Modelling Porous and Deformable Media with Several Scales ofHeterogeneity

这项研究建议发展一种非均质孔隙弹性介质理论，其材料特性由几个不同的长度尺度(例如，颗粒、层、全局)来表征。目前为止发展起来的适用于复合介质的均化理论的现代数学方法将得到推广。研究了准静态热固结本构系数和动态孔弹性本构关系。将对简单但通用的三维微结构(Wigner-Seitz多面体)进行显式计算。求解横观各向同性宏观尺度方程，可以解决地热羽流上升、点汇淹没、地震波传播等几个物理问题。

This study proposes to develop a theory of heterogeneous poroelastic media whose material properties are characterized by several distinct length scales (e.g. grains, layers, global). The modern mathematical techniques of homogenization theory, so far developed for composite media will be extended. The constitutive coefficients for quasi static thermal consolidation, and dynamic poroelasticity will be studied. Explicit calculations for a simple but versatile 3-D micro structure (Wigner-Seitz polyhedron) will be performed. The transversely isotropic macroscale equations will be solved for several physical problems such as the rising geothermal plume, the submerged point sink, etc., and seismic wave propagation.