CAREER: Multiferroic Materials - Predictive Modeling, Multiscale Analysis, and Optimal Design

该学院早期职业发展(CALEAR)计划奖的研究目标是建立对多铁性晶体和复合材料物理行为的力学和数学的基本理解，预测和优化现有和新的多铁性器件的性能，并通过实验验证理论预测和设计。通过Gamma收敛和齐化分析的方法，从热力学、电动力学、框架无关性和材料对称性的基本原理出发，建立了多铁体在各种物理和几何极限下的自洽非线性理论体系。该数值方法以有限元方法和多水平集梯度法为基础，为预测和优化多铁材料的期望性能提供了计算模型和算法。通过一个协作程序，该实验方法提供了对多铁性复合材料的预测性能和优化设计的验证。多铁性材料可以受到外界磁场、电场和弹性场的刺激和响应，具有多种功能，广泛应用于多驱动和多传感系统。理论、数值和实验相结合的策略将促进具有改进功能的多铁结构和复合材料的工程设计，并刺激新的多铁材料的发现。这些进展将在智能材料和智能系统领域提供新的机遇。与行业合作伙伴的合作将确保潜在的技术转让。与研究密切相关的教育和外联努力将产生更广泛的社会影响，包括为代表性不足的群体提供研究机会、高中访问、关于弹性与生物力学和纳米材料的现代应用的教科书、关于多功能材料和提高学生兴趣和学习体验的优化设计的互动可视化演示项目，以及在会议和公开研讨会上传播研究成果。

The research objective of this Faculty Early Career Development (CAREER) Program award is to establish a fundamental understanding of the mechanics and mathematics that dictates the physical behaviors of multiferroic crystals and composites, to predict and optimize the performance of existing and new multiferroic devices, and to validate the theoretical predictions and designs by experiments. By the method of Gamma convergence and homogenization analysis, the theoretical approach starts from the fundamental principles of thermodynamics, electrodynamics, frame indifference and material symmetries toward a hierarchy of self-consistent nonlinear theories for multiferroic bodies in a variety of physical and geometric limits. Based on the finite element method and multi-level-set gradient method, the numerical approach furnishes computational models and algorithms for predicting and optimizing desired properties of multiferroic materials. Through a collaborative program, the experimental approach provides validation of the predicted properties and optimal designs of multiferroic composites. Multiferroic materials can be stimulated by and respond to external magnetic, electric and elastic fields, serve multiple functions, and are broadly used in multi-actuating and multi-sensing systems. The integrated theoretical, numerical and experimental strategy will facilitate the engineering of multiferroic structures and composites with improved functionalities and stimulate the discovery of novel multiferroic materials. These progresses will offer new opportunities in areas of smart materials and intelligent systems. Collaborations with industrial partners will ensure the potential technology transfer. Broader social impact will be achieved by educational and outreach efforts that are closely tied to the research, including research opportunities for under-represented groups, high-school visits, a textbook on elasticity with modern applications in biomechanics and nanomaterials, an interactive visualization demonstrations project on multifunctional materials and optimal designs to enhance students' interest and learning experience, and dissemination of research findings in conferences and public seminars.