The role of microscale solid matrix compressibility on the mechanical behaviour of poroelastic materials
The role of microscale solid matrix compressibility on the mechanical behaviour of poroelastic materials
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DOI：
10.1016/j.euromechsol.2020.103996
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发表时间：
2020-09-01
影响因子：
4.1
通讯作者：
Merodio, J.
中科院分区：
文献类型：
--
作者：
Dehghani, H.;Noll, I;Merodio, J.
我们提出了各向异性Biot孔隙弹性的宏观三维数值解，其系数来自于由渐近均质化技术规定的微观力学分析。利用商业软件Abaqus实现的偏微分方程组的完全耦合热位移系统的形式化类比，利用有限元对偏微分方程组进行离散。通过与众所周知的一维Therzaghi固结问题的解析解的比较，我们的计算框架的鲁棒性得到了证实。然后，我们通过在腔中施加给定的恒定压力，在球体（代表生物组织）中对模型进行三维数值模拟。我们研究了宏观尺度径向位移（以及压力）分布如何受到微观尺度固体基质压缩性（MSMC）的影响。结果表明，随着施加恒压时间间隔的延长，MSMC对宏观尺度位移的作用越来越突出。因此，我们建议基于孔隙弹性成像（通常用于生物组织，如大脑和实体肿瘤）等技术的参数估计应该允许足够长的时间，以便对组织的机械特性进行更准确的估计。
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.