The shifted fracture method
The shifted fracture method
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DOI：
10.1002/nme.6806
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发表时间：
2021-09
影响因子：
2.9
通讯作者：
Kangan Li;N. M. Atallah;A. Rodríguez‐Ferran;D. Valiveti;G. Scovazzi
中科院分区：
文献类型：
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作者：
Kangan Li;N. M. Atallah;A. Rodríguez‐Ferran;D. Valiveti;G. Scovazzi
我们基于近似断裂几何表示与近似接口条件的近似断裂几何表示的想法，为断裂力学提出了一个新的框架。我们的方法从移动的界面方法演变出来，并引入了近似裂缝表面的概念，该裂纹表面由基础网格的完整边缘/面组成，这些网格在几何上接近真正的断裂几何形状。然后，原始界面条件通过泰勒膨胀在替代断裂几何形状上修改。移动的断裂方法不需要切割细胞计算或复杂的数据结构，因为真实断裂的行为与近似断裂表面上的标准积分模仿。此外，真正断裂的能量学在基础多项式有限元近似的准确性中表示，并且独立于网格拓扑结构。计算框架以其通用性介绍，然后在凝聚区模型的特定上下文中应用，并在两个和三个维度中进行了一组广泛的数值实验。
We propose a new framework for fracture mechanics, based on the idea of an approximate fracture geometry representation combined with approximate interface conditions. Our approach evolves from the shifted interface method, and introduces the concept of an approximate fracture surface composed of the full edges/faces of an underlying grid that are geometrically close to the true fracture geometry. The original interface conditions are then modified on the surrogate fracture geometry, by way of Taylor expansions. The shifted fracture method does not require cut cell computations or complex data structures, since the behavior of the true fracture is mimicked with standard integrals on the approximate fracture surface. Furthermore, the energetics of the true fracture are represented within the accuracy of the underlying polynomial finite element approximation and independently of the grid topology. The computational framework is presented here in its generality and then applied in the specific context of cohesive zone models, with an extensive set of numerical experiments in two and three dimensions.