AI 中文总结
该研究针对非凸、状态与历史相关动力学的耗散演化，建立博弈论全轨迹松弛框架，通过因果Volterra重构简化问题，为含记忆变量的剪切模型证明存在性，其速率群体共存机制关联Portevin–Le Chatelier效应。
AI 中文摘要
我们为具有非凸、状态相关及历史相关动力学的耗散演化建立了全轨迹松弛框架。该框架自然源于能量-耗散演化的博弈论表述，通过因果Volterra重构消除了状态-速率一致性，将问题简化为完整速率轨迹上的对角平衡条件。我们基于消失缺陷可逼近性、紧性及互补半连续性建立了直接方法，针对含非凸动力学势与局部记忆变量的简化简单剪切模型，精确计算了松弛机制；其丰富状态为完整局部历史上的Young测度，我们明确确定了纯对角缺陷的序列下半连续包络，刻画了其零集，为每个松弛零点构造了纯恢复序列，并通过冻结最优响应时间离散化证明了存在性。由此产生的具有不同记忆的不同速率群体共存，为动力学剪切带提供了简化机制，并与负应变速率敏感性及动态应变时效自然关联，而这些正是Portevin–Le Chatelier效应的基础。
英文摘要
We develop a whole-trajectory relaxation framework for dissipative evolutions with non-convex, state- and history-dependent kinetics. The framework arises naturally from a game-theoretical formulation of energy--dissipation evolution. State--rate consistency is eliminated by causal Volterra reconstruction, reducing the problem to a diagonal equilibrium condition on complete rate trajectories. We establish a direct method based on vanishing-defect approximability, compactness, and complementary semicontinuity. The relaxation mechanism is computed exactly for a reduced simple-shear model with a non-convex kinetic potential and a local memory variable. The enriched state is a Young measure on complete local histories. We identify explicitly the sequential lower-semicontinuous envelope of the pure diagonal defect, characterize its zero set, construct pure recovery sequences for every relaxed zero, and prove existence through a frozen-best-response time discretization. The resulting coexistence of distinct rate populations with distinct memories provides a reduced mechanism for kinetic shear banding and connects naturally with negative strain-rate sensitivity and dynamic strain aging such as underlie the Portevin--Le Chatelier effect.
