基于变分渐近法预测饱和多孔介质流固耦合性能的细观力学模型

饱和岩土类多孔材料内固、液相不同属性产生的各向异性和多孔微结构的不均匀性使得材料的细观力学特性计算变得十分复杂。为准确预测岩土类材料的有效弹性性能和细观应力-应变场,基于Biot多孔弹性介质理论,建立可描述岩土类多孔材料固液相运动的能量泛函和相应的多孔弹性本构关系;利用细、宏观尺度比作为小参数将能量变分泛函渐近扩展为系列近似泛函;以场变量波动函数为未知量,通过解决近似泛函的最小化问题(驻值问题)得到波动函数的解析解,从而建立逼近物理和工程真实性的细观力学模型,并通过有限元技术得以数值实现。多孔介质材料细观力学特性算例表明:与经典均匀化理论(将液体类比为具有较高泊松比的固体材料)相比,基于变分渐近均匀化细观模型预测的多孔介质材料细观力学特性更精确,尤其是能准确重构多孔微结构内局部应力-应变场分布,为损伤破坏、局部断裂分析奠定了坚实基础。

Micromechanical model for predicting fluid-solid coupling performance of saturated porous media based on variational asymptotic method

The anisotropy produced by the different properties of fluid and solid phase in saturated rock and soil-like porous materials and heterogeneity of porous microstructures made the calculation of micro mechanics properties very complex. In order to accurately predict the effective elastic properties and micro stress-strain fields of rock and soil-like materials, the energy functional and corresponding porous elastic constitutive relations were built based on the Biot porous elastic media theory. The energy variational functional is then asymptotically expended to series of approximate functional by taking advantage of the small ratio of micro scale to macro scale. With the fluctuation functions of field variables as unknown variables, the analytical solutions to the fluctuation functions can be obtained by solving the minimum problem(stationary value problem) of approximate functionals. Thus, a micromechanical model is established, which is as close as possible to the real physical and engineering problem. The developed micromechanical model is numerically implemented through the finite element technology. The examples of porous material show that the accuracy of micromechanical properties calculated by the developed model is much better than the classical homogenization theory, in which the fluid material is regarded as solid material with high Poisson's ratio; especially the local stress-strain fields distribution can be accurately recovered, laying a solid foundation for the analysis of damage and local fracture.