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.
