SBFEM Based Modelling Of Dynamic Elastoplastic And Hydraulic Fracturing And Development Of Polyhedron Element In ABAQUS

The scaled boundary finite element method(SBFEM)is a relatively new numerical method.It is now widely used in linear elastic stress analysis and crack propagation simulations due to its semi-analytical solutions,accurate calculation of stress intensity factors and flexible meshing and remeshing.In this paper,the SBFEM is further developed to simulate three types of problems:general dynamic elastoplastic problems,hydraulic fracture problems,and meso-scale concrete deformation and cohesive discrete crack propagation using ABAQUS user-defined element subroutines.Firstly,this study presents the development of SBFEM to simulate elastoplastic stress wave propagation problems subjected to transient dynamic loadings.Material nonlinearity is considered by first reformulating the SBFEM to obtain an explicit form of shape functions for polygons with an arbitrary number of sides.The material constitutive matrix and the residual stress fields are then determined as analytical polynomial functions in the scaled boundary coordinates through a local least squares fit to evaluate the elastoplastic stiffness matrix and the residual load vector semianalytically.The treatment of the inertial force within the solution of the nonlinear system of equations is also presented within the SBFEM framework.The nonlinear equation system is solved using the unconditionally stable Newmark time integration algorithm.The proposed formulation is validated using several benchmark numerical examples,whose results have demonstrated that the proposed method is capable of simulating dynamic elastoplastic problems as accurately as the traditional FEM,but the required mesh density and degrees of freedom for the same accuracy can be much less than those needed by the latter.Secondly,a numerical model based on the scaled boundary finite element method is developed to simulate the hydraulic fracturing in concrete-like quasi-brittle materials using cohesive interface elements.The shadow domain method developed previously is extended to consider crack-width-dependent hydraulic pressure and cohesive traction,so that the stress intensity factors caused by both crack-face forces are semi-analytically calculated separately in the same way.The crack propagation is determined by the criterion of K1?0,and the propagation direction by the maximum energy release rate criterion.Two examples of concrete structures are modeled,and the results are in good agreement with the experimental data and others numerical results.Thirdly,user-defined element subroutines(UEL and VUEL)in Fortran are developed in ABAQUS,to implement the SBFEM,for general static and elastodynamic stress analyses of solids.The purposes are twofold:to increase the ease-of-use and acceptability of this relatively new numerical method;and to combine advantages of both the SBFEM and ABAQUS,namely,the former's semi-analytical solutions and flexibility in domain discretization,and the latter's powerful linear and nonlinear solvers and pre/post-processing modules,for modeling complicated problems with higher accuracy and fewer degrees of freedom than the traditional FEM.Using the developed UEL and VUEL,a few 2D and 3D problems,including homogeneous solids with and without cracks,composites with inclusions of random shapes,XCT-image converted concrete mesoscale models,are simulated.The results are compared favourably with FEM simulations in terms of accuracy and degrees of freedom.Furthermore,the developed subroutines are applied to simulate heterogeneous problems,for example,meso-scale concrete models,generated by the random aggregate take-place method and converted directly from micro XCT images.The models are discretized using both Delaunay-based polygonalisation and quadtree mesh generation algorithms.Apart from 2D and 3D linear elastic analysis,3D complicated nonlinear fracture propagation is also modelled by inserting softening cohesive elements into mesoscale models with random aggregates.