We propose the governing equations for a pre-stressed poroelastic composite material. The structure that we investigate possesses a porous elastic matrix with embedded elastic subphases with an incompressible Newtonian fluid flowing in the pores. Both the matrix and individual subphases are assumed to be linear elastic and pre-stressed. We are able to apply the asymptotic homogenisation technique by exploiting the length-scale separation that exists between the porescale and the overall size of the material (the macroscale). We derive the novel macroscale model which describes a poroelastic composite material where the elastic phases possess a pre-stress. We extend the current literature for poroelastic composites by addressing the role of the pre-stresses in the functional form of the new system of derived partial differential equations and its coefficients. The latter are computed by solving appropriate periodic cell differential problems which encode the specific contribution related to the pre-stresses. The model in the first instance is derived in the most general scenario and then specified for a variety of particular cases which are associated with different macroscale behaviour of materials.

我们提出了预应力多孔弹性复合材料的控制方程。我们研究的结构具有多孔弹性基质，其中嵌入弹性子相，不可压缩牛顿流体在孔隙中流动。基体和各个子相都被假定为线弹性和预应力的。我们能够通过利用材料的孔隙尺度和整体尺寸之间存在的长度尺度分离（宏观尺度）来应用渐近均质化技术。）。我们推导了新颖的宏观模型，该模型描述了弹性相具有预应力的多孔弹性复合材料。我们通过解决预应力在导出的偏微分方程及其系数的新系统的函数形式中的作用来扩展当前的多孔弹性复合材料文献。后者是通过解决适当的周期性单元微分问题来计算的，这些问题编码与预应力相关的特定贡献。第一个实例中的模型是在最一般的场景中导出的，然后针对与材料的不同宏观行为相关的各种特定情况进行指定。