A dual-continuum model can offer a practical approach to understanding first-order behaviours of poromechanically coupled multiscale systems. To close the governing equations, constitutive equations with models to calculate effective constitutive coefficients are required. Several coefficient models have been proposed within the literature. However, a holistic overview of the different modelling concepts is still missing. To address this we first compare and contrast the dominant models existing within the literature. In terms of the constitutive relations themselves, early relations were indirectly postulated that implicitly neglected the effect of the mechanical interaction arising between continuum pressures. Further, recent users of complete constitutive systems that include inter-continuum pressure coupling have explicitly neglected these couplings as a means of providing direct relations between composite and constituent properties, and to simplify coefficient models. Within the framework of micromechanics, we show heuristically that these explicit decouplings are in fact coincident with bounds on the effective parameters themselves. Depending on the formulation, these bounds correspond to end-member states of isostress or isostrain. We show the impacts of using constitutive coefficient models, decoupling assumptions and parameter bounds on poromechanical behaviours using analytical solutions for a 2D model problem. Based on the findings herein, we offer recommendations for how and when to use different coefficient modelling concepts.

中文翻译：

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多孔力学双连续模型本构系数的基础及其实际意义

双连续模型可以提供一种实用的方法来理解多孔机械耦合多尺度系统的一阶行为。为了闭合控制方程，需要带有模型的本构方程来计算有效本构系数。文献中已经提出了几个系数模型。但是，仍然缺少对不同建模概念的整体概述。为了解决这个问题，我们首先比较和对比文献中存在的主要模型。就本构关系本身而言，早期的关系被间接假定，隐含地忽略了连续压力之间产生的机械相互作用的影响。更多，最近使用包括连续介质间压力耦合的完整本构系统的用户已经明确地忽略了这些耦合作为提供复合和成分属性之间的直接关系以及简化系数模型的手段。在微观力学的框架内，我们启发式地表明，这些显式解耦实际上与有效参数本身的界限一致。根据公式，这些界限对应于等应力或等应变的最终成员状态。我们使用二维模型问题的解析解展示了使用本构系数模型、解耦假设和参数界限对多孔力学行为的影响。基于此处的发现，我们就如何以及何时使用不同的系数建模概念提供建议。