Analysis of Algorithms for Continuum Models of Complex Materials

复杂材料连续体模型算法分析

• 批准号: 1115228
• 负责人: Noel Walkington
• 金额: $ 29.99万
• 依托单位: Carnegie-Mellon University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-10-01 至 2015-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1115228&HistoricalAwards=false
• 关键词: Analysis; Algorithms; Continuum; Models; Complex

The focus of this project is the analysis of numerical schemes, andthe development of algorithms, to simulate materials which exhibitintricate rheological behavior or mechanical response due to theirmicrostructural makeup. Examples include polymers, liquid crystals,and blood, whose elastic molecules or cells influence the macroscopicproperties at the macroscopic scale. These materials are modeled byformidable systems of partial differential equations whose structuralproperties capture important properties and physical principles, andit is important to develop numerical schemes to faithfully inheritthese. This project will bring together tools from partialdifferential equations, continuum mechanics, and numerical analysis,to analyze numerical schemes to simulate these systems. The ability to simulate complex materials is a key technology requiredfor the design and development of many next generation products suchas micro-mechanical devices, ink jets, bio-materials, solar energydevices, and prosthetic organs. Predicting material response is anessential tool needed to determine biological or physiologicalfunction; or to design and manufacture these materials; or for thedesign of the multitudes of devices which use their specialproperties. The research proposed here will result in improvedunderstanding of the mathematical models and the computational toolsused to accomplish these tasks.

该项目的重点是数值方案的分析和算法的发展，以模拟由于其微观结构组成而表现出复杂流变行为或机械响应的材料。例子包括聚合物、液晶和血液，它们的弹性分子或细胞在宏观尺度上影响宏观特性。这些材料是由强大的偏微分方程系统建模的，其结构特性捕捉了重要的特性和物理原理，开发数值方案来忠实地继承这些特性是很重要的。该项目将汇集来自偏微分方程、连续介质力学和数值分析的工具，以分析数值方案来模拟这些系统。模拟复杂材料的能力是设计和开发许多下一代产品（如微机械设备、喷墨、生物材料、太阳能设备和假体器官）所需的关键技术。预测物质反应是确定生物或生理功能所需的基本工具；或者设计和制造这些材料；或者用于设计使用其特殊属性的众多设备。这里提出的研究将导致对数学模型和用于完成这些任务的计算工具的更好理解。