This paper deals with a model for solids with porous channels filled by an incompressible isotropic fluid. The Darcy–Brinkman–Stokes law is derived, that represents a rate equation for the local mass flux of the fluid, presenting relaxation times in which this flux evolves towards its local-equilibrium value, viscous effects and a permeability tensor referring to a response of the system to an external agent, i.e. the fluid flow produced by a pressure gradient. The erosion/deposition phenomena in an elastic porous matrix are also studied and particular thermal porous metamaterials, that have interesting functionality, like in fluid flow cloaking, are illustrated as application of the obtained results. This derived model is completely in agreement with a theory formulated in the framework of the rational irreversible thermodynamics, where two internal variables are introduced (a symmetric structural porosity tensor and a symmetric second order tensor influencing viscous phenomena, that is interpreted as the symmetric part of the velocity gradient), when the results are considered in a first approximation and some suitable assumptions are done. The constitutive theory is worked out by using Liu’s and Wang’s theorems. The obtained theory has applications in several technological sectors, like physics of soil, pharmaceutics, physiology, etc., and contributes to the study of new porous metamaterials.

本文研究了一种具有不可压缩各向同性流体填充的多孔通道的固体模型。推导了达西-布林克曼-斯托克斯定律，该定律表示流体局部质量通量的速率方程，给出了弛豫时间，其中该通量朝着其局部平衡值演变，粘性效应和渗透率张量指的是响应将系统引入外部介质，即由压力梯度产生的流体流。还研究了弹性多孔基质中的腐蚀/沉积现象，并举例说明了具有热功能的特殊热多孔超材料，例如在流体流掩盖中作为获得的结果的应用。这个推导模型与在有理不可逆热力学框架内提出的理论完全一致，当在第一近似中考虑结果并做了一些适当的假设时，引入两个内部变量（对称的结构孔隙度张量和影响粘性现象的对称的二阶张量，被解释为速度梯度的对称部分） 。本构理论是利用刘定理和王定理得出的。所获得的理论在土壤物理，药物学，生理学等多个技术领域都有应用，并为新型多孔超材料的研究做出了贡献。当对结果进行初次近似并做了一些适当的假设时。本构理论是利用刘定理和王定理得出的。所获得的理论在土壤物理，药物学，生理学等多个技术领域都有应用，并为新型多孔超材料的研究做出了贡献。当对结果进行初次近似并做了一些适当的假设时。本构理论是利用刘定理和王定理得出的。所获得的理论在土壤物理，药物学，生理学等多个技术领域都有应用，并为新型多孔超材料的研究做出了贡献。