Refined elastic membrane models with new small-scale features

具有新的小规模特征的精细弹性膜模型最近在小规模膜材料的科学和技术方面提出了令人兴奋的挑战和机遇，包括MEMS(微型机电系统)/NEMS(纳米机电系统)、生物膜和原子厚度的石墨烯单分子膜。在这里，“膜”被定义为薄膜材料，其弯曲硬度较低，但对其力学行为起着至关重要的作用。新的研究机遇刺激了小规模膜材料力学研究的复兴。虽然传统的固体力学模型(如弹性板/膜模型)已经被广泛应用于研究这种小尺度弹性膜的力学行为，但人们普遍认为，由于传统模型具有新的微观结构和力的小尺度特征，因此不能很好地描述此类材料的一些关键力学现象。与传统的弹性膜(如金属膜或橡胶膜)不同，一些小尺度弹性膜和原子厚度的单层膜具有一些新的特征，如：1)厚度方向上由非连续或不均匀的微结构引起的两个独立的弯曲刚度；*基于本申请人在表面弹性、弹性膜、生物膜壳和石墨烯力学方面的研究专长，本提案旨在为小规模膜材料和原子厚度的单层膜开发新的改进的弹性模型，尤其有兴趣探索上述新的小规模特征的影响。本文的研究将有助于加深我们对小尺度膜材料力学行为的理解和建模，并对小尺度固体力学及其在微纳米膜材料中的应用产生重大影响，具有当前和未来的技术意义。这项建议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，以满足加拿大在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.******