Abstract The Regularized eXtended Finite Element Method (Rx-FEM) is a fracture mechanics based technique for progressive failure simulation when multiple damage events such as matrix cracks and delamination are introduced into the finite element model via mesh independent displacement discontinuities. In the Rx-FEM, the Heaviside step function that is used in the eXtended Finite Element Method (x-FEM) is replaced by a continuous function approximated by using the FE shape functions. This regularization offers unique possibility for the implementation of the Rx-FEM methodology in commercial FE software as a superposition of native elements as opposed to a single user defined element which is the approach taken by x-FEM implementation to date. The advantages of the novel Rx-FEM implementation lie in the ability to utilize the capabilities of the host software including contact, geometric nonlinearity as well as post-processing, and visualization. The proposed implementation of the Rx-FEM methodology is illustrated for commercial software Abaqus on a number of examples of mesh-independent crack modeling in composite laminates, and delamination between plies. The validity of the proposed implementation is demonstrated by comparing with experimental data and benchmark solutions.

中文翻译：

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在 Abaqus 框架中实现正则化扩展有限元方法在层压复合材料中进行断裂建模

摘要 正则化扩展有限元法（Rx-FEM）是一种基于断裂力学的渐进式失效模拟技术，当多种损伤事件（如基体裂纹和分层）通过网格独立位移不连续性引入有限元模型时。在 Rx-FEM 中，扩展有限元方法 (x-FEM) 中使用的 Heaviside 阶跃函数被使用有限元形状函数近似的连续函数代替。这种正则化为在商业 FE 软件中实现 Rx-FEM 方法作为原生元素的叠加提供了独特的可能性，而不是单个用户定义的元素，这是迄今为止 x-FEM 实现所采用的方法。新型 Rx-FEM 实现的优势在于能够利用主机软件的功能，包括接触、几何非线性以及后处理和可视化。Rx-FEM 方法的建议实现在商业软件 Abaqus 中以复合材料层压板中与网格无关的裂纹建模和层间分层的许多示例进行了说明。通过与实验数据和基准解决方案进行比较，证明了所提出实施方案的有效性。