不可压饱和粘弹性多孔介质固结问题的Gurtin型变分原理

基于多孔介质理论,在固相骨架和孔隙流体微观不可压,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,利用卷积积分的性质,本文首先建立了以固相骨架位移、孔隙流体相对速度和孔隙流体压力为宗量的流体饱和粘弹性多孔介质固结问题的一个Gurtin型变分原理.其次,利用Lagrange乘子法解除相关的变分约束条件,建立了流体饱和粘弹性多孔介质固结问题的若干广义Gurtin型变分原理,包括第三类的Hu-Washizu型变分原理.最后,简单讨论了等价初边值问题的相应变分原理.这些Gurtin型变分原理的建立不仅丰富了饱和粘弹性多孔介质的相关理论,而且为相关数值模拟方法,如有限元法、无网格法等的建立奠定了理论基础.

Gurtin Type Variational Principles for Incompressible Saturated Viscoelastic Porous Media

Based on the theory of porous media,with the assumptions of microscopic incompressibility of solid skeleton and pore fluid as well as the small deformation of solid phase,a Gurtintype variational principle for consolidations of fluid-saturated viscoelastic porous media,in which the solid skeleton satisfies the general linear integral-type viscoelastic constitutive equation,was first established by using convolution integral,whose basic unknowns are the displacement of solid skeleton,relative velocity and pressure of the pore fluid.With the Lagrange multiplier to release the various variational constraints,several Gurtintype variational principles,including Hu-Washizu variational principle,were developed.At last,a variational principle for an equivalent initial boundary value problem was discussed briefly.These variational principles not only enrich the context of fluidsaturated viscoelastie viscoelastic porous media,but also provide a theoretical basis for numerical simulation methods,such as finite element method and meshless method.