作的目的之一是确定意想不到的不稳定性，这可能会对技术应用中使用的结构的响应产生不利影响。 他还建议为材料行为理论做出贡献，发展控制材料行为的方法（通过使用智能 例如，涉及电磁效应的材料），并且 开发新的数学和计算方法， 这些困难和重要的应用。 ***

9623261 Antman The PI proposes to treat a variety of dynamical and steady-state nonlinear problems for rods, shells, and three-dimensional solid bodies. The bodies are composed of nonlinearly elastic, viscoelastic, plastic, viscoplastic, or magnetoelastic materials. He also intends to treat fluid-solid interactions. In each case, properly invariant, geometrically exact theories encompassing general nonlinear constitutive equations are to be used. The goals of these studies are to discover new nonlinear effects, determine thresholds in constitutive equations separating qualitatively different responses, examine important kinds of instabilities, contribute to the theory of shocks and dissipative mechanisms in solids, and develop new methods of nonlinear analysis and of effective computation for problems of solid mechanics. %%% The investigator proposes to study the behavior of various solids undergoing large dynamic deformations, including cases in which the solid is interacting with a fluid, as happens in airplanes and ships. By applying modern mathematical methods to theories of deformable solids formulated with great generality and precision, he intends to treat problems for large families of materials at one time. One aim of this work is to determine unexpected instabilities, which can adversely alter the response of structures used in technological applications. He also proposes to contribute to the theory of material behavior, to the development of methods for the control of material behavior (by using smart materials involving electromagnetic effects, for example), and to the development of new mathematical and computational methods capable of handling these difficult and important applications. ***