We present the macroscale three-dimensional numerical solution of anisotropic Biot's poroelasticity, with coefficients derived from a micromechanical analysis as prescribed by the asymptotic homogenisation technique. The system of partial differential equations (PDEs) is discretised by finite elements, exploiting a formal analogy with the fully coupled thermal displacement systems of PDEs implemented in the commercial software Abaqus. The robustness of our computational framework is confirmed by comparison with the well-known analytical solution of the one-dimensional Therzaghi's consolidation problem. We then perform three-dimensional numerical simulations of the model in a sphere (representing a biological tissue) by applying a given constant pressure in the cavity. We investigate how the macroscale radial displacements (as well as pressures) profiles are affected by the microscale solid matrix compressibility (MSMC). Our results suggest that the role of the MSMC on the macroscale displacements becomes more and more prominent by increasing the length of the time interval during which the constant pressure is applied. As such, we suggest that parameter estimation based on techniques such as poroelastography (which are commonly used in the context of biological tissues, such as the brain, as well as solid tumours) should allow for a sufficiently long time in order to give a more accurate estimation of the mechanical properties of tissues.

我们提出了各向异性比奥多孔弹性的宏观三维数值解，其系数由渐近均化技术规定的微机械分析得出。偏微分方程组（PDE）的系统由有限元离散化，它与商业软件Abaqus中实现的PDE的完全耦合热位移系统形成形式上的类比。通过与一维Therzaghi固结问题的著名分析解决方案进行比较，可以确定我们计算框架的鲁棒性。然后，通过在空腔中施加给定的恒定压力，对球体（代表生物组织）中的模型进行三维数值模拟。我们研究微观尺度的固体位移可压缩性（MSMC）如何影响宏观尺度的径向位移（以及压力）曲线。我们的结果表明，通过增加施加恒定压力的时间间隔的长度，MSMC在宏观位移上的作用变得越来越突出。因此，我们建议基于孔隙弹性成像技术（通常在诸如大脑等生物组织以及实体瘤的背景下使用）的技术进行参数估计应留出足够长的时间，以便提供更多信息。准确估计组织的机械性能。我们的结果表明，通过增加施加恒定压力的时间间隔的长度，MSMC在宏观位移上的作用变得越来越突出。因此，我们建议基于孔隙弹性成像技术（通常在诸如大脑等生物组织以及实体瘤的背景下使用）的技术进行参数估计应留出足够长的时间，以便提供更多信息。准确估计组织的机械性能。我们的结果表明，通过增加施加恒定压力的时间间隔的长度，MSMC在宏观位移上的作用变得越来越突出。因此，我们建议基于多孔弹性成像技术（通常在诸如大脑等生物组织以及实体瘤的背景下使用）的技术进行参数估计应留出足够长的时间，以便提供更多信息。准确估计组织的机械性能。