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.

中文翻译：

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位移断裂法

我们提出了一种新的断裂力学框架，基于近似断裂几何表示与近似界面条件相结合的思想。我们的方法从移动界面方法演变而来，并引入了近似断裂表面的概念，该概念由几何上接近真实断裂几何形状的底层网格的完整边缘/面组成。然后通过泰勒展开在替代裂缝几何形状上修改原始界面条件。移位断裂方法不需要切割单元计算或复杂的数据结构，因为真实断裂的行为是通过近似断裂表面上的标准积分来模拟的。此外，真实断裂的能量在基本多项式有限元近似的精度范围内表示，并且与网格拓扑无关。此处介绍了计算框架的一般性，然后将其应用于内聚区模型的特定环境中，并在二维和三个维度上进行了大量数值实验。