Chen Lin, Fathi Farshid, de Borst Rene
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 Anal Methods Geomech. 2022 Dec 10;46(17):3200-3216. doi: 10.1002/nag.3447. Epub 2022 Sep 11.
This paper addresses fluid-driven crack propagation in a porous medium. Cohesive interface elements are employed to model the behaviour of the crack. To simulate hydraulic fracturing, a fluid pressure degree of freedom is introduced inside the crack, separate from the fluid degrees of freedom in the bulk. Powell-Sabin B-splines, which are based on triangles, are employed to describe the geometry of the domain and to interpolate the field variables: displacements and interstitial fluid pressure. Due to their -continuity, the stress and pressure gradient are smooth throughout the whole domain, enabling a direct assessment of the fracture criterion at the crack tip and ensuring local mass conservation. Due to the use of triangles, crack insertion and remeshing are straightforward and can be done directly in the physical domain. During remeshing a mapping of the state vector (displacement and interstitial fluid pressure) is required. For this, a new methodology is exploited based on a least-square fit with the energy balance and mass conservation as constraints. The accuracy to model free crack propagation is demonstrated by two numerical examples, including crack propagation in a plate with two notches.
本文研究了多孔介质中流体驱动的裂纹扩展问题。采用内聚力界面单元对裂纹行为进行建模。为了模拟水力压裂，在裂纹内部引入了一个流体压力自由度，与主体中的流体自由度分开。基于三角形的鲍威尔-萨宾B样条被用于描述域的几何形状并插值场变量：位移和孔隙流体压力。由于它们的C^1连续性，应力和压力梯度在整个域内都是平滑的，这使得能够直接评估裂纹尖端的断裂准则，并确保局部质量守恒。由于使用了三角形，裂纹插入和重新网格化很简单，可以直接在物理域中进行。在重新网格化过程中，需要对状态向量（位移和孔隙流体压力）进行映射。为此，开发了一种基于最小二乘拟合的新方法，以能量平衡和质量守恒为约束条件。通过两个数值例子证明了模拟自由裂纹扩展的准确性，包括在具有两个缺口的板中的裂纹扩展。
