In this paper, an adaptive phase-field model based on variable-node elements and error-indicator is presented to predict cohesive fracture evolution. The phase-field cohesive-zone model is characterized by the parameterized energetic degradation and crack geometric functions. A staggered iteration scheme is used to solve the coupled non-linear system of displacement field and phase field. The adaptive local refinement algorithm facilitated with error-indicator and variable-node elements is developed to improve computational efficiency. To determine the adaptive local refinement regions, we apply the phase-field threshold to characterize the crack regions and a novel history field threshold to denote crack tips. The variable-node elements are acted as transition elements to flexibly yet simply link the fine and coarse meshes. In addition, a fast method to generate the variable-node elements is given. Several representative numerical examples are studied to demonstrate the performance and accuracy of the proposed adaptive phase-field model, consisting of a mixed-model fracture of L-shape panel, the wedge-splitting test, the classic three point bending experiment and a plate with a hole and multi-cracks under tensile/shear loadings. The computer codes can be accessed at: https://github.com/hhuztc/Adaptive-PFM.git.

在本文中，提出了一种基于可变节点元素和误差指示器的自适应相场模型来预测粘性断裂演化。相场内聚区模型的特征是参数化的能量退化和裂纹几何函数。采用交错迭代方案来求解位移场和相位场耦合的非线性系统。开发了带有误差指示器和变量节点元素的自适应局部细化算法，以提高计算效率。为了确定自适应局部细化区域，我们应用相场阈值来表征裂纹区域，并应用新颖的历史场阈值来表示裂纹尖端。可变节点单元充当过渡单元，灵活而简单地连接细网格和粗网格。此外，还给出了一种快速生成变量节点元素的方法。研究了几个有代表性的数值算例，以证明所提出的自适应相场模型的性能和精度，包括 L 形面板的混合模型断裂、楔形劈裂试验、经典的三点弯曲实验和具有拉伸/剪切载荷下的孔和多裂纹。计算机代码可以访问： https: //github.com/hhuztc/Adaptive-PFM.git。