CAREER: Fundamentals of Entropy-Driven Mechanics of Flexible Nanostructures

This Faculty Early Career Development (CAREER) award will support research into understanding the fundamental mechanics of flexible, plate-like nanostructures. Examples of these nanostructures include low-dimensional materials, e.g., molybdenum disulphide, phosphorene, boron nitride, and MXenes, and biomembranes. These nanostructures have applications in nanosensors, biomedical devices, gene therapy, nanoelectronics, energy harvesting, and structural composites. One special aspect of these nanostructures is that they constantly experience random deformations due to stored thermal energy, which affects their mechanical behavior and response to external stimuli. It has proven quite difficult, however, to incorporate this effect into conventional mechanical models. This project will develop coupled statistical mechanics and solid mechanics models that will account for large thermal fluctuations in flexible nanostructures. The resultant framework will enable mechanics-guided design of next-generation multifunctional nanostructures for applications in defense, healthcare, and environmental sectors. The award will also support education of next generation interdisciplinary engineers, especially promoting women and minorities, as well as facilitate STEM education for K-12 students through innovative activities, such as a Musical Math Program.Thermal fluctuations are a universal characteristic of all flexible nanostructures due to their low bending stiffness, which impacts their macroscopic mechanical behavior including properties, structural stability, and dynamics. In this project, continuum mechanics models of plates and shells will be integrated with concepts of statistical mechanics to characterize: (1) the macroscopic mechanical properties of a fluctuating membrane with imperfections, (2) the instability, imperfection sensitivity, and buckling behavior of elastic fluctuating membranes, and (3) the dynamics, and properties of free and forced vibrations of fluctuating membranes. These studies are challenging due to nonlinearities, non-traditional boundary conditions, and ubiquitous presence of thermal fluctuations and material imperfections. The developed continuum-statistical mechanics platform would be extendable to other small-scale problems including entropy-driven failure mechanism of nanomaterials, mechanically coupled properties of nanomaterials, and active matters in biology. This project is jointly funded by the Mechanics of Materials and Structures (MoMS) Program and the Biomechanics and Mechanobiology (BMMB) program in the Division of Civil, Mechanical and Manufacturing Innovation (CMMI) in the Directorate for Engineering (ENG).This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.