Porous materials are highly relevant in engineering and medical applications due to their enhanced properties and lightweight nature. Current micromechanical models of porous materials can accurately predict the response under the assumptions of small deformations and drained conditions, typically driven by imposed deformations. However, the theoretical framework for the micromechanical modeling of porous material driven by pore pressure in the large-deformation range has been understudied. In this work, we develop a finite-deformation variational framework for pressure-driven foams, i.e., materials where the pore pressure in the cavities produces the deformation. We further consider different kinematical constraints in the formulation of boundary conditions: kinematic uniform displacements, periodic displacements and uniform traction. We apply the proposed model in the numerical simulation of lung porous tissue using a spherical alveolar geometry and an image-based geometry obtained from micro-computed-tomography images of rat lung. Our results show that the stress distributions in the spherical alveolar model are highly dependent on the kinematical constraints. In contrast, the stress distribution in the image-based alveolar model is not affected by the choice of boundary conditions. Further, when comparing the response of pressure-driven versus deformation-driven models, we conclude that hydrostatic stresses experience a marked shift in their distribution, whereas the deviatoric stresses remain unaffected. Our findings of how stresses are affected by the choice of boundary conditions and geometry take particular relevance in the simulation of the lungs, where the pressure-driven and deformation-driven cases are related to mechanical ventilation and spontaneous breathing.

多孔材料由于其增强的性能和轻质的性质，在工程和医疗应用中高度相关。当前多孔材料的微观力学模型可以在小变形和排水条件的假设下准确预测响应，通常由强加变形驱动。然而，在大变形范围内由孔隙压力驱动的多孔材料微观力学建模的理论框架尚未得到充分研究。在这项工作中，我们开发了压力驱动泡沫的有限变形变分框架，即空腔中的孔隙压力产生变形的材料。我们在边界条件的公式中进一步考虑了不同的运动学约束：运动学均匀位移、周期位移和均匀牵引力。我们使用球形肺泡几何和从大鼠肺的显微计算机断层扫描图像获得的基于图像的几何，将所提出的模型应用于肺多孔组织的数值模拟。我们的结果表明，球形肺泡模型中的应力分布高度依赖于运动学约束。相比之下，基于图像的肺泡模型中的应力分布不受边界条件选择的影响。此外，当比较压力驱动模型与变形驱动模型的响应时，我们得出结论，静水应力的分布发生了显着变化，而偏应力不受影响。我们关于应力如何受边界条件和几何形状选择影响的发现与肺模拟特别相关，