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Based on the theory of porous media,a general Gurtin variational principle for theinitial boundary value problem of dynamical response of fluid-saturated elastic porous media isdeveloped by assuming infinitesimal deformation and incompressible constituents of the solid andfluid phase.The finite element formulation based on this variational principle is also derived.Asthe functional of the variational principle is a spatial integral of the convolution formulation,thegeneral finite element discretization in space results in symmetrical differential-integral equationsin the time domain.In some situations,the differential-integral equations can be reduced to sym-metrical differential equations and,as a numerical example,it is employed to analyze the reflectionof one-dimensional longitudinal wave in a fluid-saturated porous solid.The numerical results canprovide further understanding of the wave propagation in porous media.
Based on the theory of porous media, a general Gurtin variational principle for the initial boundary value problem of dynamical response of fluid-saturated elastic porous media isdeveloped by assuming infinitesimal deformation and incompressible constituents of the solid and fluid phase. The finite element formulation based on this variational principle is also derived. Asthe functional of the variational principle is a spatial integral of the convolution formulation, the general finite element discretization in space results in symmetrical differential-integral equations in the time domain. In some situations, the differential-integral equations can be reduced to sym-metrical differential equations and, as a numerical example, it is employed to analyze the reflection of one-dimensional longitudinal wave in a fluid-saturated porous solid. The numerical results canprovide further understanding of the wave propagation in porous media.