This study presents a crack phase-field approach for anisotropic continua to model, in particular, fracture of fiber-reinforced matrix composites. Starting with the variational formulation of the multi-field problem of fracture in terms of the deformation and the crack phase fields, the governing equations feature the evolution of the anisotropic crack phase-field and the balance of linear momentum, presented for finite and small strains. A recently proposed energy-based anisotropic failure criterion is incorporated into the model with a constitutive threshold function regulating the crack initiation in regard to the matrix and the fibers in a superposed framework. Representative numerical examples are shown for the crack initiation and propagation in unidirectional fiber-reinforced polymer composites under Mode-I, Mode-II and mixed-mode bending. Model parameters are obtained by fitting to sets of experimental data. The associated finite element results are able to capture anisotropic crack initiation and growth in unidirectional fiber-reinforced composite laminates.

中文翻译：

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单向纤维增强聚合物基复合材料断裂的相场模型

本研究提出了一种用于各向异性连续体的裂纹相场方法来模拟，特别是纤维增强基复合材料的断裂。从变形和裂纹相场的断裂多场问题的变分公式开始，控制方程具有各向异性裂纹相场的演化和线性动量平衡，呈现为有限和小应​​变. 最近提出的基于能量的各向异性破坏准则被纳入模型中，本构阈值函数调节叠加框架中基体和纤维的裂纹萌生。显示了在模式 I、模式 II 和混合模式弯曲下单向纤维增强聚合物复合材料中裂纹萌生和扩展的代表性数值示例。模型参数是通过拟合一组实验数据获得的。相关的有限元结果能够捕捉单向纤维增强复合材料层压板中的各向异性裂纹萌生和扩展。