Bourdin等人[20-21]的后续工作中建立由标量辅助变量(即相场

Bourdin等人[20-21]的后续工作中建立由标量辅助变量(即相场)控制的扩散裂纹区来规范材料中尖锐的裂纹表面拓扑，相场在材料的未破碎状态和破碎状态之间进行插值，通过模型证明了数值方法可行性。

In the follow-up work of bourdin et al. [20-21], the diffusion crack zone controlled by scalar auxiliary variable (i.e. phase field) is established to standardize the sharp crack surface topology in the material. The phase field is interpolated between the unbroken state and the broken state of the material. The feasibility of the numerical method is proved by the model.

In the follow-up work of Bourdin et al. [20-21], the diffusion crack area controlled by scalar auxiliary variables (i.e., phase field) was established to standardize the sharp crack surface topology in materials, and the phase field was interpolated between the unbroken state and the broken state of materials. The model proved the feasibility of the numerical method.