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首页> 外文期刊>Applied Mechanics Reviews: An Assessment of the World Literature in Engineering Sciences >Thermomechanics of Solids With Lower-Dimensional Energetics: On the Importance of Surface, Interface, and Curve Structures at the Nanoscale. A Unifying Review
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Thermomechanics of Solids With Lower-Dimensional Energetics: On the Importance of Surface, Interface, and Curve Structures at the Nanoscale. A Unifying Review

机译：具有低维能量的固体的热力学：关于纳米尺度上表面，界面和曲线结构的重要性。统一评论

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摘要

Surfaces and interfaces can significantly influence the overall response of a solid body. Their behavior is well described by continuum theories that endow the surface and interface with their own energetic structures. Such theories are becoming increasingly important when modeling the response of structures at the nanoscale. The objectives of this review are as follows. The first is to summarize the key contributions in the literature. The second is to unify a select subset of these contributions using a systematic and thermodynamically consistent procedure to derive the governing equations. Contributions from the bulk and the lower-dimensional surface, interface, and curve are accounted for. The governing equations describe the fully nonlinear response (geometric and material). Expressions for the energy and entropy flux vectors, and the admissible constraints on the temperature field, all subject to the restriction of non-negative dissipation, are explored. A particular emphasis is placed on the structure of these relations at the interface. A weak formulation of the governing equations is then presented that serves as the basis for their approximation using the finite element method. Various forms for a Helmholtz energy that describes the fully coupled thermomechanical response of the system are given. They include the contribution from surface tension. The vast majority of the literature on surface elasticity is framed in the infinitesimal deformation setting. The finite deformation stress measures are, thus, linearized and the structure of the resulting stresses discussed. The final objective is to elucidate the theory using a series of numerical example problems.
机译：表面和界面会严重影响实体的整体响应。它们的行为可以通过连续理论来很好地描述，这些理论赋予表面和界面以其自身的能量结构。当在纳米尺度上对结构的响应进行建模时，这样的理论变得越来越重要。审查的目的如下。首先是总结文献中的主要贡献。第二个方法是使用系统一致且热力学一致的过程来统一这些贡献的选定子集，以得出控制方程。考虑了来自体积和较低维表面，界面和曲线的贡献。控制方程式描述了完全非线性的响应（几何和材料）。探索了能量和熵通量向量的表达式，以及对温度场的容许约束，所有这些都受到非负耗散的限制。在界面上特别强调这些关系的结构。然后给出了控制方程的一个弱公式，该公式用作使用有限元方法进行近似的基础。给出了描述系统完全耦合的热机械响应的亥姆霍兹能量的各种形式。它们包括表面张力的贡献。关于表面弹性的绝大多数文献都以无穷小的变形为框架。因此，对有限变形应力的度量进行了线性化，并讨论了所得应力的结构。最终目标是使用一系列数值示例问题来阐明该理论。

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