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

该合作研究项目的目标是开发一种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。在宏观材料模型中整合纳米尺度材料的基本物理可以对理解材料的设计产生巨大的影响，并为量化模型中的参数敏感性和不确定性创造了可能性。为了解决后一个问题，新的不确定性量化方法将在贝叶斯统计框架中使用先进的计算来制定和实施。不确定性量化将提供量子模拟支持的宏观参数的概率密度。可交付成果将包括均质化的应力、电场和能量关系，这些关系既利用了局部量子物质关系，也利用了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的影响。由于其在固态结构和器件中的独特功能，这些材料正在被研究和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。这对于推进纳米材料向更大尺度结构的发展变得尤为重要，这些结构不能轻易地用量子模型或近似连续介质理论直接模拟。通过该计划开发的结果将被整合到工程力学和数学课程。计算方法也将被整合到每所大学的外展项目中。最后，这个项目的结果将被介绍到当地博物馆的一个推广项目中，在那里，K-12的孩子和他们的父母通过每月的动手演示来学习工程的各个方面。

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.