This article presents a nonlinear augmented finite element method (N‐AFEM) for the analysis of arbitrary crack initiation and propagation in large deformation plates and shells. The FE formulations for plate/shell elements and a shell‐like cohesive zone element, both with explicit consideration of geometric nonlinearity, have been derived in detail. The geometrically nonlinear shell‐like cohesive element has the essential feature of 3D but with crack displacements directly extracted from midplane shell element nodes, which enables an accurate description of crack propagation in shells and plates under large deformation. Furthermore, a novel augmentation process that can explicitly account for the discontinuous displacement fields of cracked elements without the need of extra nodes or nodal DoFs has been develop based on a nonlinear Newton‐Raphson method. The numerical performance of the N‐AFEM in modeling a number of benchmark shell/plate fracture problems demonstrates that the method is efficient, accurate, and robust.

中文翻译：

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大变形板壳中任意裂纹的非线性增强有限元方法

本文提出了一种非线性增强有限元方法（N‐AFEM），用于分析大变形板和壳中任意裂纹的萌生和扩展。详细推导了板/壳单元和壳状内聚区单元的有限元公式，它们都明确考虑了几何非线性。几何非线性壳状内聚单元具有3D的基本特征，但裂纹位移是直接从中平面壳单元节点提取的，从而可以准确描述大变形下壳和板中裂纹的扩展。此外，基于非线性牛顿-拉夫森方法，开发了一种新颖的增强方法，该方法可以显式地说明裂纹单元的不连续位移场，而无需额外的节点或节点自由度。N-AFEM在模拟许多基准壳/板断裂问题方面的数值性能表明，该方法高效，准确且稳健。