CDS&E/Collaborative Research: Uncertainty Quantification of an Electromechanical Nonlinear Continuum Theory

这个合作研究项目的目标是开发一个先进的材料建模框架，将量子力学集成到智能材料的宏观连续介质力学建模框架中。在宏观材料模型中集成纳米尺度的材料基本物理学可以对理解材料设计产生巨大影响，并可以量化模型中的参数敏感性和不确定性。为了解决后一个问题，新的不确定性量化方法将制定和实施使用先进的计算贝叶斯统计框架。不确定性量化将提供由量子模拟支持的宏观尺度参数的概率密度。可交付成果将包括均质化应力、电场和能量关系，这些关系利用了局部量子材料关系和在更大长度尺度上近似模型时发生的概率密度。预计量子连续尺度材料模拟的融合将对理解智能材料产生广泛影响。这些材料由于其在固态结构和器件中的独特功能而被研究并应用于各种生物医学，航空航天，汽车和能源领域。新的数据分析和计算技术有望支持这一挑战，以更好地理解先进材料。这在推进纳米材料发展成更大尺度的结构方面变得特别重要，这些结构不能轻易地用量子模型或近似连续理论直接模拟。通过该计划开发的结果将被整合到工程力学和数学课程中。计算方法也将被整合到每个大学的推广计划中。最后，该计划的结果将被引入到当地博物馆的一个推广计划中，在那里，K-12儿童和他们的父母通过每月的动手演示了解工程的各个方面。

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.