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创建一种基本的理解和方法，以预测包括沉淀固体，多相多功能复合材料和自组装晶体在内的异质媒体的性质，并利用新模型来利用这种知识，以实现异质介质和复合材料的最佳设计。 复合材料广泛用于日常生活中，从塑料袋和混凝土（用作建筑材料）到波音787 Dreamliner，其机身由碳复合材料制成。 当今研究人员面临的挑战包括将这一成功扩展到智能/多功能复合材料。 这些是具有多种功能的复合材料，并且可以通过多种外部刺激而受到兴奋并响应。 多功能复合材料的特性主要由组成相的微观结构确定。 本研究从系统地解决了微观结构如何影响多功能复合材料的性质，以及所需属性的最佳微观结构是什么，例如磁电耦合系数。 这些预测性建模和最佳设计问题是通过反向方法解决的：微观结构是“先验”，旨在找到微观结构和材料属性之间的定量关系。 此外，还将开发一个数值工具集来计算各种应用程序的最佳微观结构。许多技术的瓶颈，例如电池和涡轮发动机，取决于开发新的多功能材料。 这项研究的结果可用于为这些技术开发新的多功能复合材料和新的制造过程，这些技术有可能减轻当前能源危机的某些方面。 在教育上，将启动一个互动可视化演示项目，以促进学生学习工程学的兴趣和责任。