Modelling Porous and Deformable Media with Several Scales ofHeterogeneity

本研究提出了一种非均质多孔弹性介质的理论，其材料性质具有几个不同的长度尺度（如颗粒、层、全局）。迄今为止为复合介质发展起来的均匀化理论的现代数学技术将得到扩展。研究了准静态热固结和动态孔隙弹性的本构系数。将对一个简单但用途广泛的三维微观结构（维格纳-塞茨多面体）进行明确的计算。横向各向同性宏观方程将用于求解地温上升柱、沉点汇等物理问题和地震波传播问题。

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.