Existing solutions to Mandel's problem focus on isotropic, transversely isotropic, and orthotropic materials, the last two of which have one of the material symmetry axes coincide with the vertical loading direction. The classical plane strain condition holds for all these cases. In this work, analytical solution to Mandel's problem with the most general matrix anisotropy is presented. This newly derived analytical solution for fully anisotropic materials has all the three nonzero shear strains. Warping occurs in the cross sections, and a generalized plane strain condition is fulfilled. This solution can be applied to transversely isotropic and orthotropic materials whose material symmetry axes are not aligned with the vertical loading direction. It is the first analytical poroelastic solution considering mechanical general anisotropy of elasticity. The solution captures the effects of material anisotropy and the deviation of the material symmetry axes from the vertical loading direction on the responses of pore pressure, stress, strain, and displacement. It can be used to match, calibrate, and simulate experimental results to estimate anisotropic poromechanical parameters. This generalized solution is capable of reproducing the existing solutions as special cases. As an application, the solution is used to study the responses of transversely isotropic and orthotropic materials whose symmetry axes are not aligned with the vertical loading direction. Examples on anisotropic shale rocks show that the effects of material anisotropy are significant. Mandel‐Cryer's effects are highly impacted by the degree of material anisotropy and the deviation of the material symmetry axes from the vertical loading direction.

中文翻译：

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各向异性曼德尔问题的广义解

曼德尔问题的现有解决方案集中在各向同性，横向各向同性和正交异性材料上，其中后两种材料的材料对称轴之一与垂直载荷方向重合。所有这些情况都适用经典的平面应变条件。在这项工作中，提出了具有最一般矩阵各向异性的曼德尔问题的解析解。这个新的完全各向异性材料的解析解决方案具有所有三个非零剪切应变。截面发生翘曲，并且满足广义的平面应变条件。该解决方案可应用于材料对称轴与垂直载荷方向不对齐的横向各向同性和正交各向异性材料。它是第一个考虑弹性力学一般各向异性的多孔分析方法。该解决方案捕获了材料各向异性以及材料对称轴相对于垂直载荷方向的偏离对孔隙压力，应力，应变和位移的响应的影响。它可以用于匹配，校准和模拟实验结果，以估计各向异性的风速力学参数。该通用解决方案能够重现现有解决方案作为特殊情况。作为一种应用，该解决方案用于研究对称轴与垂直载荷方向不对齐的横向各向同性和正交异性材料的响应。各向异性页岩的例子表明，材料各向异性的影响是显着的。曼德尔·克里尔