Coupling Convected Particle Domain Interpolation Based Material Point Method For Dynamic And Contact Analysis Of Saturated Porous Media Involving Large Deformation

The mechanics of porous media has widely applications in many engineering fields, such as geotechnical engineering and biomechanics engineering. Therefore, studies on the dynamic behaviors of saturated porous media have attracted much attention in the past few decades. Saturated porous media which consisted of a skeleton and the fluid in the pore is a typical kind of porous media. The finite element methods (FEMs) have been applied to predict the dynamic response about the solid-fluid problems. Although there are many advantages of the FEMs, the limitations of themselves should not be neglected. One limitation is that large deformation may cause local mesh distortion, which leads to great numerical artifact errors. Another one is that the generation of mesh is quite tricky in three-dimensional objects with complex structure. To overcome these difficulties, many kinds of meshfree/meshless methods have been proposed and the Material Point Method (MPM) is a typical method among them. MPM has been used successfully in simulating the dynamic behaviors of saturated porous media involving small deformation. However, due to the lack of smoothness of the interpolation functions of the original MPM, some numerical noises may occur while material points crossing computational grid boundaries. The generalized interpolation material point method (GIMP) was proposed to improve the smoothness of the interpolation functions, but the procedure is quit complex. To simplify the computational procedure, a modified interpolation technique named Convected Particle Domain Interpolation (CPDI) method was proposed by some scholars.In this thesis, the Coupling Convected Particle Domain Interpolation method (CCPDI) is proposed for the dynamic analysis of saturated porous media involving large deformation based on the u-p form governing equations and the interpolation technique of CPDI. Furthermore, on the basis of the proposed CCPDI method, the dynamic contact algorithm is developed to cope with the dynamic contact problem of saturated porous media involving large deformation. The algorithm developed in this thesis could efficiently eliminate the error in simulating large deformation behavior and predicting the contact time. Computational results of several representative examples demonstrate the accuracy and efficiency of the proposed method. The organization of this thesis is as follows. In the first chapter, the background of this research and a number of meshless methods are briefly summarized. Then, the contents of the thesis are outlined at the end of the chapter. The second chapter introduces several physical quantities used in describing the porous media, some necessary assumption and the governing equation based on the Biot theory. A brief review about several particle methods include the standard MPM, the GIMP and the CPDI method is presented in chapter3.In the fourth chapter, the procedure of the coupling convected particle domain interpolation method (CCPDI) proposed in the thesis is introduced in details. The weak form is established derived from u-p form governing equations. Furthermore, a tracking method is proposed to deal with the external loads on moving boundaries during the computational process. Several representative examples demonstrate the accuracy and efficiency of the proposed method.The contact algorithm is developed in chapter5to simulate the dynamic large deformation of saturated porous media. To predict the contact area and the contact time more accurately, the particle domain is utilized in judging the contact background nodes. The validity of the developed algorithm is illustrated through the numerical calculations regarding dynamic contact problem of saturated porous media.The last chapter includes the conclusions of this thesis and the outlook of further work. In addition, the flow chart of the Poro-CCPDI code, which has been developed in this work and could be used to simulate the dynamic and contact behavior of saturated porous media involving large deformation, can be found in the Appendix.The thesis is supported by the National Natural Science Foundation of China (11072051,90715037,10902021), the lllproject (B08014), the program for Changjiang Scholar and Innovative Research Team in University (PCSIRT) and the National Key Basic Research Special Foundation of China (2010CB832704).