The paper describes a flexible computational method that can be used to represent the complex geometric evolution of a fluid-driven fracture front using an unstructured triangular element mesh. A specific motivation for the method is to allow subsequent treatment of non-planar fracture growth problems. Elastic interactions between the crack opening displacements and the surrounding medium are calculated using displacement discontinuity boundary element influence functions. A novel feature of the approach is the use of an adjustable region of tip elements to accommodate both time-dependent crack edge movements and to ensure correct velocity-dependent asymptotic behavior for viscous and viscous-toughness flow conditions. The adjustable tip element region is represented using a special-purpose data structure that allows the iteration of the moving edge element vertices to be linked directly to the flow rate and the crack opening solution values that are determined in each time step. The fringe region is periodically replaced with a set of fixed vertex elements as the fracture surface evolves. The proposed scheme has been evaluated using available analytic and experimental results for planar fracture propagation. The method is found to be both accurate and robust for a range of choices of geometric fracture shapes and time step sizes.

本文介绍了一种灵活的计算方法，该方法可用于表示使用非结构化三角单元网格的流体驱动裂缝前沿的复杂几何演化。该方法的一个特殊动机是允许对非平面性骨折生长问题进行后续治疗。利用位移不连续性边界元影响函数计算出裂缝开口位移与周围介质之间的弹性相互作用。该方法的一个新颖特征是使用了尖端元件的可调区域，以适应与时间有关的裂纹边缘移动，并确保针对粘性和粘性-韧性流动条件的正确的，与速度有关的渐近行为。可调节的尖端元素区域使用专用数据结构表示，该数据结构允许将移动边缘元素顶点的迭代直接链接到在每个时间步中确定的流速和裂纹开放解值。随着断裂表面的发展，边缘区域会定期用一组固定的顶点元素替换。利用平面裂缝扩展的可用分析和实验结果对提出的方案进行了评估。发现该方法对于一系列几何裂缝形状和时间步长大小的选择既准确又可靠。随着断裂面的发展，边缘区域会定期用一组固定的顶点元素替换。利用平面裂缝扩展的可用分析和实验结果对提出的方案进行了评估。发现该方法对于一系列几何裂缝形状和时间步长大小的选择既准确又可靠。随着断裂表面的发展，边缘区域会定期用一组固定的顶点元素替换。已使用可用的平面裂缝扩展的分析和实验结果对提出的方案进行了评估。发现该方法对于一系列几何裂缝形状和时间步长大小的选择既准确又可靠。