Refined elastic membrane models with new small-scale features

具有新小尺度特征的精细弹性膜模型*******近年来，在包括MEMS（微机电系统）/NEMS（纳米机电系统）、生物膜和原子厚石墨烯单层等小尺度膜材料的科学和技术领域提出了令人兴奋的研究挑战和机遇。这里的“膜”被定义为弯曲刚度低但在其机械行为中起重要作用的薄膜材料。新的研究机会刺激了小尺度膜材料力学研究的复苏。尽管传统的固体力学模型（如弹性板/弹性膜模型）已被广泛应用于研究此类小尺度弹性膜的力学行为，但由于此类材料具有新的微观结构和力的小尺度特征，传统模型无法捕捉其一些关键的力学现象。这给固体力学界提出了一个重大挑战。*******与传统的弹性膜（如金属膜或橡胶膜）不同，一些小尺度的弹性膜和原子厚度的单层膜具有一些新的特征，如****1)在厚度方向上由非连续或不均匀的微观结构引起的两个独立的弯曲刚度；****2)显著的表面应力和表面弹性效应；****3)极低的弯曲刚度和相关的大挠度和非线性曲率。*******基于申请人在表面弹性、弹性膜、生物膜壳和石墨烯力学方面的研究专长，本提案旨在开发小规模膜材料和原子厚单层膜的新的精细弹性模型，并特别感兴趣探索上述新的小规模特征的含义。本文的研究可以提高我们对小规模膜材料力学行为的理解和建模，并对小规模固体力学及其在当前和未来具有重要技术意义的微纳膜材料中的应用产生重大影响。该提案将有助于在关键研究领域建立一个有影响力的加拿大研究小组，并为培训新一代小型机械工程工程师做出重大贡献，以满足加拿大不久的将来的预期需求。******

Refined elastic membrane models with new small-scale features*******Exciting research challenges and opportunities have recently been raised in science and technology of small scale membrane materials including MEMS (micro-electromechanical systems)/NEMS (nano-electromechanical systems), bio-membranes, and atom-thick graphene monolayers. Here “membranes” are defined as thin film materials whose bending rigidity is low but yet plays an essential role in their mechanical behavior. The new research opportunities have stimulated a resurgence of research on mechanics of small-scale membrane materials. Although traditional solid mechanics models (such as elastic plate/membrane models) have been widely applied to study mechanical behavior of such small-scale elastic membranes, it is now widely recognized that traditional models cannot capture some key mechanics phenomena of such materials due to their new small-scale features of microstructures and forces. This has raised a major challenge to the solid mechanics community.*******Different than classical elastic membranes (such as metallic or rubber films), some small-scale elastic membranes and atom-thick monolayers are characterized by a few new features such as****1) two independent bending rigidities caused by non-continuum or inhomogeneous microstructure in thickness direction;****2) significant surface stress and surface elasticity effects;****3) extremely low bending rigidity and the associated large deflection and nonlinear curvature.*******Based on the present applicant's research expertise on surface elasticity, elastic membranes, bio-membrane shells and graphene mechanics, the present proposal aims to develop new refined elastic models for small-scale membrane materials and atom-thick monolayer membranes, with particular interest in exploring the implications of the above-mentioned new small-scale features. The proposed research could improve our understanding and modeling of mechanical behavior of small-scale membrane materials and make a significant impact on the small-scale solid mechanics and its applications to micro/nano membrane materials of current and future technical importance. The proposal will contribute to building an influential Canadian research group in the key research areas, and to make a significant contribution to the training of a new generation of engineers in small-scale mechanical engineering, to meet the anticipated needs of Canada in the near future.******