The framework of poromechanics is generalized to simulate the multiscale behavior of porous media subjected to internal loadings stemming from the growth of solid inclusions. This generalization is designed to enable the study of anisotropic internal stress generation from solid growth within the pores, while recovering isotropic fluid‐induced loading as a particular case. For this purpose, a mathematical strategy to define constitutive tensors in a thermodynamically consistent form is proposed, thus offering new opportunities for determining the poromechanical properties of a porous solid through advanced experimentation or micromechanical models. The framework is specialized by means of established elastic solutions for single pore–matrix interaction, as well as through homogenization schemes considering the interaction among congruent pores. In particular, the second Eshelby solution and the Tanaka–Mori–Benveniste homogenization scheme are used to derive a microporoelastic model. At an elemental scale, the model is tested under mixed control conditions by replicating different scenarios of geomaterial testing. In addition, the model characteristics are outlined with reference to inelastic microscopic loadings replicating chemo‐mechanical forcing, such as expansive crystal formation. Through a series of parametric analyses, it is shown that the microstructure of the pores significantly influences the properties of porous media. Most notably, it is shown that the effects of a solid forming within the pores depend in a highly nonlinear fashion on the constitutive characteristics of the inhomogeneities and can therefore not be readily quantified or predicted without models capturing the diverse multiscale interactions among pores, inhomogeneities, and matrix.

中文翻译：

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固体夹杂物诱导的内部相互作用的多孔力学框架


多孔力学的框架被推广为模拟多孔介质在固体包裹体生长引起的内部载荷下的多尺度行为。这种推广旨在能够研究孔隙内固体生长产生的各向异性内应力，同时作为特殊情况恢复各向同性流体诱导的载荷。为此，提出了一种以热力学一致形式定义本构张量的数学策略，从而为通过高级实验或微力学模型确定多孔固体的多孔力学性质提供了新的机会。该框架通过已建立的单孔-基体相互作用弹性解决方案以及考虑全等孔之间相互作用的均质化方案进行专业化。特别是，第二种 Eshelby 解和 Tanaka-Mori-Benveniste 均质方案用于推导微孔弹性模型。在元素尺度上，通过复制不同的岩土材料测试场景，在混合控制条件下对模型进行测试。此外，还参考了复制化学机械强迫的非弹性微观载荷（例如膨胀晶体形成）概述了模型特征。通过一系列参数分析，表明孔隙的微观结构显着影响多孔介质的性能。最值得注意的是，结果表明，孔隙内固体形成的影响以高度非线性的方式取决于不均匀性的本构特征，因此，如果没有模型捕获孔隙、不均匀性和基质之间的各种多尺度相互作用，就无法轻易量化或预测。