AI 中文总结
研究玻璃态聚合物屈服等力学性能的非线性响应，基于杜利特尔方程和昂萨格变分原理建立极简理论，通过剪切解冻机制解释相关现象，给出屈服应力表达式及颈缩相图，建立统一框架。
AI 中文摘要
屈服、塑性和颈缩对于材料的力学性能至关重要，但对于这些非线性响应如何产生，仍缺乏简洁统一的物理图景。我们基于遵循杜利特尔方程的经典体积依赖性弛豫时间，为玻璃态聚合物建立了一个极简理论，并使用昂萨格变分原理推导本构关系。令人惊讶的是，该简单理论通过剪切解冻机制解释了恒定应变速率加载下的屈服、塑性和颈缩起始：随着样品拉伸，体积增加的活化分子迁移率驱动剪切变形从初始冻结状态转变为解冻状态。该理论给出了屈服应力作为应变速率和温度函数的解析表达式，还预测了相同参数空间中颈缩起始的相图，提供了超越经典康西代准则的机制。我们的结果为玻璃态材料的非线性拉伸行为建立了统一框架。
英文摘要
Yielding, plasticity, and necking are central to the mechanical performance of materials, yet a concise unified physical picture of how these nonlinear responses arise remains lacking. We develop a minimal theory for glassy polymers based on a classical volume-dependent relaxation time following the Doolittle equation, and derive the constitutive relation using the Onsager variational principle. Surprisingly, this simple theory explains yielding, plasticity, and neck initiation under constant strain rate loading via a shear unfreezing mechanism: as the sample is stretched, volume-increasing activated molecular mobility drives shear deformation from an initially frozen state to an unfrozen state. The theory yields an analytical expression for the yielding stress as a function of strain rate and temperature. It also predicts a phase diagram for necking initiation in the same parameter space, providing a mechanism beyond the classical Considère criterion. Our results establish a unified framework for nonlinear tensile behavior in glassy materials.
Comments6pages, 4 figures
