A variational phase field model for dynamic ductile fracture is presented. The model is designed for elasto-viscoplastic materials subjected to rapid deformations in which the effects of heat generation and material softening are dominant. The variational framework allows for the consistent inclusion of plastic dissipation in the heat equation as well as thermal softening. It employs a coalescence function to degrade fracture energy during regimes of high plastic flow. A variationally consistent form of the Johnson–Cook model is developed for use with the framework. Results from various benchmark problems in dynamic ductile fracture are presented to demonstrate capabilities. In particular, the ability of the model to regularize shear band formation and subsequent damage evolution in two- and three-dimensional problems is demonstrated. Importantly, these phenomena are naturally captured through the underlying physics without the need for phenomenological criteria such as stability thresholds for the onset of shear band formation.

中文翻译：

---

用于热软化和动态韧性断裂的变分相场框架


提出了动态韧性断裂的变分相场模型。该模型专为承受快速变形的弹性粘塑性材料而设计，其中热量产生和材料软化的影响占主导地位。变分框架允许在热方程中一致地包含塑料耗散以及热软化。它采用聚结函数在高塑性流动状态下降低断裂能。开发了 Johnson-Cook 模型的变分一致形式，以便与该框架一起使用。介绍了动态韧性断裂中各种基准问题的结果以证明其能力。特别是，证明了该模型在二维和三维问题中规范剪切带形成和随后损伤演变的能力。重要的是，这些现象是通过基础物理学自然捕获的，而不需要现象学标准，例如剪切带形成开始的稳定性阈值。