作为方向平稳性的塑性：从一个泛函出发的屈服、流动与硬化
Plasticity as Directional Stationarity: Yielding, Flow, and Hardening from One Functional
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中文总结 AI 辅助
该研究以一个标量泛函的方向平稳性统一塑性理论的核心关系，涵盖关联与非关联流动，扩展至率相关演化，通过闭式解验证多机制塑性行为，完善了塑性本构的统一框架。
中文摘要 AI 辅助
传统塑性理论通常由弹性定律、屈服条件、流动规则、硬化关系及加载-卸载条件构成。本文通过对单侧容许塑性路径上的一个标量泛函的方向平稳性来表述这些关系。一阶变分确定应力、内变量力及活动阻力。对容许塑性切向量的限制为每个机制定义了一个简化方向力；其符号与单侧平稳性给出弹性不等式、互补性、加载-卸载条件及活动一致性。关联响应对应于容许切向量与所得屈服面法向量的对齐，而不平行的切向量则代表非关联流动。自相似性分析将正齐次应力度量识别为一类广泛的关联族，并区分了屈服面形状、各向同性膨胀与运动学平移的作用。存储项与阻力项涵盖各向同性、运动学、耦合及梯度硬化，而多个活动变量描述独立激活的机制。粘性势将该构造扩展至率相关演化。四个闭式解分别展示了多活动区域、运动学硬化场、压敏极限状态，以及与法向和非正态流动相关的不同位移场。时间离散本构积分与量纲校验收录于附录。
英文摘要
Traditional plasticity theory is commonly organized through an elastic law, a yield condition, a flow rule, hardening relations, and loading--unloading conditions. This paper formulates these relations through directional stationarity of one scalar functional evaluated over one-sided admissible plastic paths. The first variation determines stress, internal-variable forces, and activity resistance. Restriction to an admissible plastic tangent defines a reduced directional force for each mechanism; its sign and one-sided stationarity give the elastic inequality, complementarity, loading--unloading conditions, and active consistency. Associated response corresponds to alignment between the admissible tangent and the normal to the resulting yield boundary, whereas a nonparallel tangent represents non-associated flow. A self-similarity analysis identifies positively homogeneous stress gauges as a broad associated family and separates the roles of yield-surface shape, isotropic expansion, and kinematic translation. The storage and resistance terms cover isotropic, kinematic, coupled, and gradient hardening, while multiple activity variables describe independently activated mechanisms. A viscous potential extends the construction to rate-dependent evolution. Four closed-form solutions illustrate multi-activity regions, kinematic-hardening fields, pressure-sensitive limit states, and the distinct displacement fields associated with normal and non-normal flow. Time-discrete constitutive integration and dimensional checks are collected in the appendices.
