Chen Lin, de Borst René
Key Laboratory of Ministry of Education on Safe Mining of Deep Metal Mines Northeastern University Shenyang China.
Department of Civil and Structural Engineering University of Sheffield Sheffield UK.
Int J Numer Methods Eng. 2023 Jan 15;124(1):264-281. doi: 10.1002/nme.7120. Epub 2022 Sep 16.
Powell-Sabin B-splines are employed to model progressive fracturing in a fluid-saturated porous medium. These splines are defined on triangles and are -continuous throughout the domain, including the crack tips, so that crack initiation can be evaluated directly at the tip. On one hand, the method captures stresses and fluid fluxes more accurately than when using standard Lagrange elements, enabling a direct assessment of the fracture criterion at the crack tip and ensuring local mass conservation. On the other hand, the method avoids limitations for discrete crack analysis which adhere to isogeometric analysis. A crack is introduced directly in the physical domain. Due to the use of triangles, remeshing and crack path tracking are straightforward. During remeshing transfer of state vectors (displacement, fluid pressure) is required from the old to the new mesh. The transfer is done using a new approach which exploits a least-squares fit with the energy balance and conservation of mass as constraints. The versatility and accuracy to simulate free crack propagation are assessed for mode-I and mixed-mode fracture problems.
鲍威尔 - 萨宾B样条被用于对流体饱和多孔介质中的渐进断裂进行建模。这些样条定义在三角形上，并且在整个区域内，包括裂纹尖端，都是(C^1)连续的，这样就可以直接在尖端评估裂纹萌生。一方面，该方法比使用标准拉格朗日单元时能更精确地捕捉应力和流体通量，从而能够直接在裂纹尖端评估断裂准则并确保局部质量守恒。另一方面，该方法避免了离散裂纹分析中采用等几何分析时的局限性。裂纹直接在物理域中引入。由于使用了三角形，重新划分网格和裂纹路径跟踪都很简单。在重新划分网格期间，需要将状态向量（位移、流体压力）从旧网格转移到新网格。这种转移是使用一种新方法完成的，该方法利用以能量平衡和质量守恒为约束的最小二乘拟合。针对I型和混合模式断裂问题评估了模拟自由裂纹扩展的通用性和准确性。
