Towards a New Framework for the Mechanics of Nonequilibrium Continua

连续介质力学一直是描述和理解材料力学的主要理论工具。然而，随着科学和工程的发展，经典连续介质力学已被证明是不够的，例如，涉及多个长度/时间尺度的物理过程或具有未知热传递机制的动态现象。本研究旨在通过开发一种新的形式来克服这些限制，该形式将增强连续介质力学在描述从原子到宏观的多尺度力学变形和热传递过程中的适用性。将根据该公式开发一种模拟工具，并将自由和广泛地传播，以使力学和材料界受益。此外，该项目将被设计为研究生和本科生的科学训练基地。PI还将接触来自代表性不足的群体的学生以及身体残疾的学生，为他们提供动手研究经验，以便他们开始自己的职业生涯。与经典连续介质力学自上而下的表述不同，本研究将采用自下而上的形式来重新推导平衡定律的场表示。该公式将建立在材料的并发原子和连续体描述上，包括嵌入在每个材料点中的原子自由度；这将允许原子尺度的不连续和热波动被明确地包括在公式中。分布理论将被用作公式的数学工具，它将为涉及不连续或奇异函数的物理行为的粒子和场描述联系起来的数学困难提供严格的解决方案。该研究还将温度重新定义为一个衍生量，从而使连续介质力学中所有场量的描述与实验测量或原子模拟计算的描述完全一致。此外，将开发、演示和验证一个模拟工具，通过再现两个高度非平衡的过程，这两个过程都是温度和尺寸相关的：异质外延生长和热激活的位错运动。期望这项研究将为连续体力学提供一个新的框架，可以预测高度非平衡的变形过程和现象，并揭示潜在的机制，除了原子间的相互作用势之外，没有经验规则或参数。该项目由土木、机械和工业创新部（CMMI）的材料和结构力学（mom）项目以及化学、生物工程、环境和运输系统部（CBET）的热传输过程（TTP）项目共同资助。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Continuum mechanics has been the major theoretical tool for the description and understanding of the mechanics of materials. As science and engineering advance, however, classical continuum mechanics has been shown to be insufficient, e.g., for physical processes involving multiple length/time scales or for dynamic phenomena with unknown thermal transport mechanisms. This research aims to overcome these limitations by developing a new formalism that will enhance the applicability of continuum mechanics to describe multiscale mechanical deformation and thermal transport processes from the atomic to the macroscopic. A simulation tool will be developed based on the formulation and will be freely and broadly disseminated to benefit mechanics and materials communities. In addition, the project will be designed to serve as a scientific training ground for graduate and undergraduate students. The PI will also reach out to students from underrepresented groups as well as students with physical disabilities to provide them with hands-on research experiences from which they may launch their careers. Different from the top-down formulation of classical continuum mechanics, this research will employ a bottom-up formalism to rederive the field representation of balance laws. The formulation will build on a concurrent atomistic and continuum description of materials by including the atomic degrees of freedom embedded within each material point; this will allow atomic-scale discontinuities and thermal fluctuations to be explicitly included in the formulation. The Theory of Distributions will be used as the mathematical tool for the formulation, which will provide a rigorous solution to the mathematical difficulties in linking particle and field descriptions of physical behavior involving discontinuous or singular functions. The research will also redefine temperature as a derived quantity, thus enabling the descriptions of all the field quantities in continuum mechanics to be fully consistent with those measured in experiments or calculated from atomistic simulations. In addition, a simulation tool will be developed, demonstrated, and validated by reproducing two highly nonequilibrium processes that are both temperature- and size-dependent: heteroepitaxial growth and thermally activated dislocation motion. It is expected that this research will lead to a new framework for the mechanics of continua that can predict highly non-equilibrium deformation processes and phenomena, as well as reveal the underlying mechanisms, with no empirical rules or parameters other than an interatomic potential. This project is co-funded by the Mechanics of Materials and Structures (MOMS) program in the Division of Civil, Mechanical and Industrial Innovation (CMMI) and the Thermal Transport Processes (TTP) program in the Division of Chemical, Bioengineering, Environmental and Transport Systems (CBET).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.