The rate‐dependent behavior associated with deformation and fracturing of materials, such as natural rocks, poses significant challenges for modeling. In addition to the complications of the viscoelastic response, the speed of fracture propagation reflects micromechanical mechanisms in the fracture process zone (FPZ). In order to represent these complicated behaviors, a thermodynamically consistent, rate‐dependent fracture model is required. Based on rigorous thermodynamic principles, we derive a rate‐dependent phase‐field mechanical model coupled with single‐phase fluid flow in both the matrix and the fracture. The model is guaranteed to satisfy energy conservation during fracture propagation. The system of equations is solved using the introduced solution procedure and a novel preconditioner that accounts for the complex fluid–structure interaction. The proposed phase‐field model is tested against several benchmark problems on solid‐fluid coupling, fluid‐driven fracture propagation and rate‐dependent viscoelastic deformation. The model serves as a strong basis for investigating rate‐dependent fracturing experiments and for making predictions of material behaviors under new conditions.

中文翻译：

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速率相关的流体驱动裂缝萌生和扩展的相场建模

与材料（例如天然岩石）的变形和破裂相关的与速率相关的行为对建模提出了重大挑战。除了粘弹性响应的复杂性外，裂缝传播的速度还反映了裂缝加工区（FPZ）中的微机械机制。为了表示这些复杂的行为，需要一个热力学上一致的，速率相关的断裂模型。基于严格的热力学原理，我们推导出了速率相关的相场力学模型，并结合了基质和裂缝中的单相流体流动。该模型可以保证满足裂缝扩展过程中的能量守恒要求。使用引入的求解程序和考虑了复杂的流固耦合的新型预处理器来求解方程组。所提出的相场模型针对固-液耦合，流体驱动的裂缝扩展和速率依赖的粘弹性变形等几个基准问题进行了测试。该模型为研究与速率相关的压裂实验和预测新条件下的材料行为提供了坚实的基础。