Nonlinear Dynamics and Elasticity

该基金支持非线性动力学和弹性的理论研究，特别是变形固体的物理学。这些问题涉及到由原子组成的物质在大尺度上决定其力学行为的方式。在固体物体变形很小的情况下，这些问题在很大程度上得到了解决。然而，当变形大到足以将原子从邻近的原子中撕裂开来时，问题就变得更加困难，小尺度和大尺度之间的联系也更难以定量确定。要解决的一些具体问题包括：为什么硅的断裂能理论和实验仍然相差两倍，如何解决这个问题？成功解决脆性断裂问题的方法能否推广到具有多尺度结构的更复杂材料中？如何描述橡胶中比横波速度更快的裂缝？为什么它们会自发地开始振荡？干滑动摩擦可以用成千上万个类似地震的自愈裂缝的运动来解释吗？受千瓦激光脉冲的影响，金属和半导体中会形成什么样的冲击波？叶子、花朵和被撕破的垃圾袋是否都被类似地描述为非均匀度量？它们的宏观几何特性如何依赖于微观长度？虽然这些问题来自物理学和工程学的许多不同的分支学科，但它们被基本的理论技术、一套通用的数值工具和凝聚态物理学中的首要问题统一起来，即宏观世界是如何从微观基础出发的。这项研究将产生解决多尺度物理问题的理论和计算工具，将为工程力学提供包括商业价值概念在内的新概念，将为教师准备创造材料，并将提供有趣的新物理问题，容易被广大公众理解。该基金支持非线性动力学和弹性的理论研究，特别是变形固体的物理学。这些问题涉及到由原子组成的物质在大尺度上决定其力学行为的方式。在固体物体变形很小的情况下，这些问题在很大程度上得到了解决。然而，当变形大到足以将原子从邻近的原子中撕裂开来时，问题就变得更加困难，小尺度和大尺度之间的联系也更难以定量确定。该研究将产生解决多尺度物理问题的理论和计算工具，将为工程力学提供包括商业价值概念在内的新概念，将为教师准备创造材料，并将提供有趣的新物理问题，易于为广大公众理解

This grant supports theoretical research on nonlinear dynamics and elasticity, in particular, the physics of deformed solids. The problems concern the way that building matter from atoms determines its mechanical behavior on large scales. These problems have largely been solved in cases where the solid object deforms only a small amount. However, when the deformations are large enough to rip atoms apart from their neighbors the problems become more difficult and the connection between small and large scales is more challenging to determine quantitatively. Some particular questions to be addressed include: Why do theory and experiment still differ by a factor of two for the fracture energy of silicon, and how can the problem be resolved? Can methods that successfully solve brittle fracture problems be generalized to more complicated materials with structure on multiple scales? How can one describe cracks traveling faster than the shear wave speed in rubber, and why do they spontaneously begin to oscillate? Can dry sliding friction be explained by the motion of thousands of earthquake-like self-healing fractures? What sorts of shock waves form in metals and semiconductors impacted by petawatt laser pulses? Are leaves, flowers, and ripped garbage bags all similarly described as sheets of non-uniform metrics, and how do their macroscopic geometrical properties depend on microscopic lengths? While these questions come from many different subdisciplines of physics and engineering, they are unified by underlying theoretical techniques, by a common set of numerical tools, and by the overarching question in condensed matter physics, of how the macroscopic world follows from its microscopic foundation.The research will generate theoretical and computational tools to solve multiscale physics problems, will provide new concepts for engineering mechanics including concepts of commercial value, will create material for teacher preparation, and will supply interesting new physics problems easily understood by a broad public.%%% This grant supports theoretical research on nonlinear dynamics and elasticity, in particular, the physics of deformed solids. The problems concern the way that building matter from atoms determines its mechanical behavior on large scales. These problems have largely been solved in cases where the solid object deforms only a small amount. However, when the deformations are large enough to rip atoms apart from their neighbors the problems become more difficult and the connection between small and large scales is more challenging to determine quantitatively. The research will generate theoretical and computational tools to solve multiscale physics problems, will provide new concepts for engineering mechanics including concepts of commercial value, will create material for teacher preparation, and will supply interesting new physics problems easily understood by a broad public.***