广义混合律及其在地球材料流变学中的应用

Generalized mixture rule and its applications to rheology of the Earth materials.

本文总结了广义混合律的基本特征,并以具弱相支撑结构的固液相悬浮液(岩浆)和具强相支撑结构的多孔材料(玄武岩、砂岩或部分熔融岩石)为例,系统地介绍了广义混合律在预测多矿物岩石或复合材料弹性力学或流变学性质随组分性质、体积分数和显微构造而变化的应用。广义混合律与现存理论的紧密吻合以及对多矿物岩石和复合材料力学性质描述的准确性绝非偶然,隐藏其后必有尚未人知的物理基础。严格的理论证明极可能是数学力学上富于挑战性的课题。

Efforts to model the tectonic deformation behavior of the Earth＇s crust and mantle will become easier if a simple but robust expression is available to make accurate predictions of the elastic and rheological properties of candidate multiphase rocks under various conditions. For this intent, a generalized mixture rule （GMR） is established to provide a unified description of the mechanical properties of polyphase composites or polymineralic rocks in terms of component properties, volume fractions, and microstructures. Taking solid-liquid suspensions （e. g. , magmas） and porous materials （e. g. , basalts and sandstones ） as end-members of two-phase composites in which solid particles or pores are dispersed within a continuous liquid or solid framework, the GMR yields a rigorous expression for the relationship between the mechanical properties and component volume fractions. Although the GMR is purely mathematical in origin, its connection to the existing physical theories and its consistence with extensive high-quality experimental data suggests that it should have some physical validity as a very handy tool for a general description of the elastic and rheological properties of muhiphase materials including suspensions and porous solids. Rigorous theoretical analyses could be a very challenging topic.