AI 中文总结
本研究通过有限应变下广义连续介质的规范理论公式化，解决了广义连续介质模型选择准则与局部标架物理地位的问题，实现了力学模型的统一分类。
AI 中文摘要
广义连续介质理论耦合了基础微结构的宏观变形与微/介观变形，能够解释经典柯西弹性理论中缺失的内部长度尺度效应与高阶力学载荷，在超材料建模中展现出高效性。这催生了大量高阶与更高阶次的模型（如应变梯度、微形态、微极模型），但这些模型的基础运动学简化策略（尤其是减少材料参数数量的策略）仅从自由能角度难以识别，由此留下两个未解决的问题：一是缺乏选择合适模型的系统准则，二是运动学描述中所用局部标架（“物质 directors”）的物理地位长期存在歧义——它们是描述给定微结构状态变化的物理量，还是其变形的任意运动学描述符？本研究通过有限应变下广义连续介质的规范理论公式化来解决这两个问题。本方法虽依赖于连续介质力学现有几何文献中一致的工具与建模选择，但其目标与现有文献不同，旨在对现有力学模型进行统一分类，而非描述缺陷等特定微结构现象。本研究将广义构型定义为经典构型上的活动标架，且相对于参考广义构型的不变性被证明是规范不变性的充分必要条件，由此将微形态理论作为任意物质 directors 变形的通用理论。通过结构群约简可得到一阶广义介质的系统分类，应变梯度连续介质可通过对流标架还原，最终还探讨了约束介质（如偶应力介质）。
英文摘要
Generalised continuum theories couple the macroscopic deformation and the micro-/meso-scopic deformation of an underlying micro-structure. They can account for internal length-scale effects and higher-order mechanical loadings absent from classical Cauchy elasticity and has shown its efficiency in modelling metamaterials. This has led to a proliferation of higher-grade and higher-order models (e.g. strain-gradient, micromorphic, micro-polar) whose underlying kinematic reduction strategies, in particular to reduce the number of material parameters, are rarely identifiable from the free energy alone. It leaves two open issues: the lack of a systematic criterion for selecting an appropriate model, and a persistent ambiguity regarding the physical status of the local frames (''directors of matter'') used in their kinematic description. Are they physical quantities describing the change of state of the given micro-structure or arbitrary kinematic descriptors of its deformation\,? This work addresses both questions through a gauge-theoretic formulation of generalised continua in finite strains. While relying on tools and modelling choices consistent with the existing geometric literature on continuum mechanics, the present approach departs from it in its objectives, aiming at a unifying classification of available mechanical models rather than the description of a specific microstructural phenomenon such as defects. In this work, generalised configurations are defined as moving frames over classical configurations, and invariance with respect to the reference generalised configuration is shown to be a necessary and sufficient condition for a gauge invariance, recovering the micromorphic theory as the general-purpose theory of the deformation of arbitrary directors of matter. A systematic classification of first-order generalised media follows from structural group reduction, while strain-gradient continua are recovered through convected frames, and finally constrained media (e.g. couple-stress) are addressed.
