Variational Inequalities and their Applications in the Predictive Modeling of Heterogeneous Media

变分不等式及其在异质介质预测建模中的应用

• 批准号: 1101030
• 负责人: Liping Liu
• 金额: $ 20.01万
• 依托单位: University of Houston
• 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: 2011-07-15 至 2012-10-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1101030&HistoricalAwards=false
• 关键词: Variational; Inequalities; their; Applications; Predictive

The research objective of this project is to create a fundamental understanding and methods for predicting the properties of heterogeneous media including precipitated solids, multiphase multifunctional composites and self-assembled crystals, and to exploit such knowledge for new models for heterogeneous media and optimal design of composite materials. Composites are broadly used in daily life ranging from plastic bags and concrete (used as a construction material) to the Boeing 787 Dreamliner whose fuselage is made of carbon composites. The challenge facing researchers today consists of extending this success to smart/multifunctional composites. These are composites that serve several functions and can be excited by and respond to multiple external stimuli. The properties of multifunctional composites are predominantly determined by the microstructure of the constituent phases. The present research systematically addresses how microstructures influence the properties of multifunctional composites and what are the optimal microstructures for a desired property, e.g., the magnetoelectric coupling coefficient. These predictive modeling and optimal design problems are addressed by an inverse method: microstructures are "a priori" designed to find the quantitative relation between microstructures and material properties. Also, a numerical toolset will be developed to compute optimal microstructures for various applications. The bottleneck of many technologies, e.g., batteries and turbine engines, hinges on the development of new multifunctional materials. The results of this research can be used to develop new multifunctional composites and new manufacturing processes for these technologies, which have the potential to mitigate some aspects of the current energy crisis. Educationally, an interactive visualization demonstrations project will be launched to promote students' interest and responsibility to learn engineering.

该项目的研究目标是建立一个基本的理解和方法来预测非均匀介质的性质，包括沉淀固体，多相多功能复合材料和自组装晶体，并利用这些知识为非均匀介质和复合材料的优化设计的新模型。 复合材料广泛应用于日常生活中，从塑料袋和混凝土（用作建筑材料）到波音787梦想飞机，其机身由碳复合材料制成。 今天研究人员面临的挑战包括将这种成功扩展到智能/多功能复合材料。 这些复合材料具有多种功能，可以被多种外部刺激激发并做出反应。 多功能复合材料的性能主要由组成相的微观结构决定。 本研究系统地讨论了微结构如何影响多功能复合材料的性能，以及对于所需性能，例如，磁电耦合系数。 这些预测建模和优化设计的问题是由一个逆的方法：微结构是“先验”的设计，以找到微观结构和材料性能之间的定量关系。 此外，还将开发一套数值工具，以计算各种应用的最佳微观结构。许多技术的瓶颈，例如，电池和涡轮机发动机，取决于新的多功能材料的开发。 这项研究的结果可用于开发新的多功能复合材料和新的制造工艺，这些技术有可能缓解当前能源危机的某些方面。 在教育方面，我们将推出一个互动的可视化演示项目，以提高学生学习工程的兴趣和责任感。