标题： 经典的变分相场模型无法预测裂纹起始 显示英文标题

标题： Classical variational phase-field models cannot predict fracture nucleation

摘要： 尽管有证据表明它们存在不足，经典的变分相场模型仍在继续被使用和研究，以期描述弹性脆性材料中的裂纹起始现象。 本文的主要目的就是在这一背景下，全面回顾反对将此类模型作为裂纹起始描述符的现有证据。 为此，首先综述了名义上弹性脆性材料在准静态加载条件下的裂纹起始实验观测结果，以及经典变分相场模型（包括和不包括能量分解）。 随后，这些模型与实验观测进行了对比。 结论是，这些经典变分相场模型无法普遍描述裂纹起始现象。 这是因为经典变分相场模型无法将材料强度视为独立的宏观材料属性。 文章的最后一部分简要总结了一类能够描述裂纹起始的相场模型，并讨论了在大尺度断裂分析中如何广泛忽略了材料强度，还展望了在弹性脆性材料基本设置之外的裂纹起始建模方向。 显示英文摘要

摘要： Notwithstanding the evidence against them, classical variational phase-field models continue to be used and pursued in an attempt to describe fracture nucleation in elastic brittle materials. In this context, the main objective of this paper is to provide a comprehensive review of the existing evidence against such a class of models as descriptors of fracture nucleation. To that end, a review is first given of the plethora of experimental observations of fracture nucleation in nominally elastic brittle materials under quasi-static loading conditions, as well as of classical variational phase-field models, without and with energy splits. These models are then confronted with the experimental observations. The conclusion is that they cannot possibly describe fracture nucleation in general. This because classical variational phase-field models cannot account for material strength as an independent macroscopic material property. The last part of the paper includes a brief summary of a class of phase-field models that can describe fracture nucleation. It also provides a discussion of how pervasively material strength has been overlooked in the analysis of fracture at large, as well as an outlook into the modeling of fracture nucleation beyond the basic setting of elastic brittle materials.