Time-discontinuous Material Point Method For The Dynamic Analysis Of Saturated Porous Media

Porous media are widely used in production and life.The study of the mechanical behavior of porous media has important research value and application prospects in the fields of geotechnical engineering,material science and biological and medical engineering.When seismic waves propagate in the earth crust or other saturated porous materials are subjected to impact loads,their stress waves and pore pressure waves propagate within the structure,and the waveform distribution usually exhibit discontinuities and steep gradient characteristics.Existing computational methods often cannot accurately characterize the discontinuity of stress waves and pressure waves when dealing with such working conditions,and false highfrequency numerical oscillations often occur in the computational process.In nonlinear problems such as contact and elastoplasticity of saturated porous media,the computational accuracy of contact force and equivalent plastic strain is often reduced due to the numerical oscillations of stress.Therefore,in this thesis,the research on the dynamic problems of saturated porous media is mainly carried out as follows:First,a time-discontinuous material point method for the transient coupling fluid-solid problems of saturated porous media is proposed to solve the problems of original material point methods in dealing with wave propagations process of saturated porous media.On the one hand,based on the u-U and u-p governing equations of saturated porous media,combined with the original material point method,discrete forms of saturated porous media governing equations on the background grid are obtained,and interpolation particle domain interpolation function is adopted.On the other hand,based on the time-discontinuous material point method,discretized the continuous time domain,and the weak form of the the time-discontinuous governing equations are established by combining the spatially discrete governing equations,the constraint equations between the displacements and velocities,and the discontinuous conditions.which are used to compute the reconstructed nodal displacements and nodal velocities.The displacement and velocity fields are interpolated and reconstructed by piecewise cubic and linear interpolations,respectively,within each interval.In the formula,the displacement field remains continuous at each time instant,while the velocity field may become discontinuous,which enables the method to capture correctly the discontinuous characteristics and control effectively the spurious numerical oscillation.A constitutive update algorithm for the u-U and u-p governing equations for the time-discontinuous material point method of saturated porous media is also given.The program computation flow of the time-discontinuous material point method for saturated porous media is given,including the iterative process of nodal velocities.Second,a time-discontinuous material point method for linear dynamic problems of saturated porous media is proposed.The effectiveness of the proposed algorithm in onedimensional and two-dimensional wave propagation problems of saturated porous media is verified by representative examples.The effects of time step size,the number of material points,saturated porous media governing equation and two-phase material point damping force term interpolation methods on the computation results are also studied.The numerical computation results show that:(1)the proposed algorithm can effectively control the severe numerical oscillations occured in the original material point method,and which can better characterize the discontinuities of the stress waves;(2)the change of time step can affect the computation results of time discontinuous material point method to a great extent,that is,the increase of the time step will make the stress wave curve smooth,but the discontinuities cannot be well described;(3)the more material points,the better the computational results will be;(4)different governing equations and the different interpolation methods of the damping force term has little effect on the results;(5)compared with the original material point method,the time computation cost of the proposed method does not increase much.Third,for the contact problems and the elastoplastic problems,a time discontinuous material point method for nonlinear dynamic problems of saturated porous media is proposed.It includes the dynamic contact algorithm of saturated porous media,the constitutive model of single-phase solid and saturated porous media elastoplastic problems,and the corresponding time-discontinuous program computation flow is given.The effectiveness of the proposed algorithm in contact problems and elastoplastic problems are verified by representative examples.The proposed algorithm can effectively eliminate cluttered high-frequency numerical oscillations during the stress waves propagation of two objects in contact,which are closer to the theoretical solution than the original material point method.It can also predict the evolution of contact force and eliminate the numerical oscillations in the contact force curve.In the elastoplastic problems,for single-phase solid and saturated porous media,it can better characterize the propagation and reflection of elastoplastic stress waves,control the numerical oscillations and can effectively control the false equivalent plastic strain caused by numerical oscillation Overall,simple contact and elastoplastic problems do not add much time cost.