The goal of this collaborative research project is to develop an advanced materials modeling framework that integrates quantum mechanics into a macroscale continuum mechanics modeling framework for smart materials. The integration of fundamental physics of materials at nanometer scales within a macroscopic material model can have a tremendous impact on understanding the design of materials as well as create the possibility of quantifying parameter sensitivities and uncertainties in the models. To address this latter issue, novel uncertainty quantification methods will be formulated and implemented using advanced computations in a Bayesian statistical framework. The uncertainty quantification will provide probability densities of the macroscale parameters supported by quantum simulations. The deliverables will include homogenized stress, electric field, and energy relations that utilize both the local quantum material relations and probability densities that occur when approximating the model at larger length scales.
It is anticipated that the fusion of quantum-continuum scale material simulations will have a broad impact on understanding smart materials. These materials are being investigated for and applied in various biomedical, aerospace, automotive, and energy fields due to their unique functionality in solid state structures and devices. The new data analysis and computational techniques are expected to support this challenge to better understand advanced materials. This becomes particularly important in advancing the development of nanomaterials into larger scale structures that cannot be easily simulated directly with quantum models or approximate continuum theories. The results developed through this program will be integrated into engineering mechanics and mathematics courses. The computational methods will also be integrated into outreach programs at each university. Lastly, the results of this program will be introduced into an outreach program at a local museum where K-12 children and their parents learn about various aspects of engineering through monthly hands-on demonstrations.
