CAREER: Effects of Microstructural Randomness in Composite Processing

9875067BaxterA CAREER奖支持材料加工和性能数学建模的研究和教育。研究了金属基复合材料固结后冷却过程中随机微观结构对热-机械应力发展和应力集中的影响。为了研究加工过程中微观结构的随机性对应力发展的影响，本工作将采用移动窗口- gmc技术。它使用被称为广义单元法（GMC）的微力学模型，在移动窗口程序中生成给定材料微观结构的材料属性场。然后使用统计方法来开发与场相关的概率密度、自相关和互相关函数。这些函数将与蒙特卡罗技术一起使用，以生成具有与原始相同统计信息的附加材料属性字段。用于模拟固结冷却的标准有限元方法将使用原始和模拟的属性作为输入。对这些模型输出的分析，例如残余应力状态，将用于改进对复合材料有效使用前性能的预测。与这个项目相关的教育计划有几个重点领域。计划开发两个新球场。第一门课是数值方法的高级本科课程。这门课的重点是解决问题的技巧；通过识别经典工程问题来定义问题，选择解决方法并通过适当的技术平台实现方法。第二节课是本科数学建模课。它将提高本科工程师设置和定义问题的能力。此外，还计划为本科生开设专题短期课程，以研讨会或跨学科课程的形式，以及开发与本奖项研究工作相结合的有竞争力的本科生研究项目。***

9875067BaxterA CAREER award supports research and education in mathematical modeling of materials processing and properties. The research work will examine the influence of random microstructure on the development of thermo-mechanical stresses and stress concentrations in metal matrix composites during cooling after consolidation processing. In order to investigate the effect of randomness in microstructure on the development of stresses during processing this work will employ the Moving Window-GMC technique. It uses the micromechanics model, known as the generalized method of cells (GMC), in a moving window procedure to generate material property fields for a given material microstructure. Statistical methods are then used to develop probability density, auto- and cross correlation functions associated with the fields. These functions will be used with Monte Carlo techniques to generate additional material property fields with the same statistics as the original. Standard finite element methods, used to model consolidation cool down, will use the original and simulated properties as input. The analysis of the output from these models, e.g. residual stress states, will be used to improve predictions of the effective pre-use properties of the composite material.The educational plan associated with this project has several focus areas. The development of two new courses is planned. The first is an advanced undergraduate class in Numerical Methods. The emphasis of this class would be on problem solving techniques; problem definition through identification with classic engineering problems, choice of solution technique and implementation of the method via appropriate technological platforms. The second class is an undergraduate class in mathematical modeling. It will improve the ability of undergraduate engineers to set up and define problems. Also planned are short courses for undergraduates on special topics, in the format of seminars or interdisciplinary classes, as well as development of competitive undergraduate research projects integrated with the research work under this award.***