We derive the balance equations for a double poroelastic material which comprises a matrix with embedded subphases. We assume that the distance between the subphases (the local scale) is much smaller than the size of the domain (the global scale). We assume that at the local scale both the matrix and subphases can be described by Biot’s anisotropic, heterogeneous, compressible poroelasticity (i.e. the porescale is already smoothed out). We then decompose the spatial variations by means of the two-scale homogenization method to upscale the interaction between the poroelastic phases at the local scale. This way, we derive the novel global scale model which is formally of poroelastic-type. The global scale coefficients account for the complexity of the given microstructure and heterogeneities. These effective poroelastic moduli are to be computed by solving appropriate differential periodic cell problems. The model coefficients possess properties that, once proved, allow us to determine that the model is both formally and substantially of poroelastic-type. The properties we prove are a) the existence of a tensor which plays the role of the classical Biot’s tensor of coefficients via a suitable analytical identity and b) the global scale scalar coefficient \(\bar{\mathcal {M}}\) is positive which then qualifies as the global Biot’s modulus for the double poroelastic material.

我们推导出了双多孔弹性材料的平衡方程，该材料包括具有嵌入亚相的基体。我们假设子阶段之间的距离（局部尺度）远小于域的大小（全局尺度）。我们假设在局部范围既矩阵和子阶段可以通过比奥各向异性描述，异构的，可压缩多孔弹性（即在porescale已经平滑了）。然后，我们通过两尺度均质化方法分解空间变化，以在局部尺度上放大多孔弹性相之间的相互作用。通过这种方式，我们推导出了形式上为多孔弹性类型的新型全局比例模型。全局尺度系数说明了给定微观结构和异质性的复杂性。这些有效的多孔弹性模量将通过求解适当的微分周期单元问题来计算。模型系数具有的特性一旦得到证明，就可以让我们确定该模型在形式上和实质上都属于多孔弹性类型。我们证明的性质是 a) 存在一个张量，它通过合适的分析恒等式扮演经典 Biot 系数张量的角色，以及 b) 全局标量系数\(\bar{\mathcal {M}}\)是正数，它可以作为双多孔弹性材料的全局 Biot 模量。