In the present manuscript fracture propagation in a saturated porous medium is modeled based on the classical Biot theory, where solid skeleton and fluid flow are represented by separate two layers. The non-ordinary state-based peridynamics (NOSBPD) layer is employed to capture deformation including fracturing of the solid skeleton, while the fluid flow is controlled by the finite element method (FEM) layer. The interaction between the layers is realized by considering the effects of pore pressure from the FEM layer on the NOSBPD layer and, vice versa, the effect of the volumetric strain, porosity, and permeability variations from the NOSBPD layer on the FEM layer. The coupling terms retain their parent characteristics, that is, the interaction term in the momentum balance equation is approximated by the local FEM formulation whereas the interaction term in the mass balance equation is approximated by the nonlocal NOSBPD formulation. By doing so, the model retains the flexibility of coupling two independent discretizations. The coupled system is solved by a fully implicit solution scheme. The accuracy of the proposed method has been verified against available closed-form solutions and published numerical approaches for the pressure- and fluid-driven facture propagation problems.

中文翻译：

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非寻常态近场动力学与饱和多孔介质裂缝扩展有限元方法的耦合

在本手稿中，饱和多孔介质中的裂缝扩展是基于经典 Biot 理论建模的，其中固体骨架和流体流动由单独的两层表示。非常规状态近场动力学 (NOSBPD) 层用于捕获变形，包括固体骨架的破裂，而流体流动由有限元方法 (FEM) 层控制。层之间的相互作用是通过考虑来自 FEM 层的孔隙压力对 NOSBPD 层的影响，反之亦然，来自 NOSBPD 层的体积应变、孔隙度和渗透率变化对 FEM 层的影响来实现的。耦合项保留其父特征，即 动量平衡方程中的相互作用项由局部 FEM 公式近似，而质量平衡方程中的相互作用项由非局部 NOSBPD 公式近似。通过这样做，该模型保留了耦合两个独立离散化的灵活性。耦合系统通过完全隐式求解方案求解。所提出的方法的准确性已经根据可用的封闭形式解决方案和已发表的压力和流体驱动断裂传播问题的数值方法进行了验证。