塑性屈服准则的几何基础：一种统一理论
Geometrical foundations of plasticity yield criteria: A unified theory
AI总结：
该研究提出一种基于微分几何与群论的塑性屈服准则统一模型，通过张量函数分析与级数展开预测应力依赖关系，可涵盖经典屈服准则、解释金属异常行为并预测新应力依赖实例，助力塑性现象研究。
摘要：
本文提出了一种阐明塑性屈服准则数学基础的新模型。该拟议的假设模型除采用基于成熟实验证据的基本假设外，还运用了微分几何与群论概念。其理论推导涉及张量函数分析，并给出了一个级数展开式，可对塑性屈服准则的应力依赖函数关系进行预测。该模型的理论框架包含一系列空间系数，为深入研究致密固体材料的对称性与各向异性提供了更具灵活性的理论。它能够描述经典屈服准则（如Tresca、Von Mises、Hosford、Hill等人提出的准则），还可准确描述Hill（1979）曾阐明的铝等金属的异常行为。此外，该模型还预测了全新的应力依赖实例，这使其非常适用于拟合实验数据，以研究塑性背后的相关现象。
英文摘要：
A new model for elucidating the mathematical foundation of plasticity yield criteria is proposed. The proposed ansatz uses differential geometry and group theory concepts in addition to elementary hypotheses based on well-established experimental evidence. Its theoretical development involves the analysis of tensor functions and provides a series expansion which allows the functional stress-dependence of plasticity yield criteria to be predicted. The theoretical framework for the model includes a series of spatial coefficients that provide a more flexible theory for in-depth examination of symmetry and anisotropy in compact solid materials. It describes the classical yield criteria (like those of Tresca, Von Mises, Hosford, Hill, etc) and accurately describes the anomalous behaviour of metals such as aluminium, which was elucidated by Hill (1979). Further, absolutely new instances of stress-dependence are predicted; this makes it highly useful for fitting experimental data with a view to studying the phenomena behind plasticity.
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