Collaborative Research: Extraction of local strain and stress

该奖项将支持开发用于局部应力和应变场多尺度分析的新策略，以确定结构部件失效的开始。该方法的核心是最近在椭圆二阶散度偏微分方程近似理论方面的发现，该理论是由原NSF资助的主要研究人员获得的。该逼近方案提供了一类新的局部逼近空间，其误差相对于局部自由度呈指数递减。该奖项下的研究将把该理论扩展到线弹性系统和具有残余应力和内部缺陷的非均质介质。这些结果将提供一种新的方法来估计局部应力和应变超过材料构件失效阈值的区域的大小和位置。本文开发的局部现场恢复技术将应用于由表面应变数据和复合样品内部预定义区域的实际CT图像组成的数据集。目标是提供一套预测工具，用于评估缺陷和复合体系结构之间的弹性相互作用，过量应变区域的产生，以及失效的开始。航空、运输和能源收集领域对先进复合材料的需求日益增长。这种需求是由优异的各向异性刚度特性驱动的，这种特性可以通过使用轻质层压、编织和编织纤维增强复合材料结构来实现。复合材料结构的例子包括波音787梦想飞机的机身，风力发电的涡轮叶片和美国杯游艇的船体。该奖项将支持开发用于局部应力和应变场多尺度分析的新策略，以确定结构部件失效的开始。预计本研究成果将提高商用航空复合材料飞机部件新型节能设计的能力。主要操作模式之一将是路易斯安那州立大学和德克萨斯大学的主要研究人员与赖特帕特森空军基地空军研究实验室材料和制造理事会的研究科学家之间的互动。拟议的努力将加强这些研究所之间的研究联系。获得该资助的博士生将于每年夏天在空军实验室从事研究活动，并在层压和纺织航空航天复合材料的损伤预测科学方面获得实践经验。

This award will support the development of new strategies for multi-scale analysis of local stress and strain fields to identify the onset of failure in structural components. At the core of the method lies a recent discovery in approximation theory for elliptic second order divergence form partial differential equations obtained by the principal investigators under previous NSF support. The approximation scheme delivers a new class of local approximation spaces exhibiting exponentially decreasing error with respect to the local degrees of freedom. The research carried out under this award will extend the theory to linear elastic system and to heterogeneous media with residual stress and internal flaws. These results will deliver a new methodology for estimating the size and location of zones where the local stress and strain exceeds the failure threshold for material components. The local field recovery technique developed here will be applied to data sets consisting of surface strain data and actual CT images of predefined regions inside composite samples. The goal is to provide a suite of predictive tools for assessing the elastic interaction between flaws and composite architectures, the generation of zones of excess strain, and the onset of failure.There is a growing demand for advanced composite materials for use in aviation, transportation and energy harvesting. This demand is driven by the superior anisotropic stiffness properties that can be achieved through the use of lightweight laminated, woven and braided fiber reinforced composite architectures. Examples of composite structures include the fuselage of the Boeing 787 Dreamliner, turbine blades for wind power generation and hulls for America's cup yachts. This award will support the development of new strategies for multi-scale analysis of local stress and strain fields to identify the onset of failure in structural components. It is anticipated that the outcome of this research will enhance the capability for novel energy efficient design of composite aircraft components for use in commercial aviation. One of the primary modes of operation will be the interaction between the Principal Investigators at Louisiana State University and the University of Texas with research scientists at the Materials and Manufacturing Directorate of the Air Force research laboratories, Wright Patterson Air Force Base. The proposed effort will strengthen research ties between these institutes. The Ph.D. student supported by this grant will engage in research activity at the Air Force Labs each Summer and gain hands-on experience in the science of predicting damage for laminated and textile aerospace composites.