Enriched finite element methods have gained traction in recent years for modeling problems with material interfaces and cracks. By means of enrichment functions that incorporate a priori behavior about the solution, these methods decouple the finite element (FE) discretization from the geometric configuration of such discontinuities. Taking advantage of this greater flexibility, recent studies have proposed the adoption of Non‐Uniform Rational B‐Splines (NURBS) to preserve the interfaces' exact geometries throughout the analysis. In this article, we investigate NURBS‐based geometries in the context of the Discontinuity‐Enriched Finite Element Method (DE‐FEM) based on linear field approximations. While optimal convergence is retained for problems with weak discontinuities without singularities, representing exact geometry via NURBS does not yield noticeable improvements when extracting stress intensity factors of cracked specimens. For low‐order elements, we conclude that the benefits of exact geometry representation do not outweigh the increased complexity in formulation and implementation. The choice of linear FEs hinders the accuracy of the proposed formulation, suggesting that its full potential may only be unleashed by increasing the field representation order.

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关于使用非均匀有理B样条线改善富集有限元方法中的几何表示的批判性观点

近年来，随着有限元方法对材料界面和裂纹问题的建模，丰富的有限元方法得到了广泛的关注。通过合并先验的丰富功能关于解的行为，这些方法使有限元（FE）离散与这种不连续性的几何结构脱钩。利用这种更大的灵活性，最近的研究建议采用非均匀有理B样条（NURBS），以在整个分析过程中保留界面的精确几何形状。在本文中，我们将在基于线性场近似的非连续性丰富有限元方法（DE-FEM）的背景下研究基于NURBS的几何。对于不具有奇异点的不连续性较弱的问题，虽然保留了最佳收敛性，但在提取破裂试样的应力强度因子时，通过NURBS表示精确的几何形状不会产生明显的改善。对于低阶元素，我们得出的结论是，精确的几何图形表示所带来的好处并不超过制定和实施过程中增加的复杂性。线性有限元的选择阻碍了所提出公式的准确性，这表明只有通过增加场表示顺序才能释放其全部潜力。