Abstract The present paper presents the key steps to model internally pressurized fractures in a homogeneous elastic medium. Internal pressure in the cracks transforms the displacement field, which alters the associated stress concentration. The displacements are solved analytically using a Linear Superposition Method (LSM), and stresses are solved under the assumption of linear elasticity. The method allows for the fractures to have any location, geometry, and orientation. Additionally, each crack may be pressurized by either equal or individual pressure loads. Solution methodology are explained, and results are generated for several cases. Selected LSM model results show excellent matches against other independent methods (photo-elastics for multiple crack problems, and prior analytical solutions for single crack problems). The grid-less, closed-form LSM solution is able to achieve fast computation times by side-stepping adaptive grid-refinement, while achieving high target resolution.

中文翻译：

---

使用线性叠加法 (LSM) 求解多个压力加载裂缝周围的应力张量场

摘要 本文介绍了在均匀弹性介质中模拟内部加压裂缝的关键步骤。裂缝中的内部压力会改变位移场，从而改变相关的应力集中。使用线性叠加法 (LSM) 解析位移，并在线性弹性假设下求解应力。该方法允许裂缝具有任何位置、几何形状和方向。此外，每个裂缝可以通过相等或单独的压力载荷加压。解释了解决方案方法，并为几种情况生成了结果。选定的 LSM 模型结果显示与其他独立方法（多裂纹问题的光弹性，以及单裂纹问题的先前分析解决方案）非常匹配。无网格，