标题： 通过梯度增强损伤模型捕捉脆性粘结长度尺度的弹性体 显示英文标题

标题： Capturing the fractocohesive length scale through a gradient-enhanced damage model for elastomers

摘要： 本研究旨在揭示分形粘结长度尺度在现代断裂力学中作为核心概念的微观机械基础。 开发了一种热力学一致的损伤和断裂模型，用于弹性体，结合了聚合物链统计力学的要素。 这种方法使得可以直接将聚合物链响应纳入连续梯度增强损伤公式中，从而能够对扩散链损伤及相应的断裂事件进行物理上有意义的描述。 通过一系列数值实验，我们模拟裂纹扩展并提取断裂能作为模型的输出，同时跟踪适应断裂扩展的扩散链损伤的微机械特征。 此外，我们研究了缺陷敏感性，并证明当缺陷尺寸小于临界长度尺度时，材料响应对缺口尺寸变得不敏感。 最后，通过结合断裂韧性与断裂功，我们确定了材料的分形粘结长度，该长度对应于损伤区的完整宽度，并代表不可逆耗散过程（即键断裂）发生的区域。 由于在所提出的FED模型中，该区域通过引入与损伤和断裂过程非局部性质相关的长度尺度来确定，因此讨论了这两个长度尺度之间的相互关系，有效地将损伤的微观特性与有效的宏观响应联系起来。 显示英文摘要

摘要： This study aims to unravel the micro-mechanical underpinnings of the emergence of the fractocohesive length scale as a central concept in modern fracture mechanics. A thermodynamically consistent damage and fracture model for elastomers is developed, incorporating elements of polymer chain statistical mechanics. This approach enables the direct incorporation of polymer chain response into a continuum gradient enhanced damage formulation, that in turn allows a physically meaningful description of diffuse chain damage and corresponding fracture events. Through a series of numerical experiments, we simulate crack propagation and extract the fracture energy as an output of the model, while keeping track of the micromechanical signatures of diffuse chain damage that accommodate fracture propagation. Furthermore, we investigate flaw sensitivity and demonstrate that when flaw sizes are smaller than a critical length scale, the material response becomes largely insensitive to notch size. Finally, by combining the fracture toughness and the work to rupture, we identify a fractocohesive length of the material, corresponding to the full width of the damage zone and representing the region where the irreversible dissipation process (i.e., bond scission) is happening. As this region is dictated in the proposed FED model through the introduction of a length scale associated with the non-local nature of the damage and fracture process, the emerging relationship of the two length scales is discussed, effectively connecting the microscopic characteristics of damage to the effective macroscopic response.