| As a kind of mixed material consisting of solid skeleton and tiny pores filled with fluid and/or gas,porous media exist widely in natural environment and engineering applications.Especially,soil and rock,as a kind of universal and inexpensive materials,are widely used in civil engineering structures such as buildings,road tunnels,bridges and dams.The main mechanical problems involved in the above civil engineering are consolidation,dynamic response and fracture problems,etc.Because porous media are multi-phase materials,the corresponding mechanical problems belong to the coupling multi-physical field problems.For example,it is not only needed to consider the effect of the deformation of solid skeleton on the flow of pore fluid in the saturated porous media,but also the effect of the flow of pore fluid on the deformation of solid skeleton should be taken into account.At the same time,the porous media have strong heterogeneities due to their complex geological changes in a long period.Therefore,for the mechanical analysis of large-scale engineering structures,it is often needed to make the mesh grids fine enough to reflect the microscopic heterogeneous characteristics of the material and meet the requirements of computational accuracy using the finite element method,which leads to large amount of computation and cause that the computational efficiency is very low and even the calculation becomes failed.In addition,for the complex fracture problems in porous media,the computational efficiency by using the finite element method is also very low and it is even difficult to realize because it is needed to consider both the discontinuities on the crack tip and the interaction between the multiple fields.Therefore,according to the high computational efficiency of multiscale finite element method and the advantage of peridynamic method in dealing with fracture problems,it is of great significance to develop more efficient new numerical algorithms for the consolidation,dynamic and fracture problems in porous media such as soil and rock.This is helpful to understand and study the mechanical properties and deformational mechanisms of porous media,as well as the design,the detection and evaluation of stability and safety in engineering applications.Based on the theoretical foundations of multiscale finite element and peridynamic methods,this dissertation is mainly contributed to the studies on the multiscale finite element method and peridynamic method for the fracture problems in single phase solids and the fluid-solid coupling consolidation,dynamic response and hydraulic fracture problems in saturated porous media.The main research work of this dissertation contains the following five parts:Firstly,a extended multiscale finite element method is proposed for the fluid-solid coupling dynamic problems of homogeneous and heterogeneous saturated porous media.Different from the previous extended multiscale finite element method for static problems,each coarse element is discretized with fine finite element in temporal and spatial spaces for the dynamic problems.Then the upscaling and downscaling calculations are carried out by using the equivalent static equilibrium equation.Among them,because the equivalent numerical basis functions are calculated by using the equivalent stiffness matrix with the given linear boundary conditions,they can not only reflect the static and dynamic characteristics of the coarse element,but also can reflect the interaction between the displacements of solid skeleton and pore fluid.In addition,a uniform formulation of numerical base functions is given out.The improved downsacle calculating formulation is developed and the multi-node coarse element is used to improve the computational accuracy.At last,the validity and efficiency of the coupling extended multiscale finite element method are verified by the numerical examples of the dynamic analysis of homogeneous and heterogeneous saturated porous media.Secondly,a peridynamic method is proposed for the fluid-solid coupling consolidation and dynamic response problems of saturated porous media.In this method,the peridynamic governing equations for the fluid-solid coupling consolidation and dynamic problems of saturated porous media are derived according to the principle of effective stress and the basic peridynamic theory.Then,the implicit peridynamic formulations are derived by the linearization of the governing equations on the basis of the first-order Taylor expansion technique.At last,the validity and efficiency of proposed peridynamic method are verified by the numerical examples of the consolidation and dynamic analysis of saturated porous media.Thirdly,a coupling finite element and peridynamic method is proposed for the dynamic problems of single phase solids with crack propagation.In this method,based on the bond-based peridynamic model,the peridynamic equivalent implicit incremental equations for the dynamic problems of single phase solids are derived according to the Newmark integration and Newton-Raphson schemes,and the Taylor expansion technique.Then,the whole system is partitioned into two kinds subregions.The subregion where the boundary conditions are often applied or the continuous deformation appears can be solved by the finite element formulation while the subregion where the failure is expected is solved by the peridynamic formulation.The coupling equivalent implicit incremental equations are obtained based on the proposed coupling strategy according to the mesh grids and material points.Next,the displacement control and load control based incremental-iterative algorithm and the corresponding computational procedure are given out.At last,the validity and accuracy of the coupling finite element and peridynamic method are verified by the numerical examples of the dynamic analysis of single phase solids with crack propagation.Fourthly,a coupling extended multiscale finite element and peridynamic method is proposed for the quasi-static problems of single phase solids with crack propagation.In this method,based on the state-based peridynamic model,the peridynamic implicit incremental equations for the quasi-static problems of single phase solids are derived according to the first-order Taylor expansion technique.Then,the whole system is partitioned into two kinds of subregions.The subregion ?EMsFEM can be solved by the finite element formulation while the subregion ?PD is solved by the peridynamic formulation.Among the coupling domain,the displacements of the fine element nodes and the material points in the coupling domain are bonded to each other.According to the numerical base functions of the coarse elements,the displacement constraint relationships between the coarse element nodes and the material points are constructed and introduced into the coupling strain energy density function on the basis of the Lagrange multiplier method.Moreover,a bilinear softening material law is adopted in the failure model and the computational procedure of the present coupling method is given out in details on the basis of the load control or displacement control based incremental-iterative algorithms.At last,the validity and efficiency of the coupling extended multiscale finite element and peridynamic method are verified by the numerical examples of the quasi-static analysis of single phase solids with crack propagation.Finally,a coupling extended multiscale finite element and peridynamic method is proposed for the hydraulic fracture problems of saturated porous media.In this method,the equations of motion of solid skeleton,flow of pore fluid and motion of fluid in the crack are given out for the hydraulic fracture problems of saturated porous media in the peridynamic model.Comparing with the dynamic problems,the primary distinction is that a scalar used to describe the crack is introduced into the equation of motion of solid skeleton and an equation is added to describe the motion of fluid in the crack.The corresponding incremental equivalent static equilibrium equations are obtained according to the linearized method on the basis of Taylor expansion technique,Newmark integration method and Newton-Raphson method.Next,the incremental equivalent static equilibrium equations of dynamic problems of saturated porous media in the extended multiscale finite element method are derived based on the corresponding continuum theory.In the coupling strategy,the constraint relationships between the coarse element nodes and material points are introduced into the strain energy function using the Lagrange multiplier method.The final coupling equivalent static equilibrium equations can be obtained by the variational method.In addition,the displacement control and load control based incremental-iterative algorithms are given out for this nonlinear problems.At last,the validity and accuracy of the coupling extended multiscale finite element and peridynamic method are verified by the hydraulically pressurized crack examples. |
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