Finite Element Analysis On The Elastic And Plastic Dynamic Behaviors Of Saturated Porous Media

The saturated porous media model, which is based on the mixture theory in modern continuum mechanics frame, is very excellent in both mathematics and physics. Nowadays, it has been accepted by more and more people. The finite element numerical analysis is one of the important methods in the dynamic response investigation of biphasic saturated porous media model.The paper has reviewed the developments of biphasic saturated porous media model and its numerical analysis methods first. Then we suppose that the solid bone is isotropic media ,and the liquid in the cavity is ideal fluid in simulation. The dynamic governing equations can be established through combining the saturated porous media model, which describe the coupling between the distortion and fluid flow. By using the Laplace transform technique, the one-dimensional analytical solution of dynamic response for biphasic saturated porous media. Meanwhile the penalty finite element formulation for dynamic response of biphasic saturated porous media is obtained by using Galerkin weighted residual method for the saturated porous media model with corresponding initial an boundary conditions, the node's degree of freedom and the scale of p and penalty parameter beta in the continuum equation and ,in turn, eliminated the pressure in governing equations. A two-dimensional elastic finite element program is obtained with the above-mentioned methods includes rectangular elements for saturated porous media. To test the methods and program, the paper calculates the dynamic response of biphasic saturated porous media under the sine load and the step load. These numerical results are coincided with the corresponding theoretical result, which illustrates that the method and the program is efficient and available.The porous media material should be regarded as nonlinear material under general conditions. The paper develops the constitutive relation of solid bone from elasticity to elastoplasticity. Derived the elastoplastic dynamic finite element equation for biphasic saturated porous media. And deduces the process of nonlinear iterative solution with the Newmark integration method. Then a two-dimensional elastic-plastic dynamic finite element program is obtained .The program includes rectangular elements for plane stress,plane strain and axisymmetric problems. With above program, the paper calculates two samples of one-dimension elastic-plastic dynamic response of biphasic saturated porous media under impact load and the subsidence of two-dimension biphasic saturated porous media body under the step load. The result is satisfactory.