Nonlinear Problems of Solid Mechanics

固体力学非线性问题

• 批准号: 0708180
• 负责人: Stuart Antman
• 金额: --
• 依托单位: University of Maryland, College Park
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2007
• 资助国家: 美国
• 起止时间: 2007-07-01 至 2011-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0708180&HistoricalAwards=false
• 关键词: Nonlinear; Problems; Solid; Mechanics

Antman0708180 S. S. Antman and his coworkers treat a variety of dynamicaland steady-state nonlinear problems for deformable rods, shells,and three-dimensional solid bodies that can suffer large andrapid deformations. The bodies are composed of nonlinearlyelastic, viscoelastic, plastic, viscoplastic, or magnetoelasticmaterials. In each case, properly invariant, geometrically exacttheories encompassing general nonlinear constitutive equationsare used. The goals of these studies are to (i) discover newnonlinear effects, (ii) determine thresholds in constitutiveequations separating qualitatively different responses, (iii)determine general classes of constitutive equations that are bothphysically and mathematically natural, (iv) examine and predictimportant kinds of instabilities, (v) determine how existence,regularity, and well-posedness of solutions of the governingquasilinear systems of partial differential equations depend onmaterial behavior, (vi) contribute to the theory of shocks anddissipative mechanisms in solids, and (vii) develop new methodsof nonlinear analysis and of effective computation for problemsof solid mechanics. Antman is continuing to make carefullyformulated physical theories accessible to mathematicians, and tomake modern techniques of applicable analysis accessible toscientists and engineers, with special attention to graduatestudents. S. S. Antman and his coworkers develop powerful newmathematical methods for analyzing the large and rapiddeformations of solid bodies. This work has applications both tonew technological materials including "smart" materials and toold biological materials, such as living tissue. (Although ithas been known for 50 years how to derive the equations governingsuch deformations cleanly from first principles without ad hocapproximations, the mathematical tools for treating theseequations are only now being developed and refined.) Thespecific problems under study include (1) the deformation of thinshell-like bodies in a fluid flow, (2) the loss of stability ofsuch a shell subjected to pulsating pressures, (3) the swimmingof eels, (4) the rigorous justification of useful approximationsfor the motions of the body when the loads it bears are appliedslowly or when the loads are very large or when the body is oflight weight, (5) the buckling of shells, (6) strange effects forspinning bodies, (7) the development and the preclusion of shocks(which are large and sudden discontinuities in velocity anddeformation), and (8) the construction of effective methods ofcomputation. Antman is continuing to make carefully formulatedphysical theories accessible to mathematicians, and to makemodern techniques of applicable mathematics accessible toscientists and engineers, with special attention to graduatestudents.

Antman0708180 S. S. Antman和他的同事将可变形的杆，壳和三维固体物体治疗各种动态和稳态非线性问题，这些固体可能会遭受较大的雄激素变形。 这些身体由非线弹性，粘弹性，塑料，粘塑料或磁弹性材料组成。 在每种情况下，适当不变，几何精确的理论包括使用一般非线性本构方程。 The goals of these studies are to (i) discover newnonlinear effects, (ii) determine thresholds in constitutiveequations separating qualitatively different responses, (iii)determine general classes of constitutive equations that are bothphysically and mathematically natural, (iv) examine and predictimportant kinds of instabilities, (v) determine how existence,regularity, and well-posedness of solutions of the governingquasilinear systems of partial微分方程取决于物质行为，（vi）有助于固体中的冲击理论和解剖机制，（vii）开发非线性分析的新方法和固体力学问题的有效计算。 安特曼（Antman）正在继续使数学家可以仔细化的物理理论，并特别关注毕业生的现代分析现代技术。 S. S. Antman和他的同事开发了有力的新数学方法，用于分析固体的大型和快速变化。 这项工作具有Tonew技术材料的应用，包括“智能”材料和Toold生物材料，例如生物组织。 （尽管ITHA已知已有50年了，如何在没有临时临时的情况下从第一原理中得出统一变形，但仅开发和完善了用于治疗以下问题的数学工具。鳗鱼的游泳，（4）在载荷时，对身体运动的有用近似值进行了严格的理由。 （8）构建有效的计算方法。 安特曼（Antman）继续使数学家可以访问精心构造的身体理论，并特别关注毕业生的适用数学访问的技术。