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

该项目研究了模拟耗散物理系统的计算技术，这些系统经历了接触、冲击、摩擦和塑性。随之而来的优化问题本质上是强非线性、非光滑和非凸的，需要发展新的数值方法。该研究通过建立在离散几何力学和变分积分器的基础上发展了这些方法，它们以离散的形式重申了物理的基本原理，因此可以立即计算。该研究考察了由该原理产生的五种核心行为（动量/能量/对称保持、断裂接触和非互穿），从而推导出其输出捕捉这些物理行为的计算机算法。衡量项目成功的标准是：(a)能够比以往更准确、更有效地模拟耗散物理现象的新型计算机算法的产生，(b)对模拟这些现象的计算机算法的预期的新理论结果，以及(c)行业合作伙伴成功采用新技术。项目成果通过期刊文章公开传播，在万维网上发布源代码，并向工业伙伴转让技术专长和数据。改进模拟接触、冲击和耗散现象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、外科训练工具和工业制造模拟更好地预测现实。精确捕捉物理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地球物理学的理解，高频微纳米电子机械设备的小规模耗散，平凡的家庭现象，如粉笔在黑板上的抖动，甚至小提琴弦的激发。

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.