CGV: Small: Discrete Variational Contact, Impact, and Dissipative Dynamics

这个项目研究了模拟接触、冲击、摩擦和塑性耗散物理系统的计算技术。伴随而来的优化问题是强非线性，非光滑，非凸的性质，有必要发展新的数值方法。该研究的理由，这些方法的发展，建立在离散几何力学和变分积分，重申了物理学的基本原理在一个离散的，因此立即可计算的形式。该研究考察了由该原理产生的五种核心行为（动量/能量/对称性保持，破坏接触和非渗透），从而推导出计算机算法，其输出捕获这些物理行为。项目成功的衡量标准是：（a）产生新的计算机算法，能够比以往任何时候都更准确和有效地模拟耗散物理现象，（B）对模拟这些现象的计算机算法的新的理论结果，以及（c）行业合作伙伴成功采用新技术。项目成果通过在期刊上发表文章、在万维网上发布源代码以及向工业伙伴转让技术专门知识和数据等方式公开传播。改进接触、冲击和耗散现象模拟的计算技术有助于工程安全分析、生物力学模型、计算机可视化、手术培训工具和工业制造模拟更好地预测现实。准确捕捉物理学的算法有助于对许多悬而未决的问题获得重要的新见解，这些问题影响我们对地震和冰山崩解的大规模物理学，高频微和纳米电子机械设备中的小规模耗散，常见的国内现象，如粉笔在板上的颤动，甚至小提琴弦的激励。

This project investigates computational techniques for modeling dissipative physical systems experiencing contact, impact, friction and plasticity. The attendant optimization problems are strongly nonlinear, nonsmooth, and nonconvex in nature, necessitating the development of novel numerical methods. The research grounds the development of these methods by building on discrete geometric mechanics and variational integrators, which restate the fundamental principles of physics in a discrete, hence immediately computable form. The research examines five core behaviors arising from the Principle (momentum/energy/symmetry preservation, breaking contact, and non-interpenetration) and thereby derives computer algorithms whose outputs capture these physical behaviors. The project success is measured by (a) the production of novel computer algorithms that are able to simulate dissipative physical phenomena more accurately and efficiently than ever before, (b) new theoretical results on what can be expected of computer algorithms that simulate these phenomena, and (c) the successful adoption of the novel techniques by industry partners. The project results are publicly disseminated via articles in journals, release of source code on the world wide web, and transfer of technological expertise and data to industrial partners. Improving computational techniques for the simulation of contact, impact, and dissipative phenomena helps make engineering safety analyses, biomechanical models, computer visualizations, surgical training tools, and industrial manufacturing simulations that better predict reality. Algorithms that accurately capture the physics help to gain important new insights into many open questions that influence our understanding of large-scale geophysics of earthquakes and calving of icebergs, small-scale dissipation in high-frequency micro- and nano-electronic mechanical devices, prosaic domestic phenomena such as the chattering of chalk on a board and even the excitation of violin strings.