不可压饱和粘弹性多孔介质的变分原理及其无网格模拟

基于饱和多孔介质理论,在固相和液相微观不可压,固相骨架小变形且满足线性粘弹性积分型本构关系的假定下,建立了流体饱和粘弹性多孔介质动力响应的若干Gurtin型变分原理,包括Hu-Washizu变分原理.利用所建立的变分原理,导出了流体饱和粘弹性多孔介质动力响应无网格数值模拟的离散控制方程,此方程是一个关于时间的对称微分方程组,便于分析计算.作为数值例子,研究了流体饱和粘弹性多孔柱体的一维动力响应,数值结果揭示了流体饱和粘弹性多孔柱体中波的传播特性以及固相粘性的影响.

VARIATIONAL PRINCIPLES AND MESHLESS SIMULATIONS FOR INCOMPRESSIBLE SATURATED VISCOELASTIC POROUS MEDIA

Based on the theory of porous media,with assumptions of the microscopic incompressibility of the solid skeleton and pore fluid as well as the small deformation of the solid phase,Gurtin-type variational principles,especially the Hu-Washizu type variational principle,for the dynamical responses of the fluid-saturated viscoelastic porous media,in which the solid skeleton satisfies the general linear integral-type viscoelastic constitutive equation,are presented.The space discrete governing equations of the meshless simulations for dynamical responses of the saturated viscoelastic porous media are derived based on one of the variational principles.These discrete equations are the symmetrical differential equations in time and are simple for analysis.As a numerical example,one-dimensional dynamical responses of a fluid-saturated viscoelastic porous column are investigated.The numerical results reveal the characteristics of the wave propagation in the saturated viscoelastic porous column,and the effect of solid viscosity on the dynamical behavior is investigated.