Collaborative Research: Extraction of local strain and stress fields inside complex multi-scale composite architectures

该奖项将支持开发新的策略，用于对局部应力和应变场进行多尺度分析，以确定结构部件的故障发生。在该方法的核心在于最近发现的椭圆二阶发散形式的偏微分方程的近似理论的主要研究人员根据以前的NSF的支持。该近似方案提供了一类新的局部近似空间，表现出指数下降的误差相对于当地的自由度。在该奖项下进行的研究将把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匀介质。这些结果将提供一种新的方法，用于估计局部应力和应变超过材料组件失效阈值的区域的大小和位置。在这里开发的局部场恢复技术将被应用到由表面应变数据和复合材料样品内预定义区域的实际CT图像组成的数据集。其目标是提供一套预测工具，用于评估缺陷与复合材料结构之间的弹性相互作用、过度应变区的产生以及失效的发生。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。这种需求是由上级各向异性刚度特性驱动的，所述各向异性刚度特性可以通过使用轻质层压、织造和编织纤维增强复合材料架构来实现。复合结构的例子包括波音787梦幻客机的机身、风力发电用的涡轮机叶片和美洲杯游艇的船体。该奖项将支持开发新的策略，用于对局部应力和应变场进行多尺度分析，以确定结构部件的故障发生。预计这项研究的成果将提高用于商业航空的复合材料飞机部件的新型节能设计的能力。主要的工作模式之一将是路易斯安那州立大学和得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局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。的博士该奖学金资助的学生每年夏天将在空军实验室从事研究活动，并获得预测层压和纺织航空航天复合材料损伤的科学实践经验。

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.