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Summary: This study presents the development of the scaled boundary finite element method (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. [ABSTRACT FROM AUTHOR]

A novel method coupling the scaled boundary finite element method (SBFEM) and the finite element method (FEM) is developed for linear elastic fracture modelling. A very simple but effective remeshing procedure based on the FE mesh only is used to accommodate crack propagation. The crack-tip region is modelled by an SBFE subdomain whose semi-analytical displacement solutions are used to extract accurate stress intensity factors. The SBFE subdomain is coupled with the surrounding FE mesh through virtual interfaces so that non-matching nodal discretisations of the shared boundaries can be used and only one SBFE subdomain is needed at a crack-tip. A few plane problems are modelled to validate the new method. [ABSTRACT FROM AUTHOR]

Abstract: A posteriori h-hierarchical adaptive scaled boundary finite element method (ASBFEM) for transient elastodynamic problems is developed. In a time step, the fields of displacement, stress, velocity and acceleration are all semi-analytical and the kinetic energy, strain energy and energy error are all semi-analytically integrated in subdomains. This makes mesh mapping very simple but accurate. Adaptive mesh refinement is also very simple because only subdomain boundaries are discretised. Two 2D examples with stress wave propagation were modelled. It is found that the degrees of freedom needed by the ASBFEM are only 5%–15% as needed by adaptive FEM for the examples. [Copyright &y& Elsevier]

Abstract: This study develops a novel hybrid method that combines the finite element method (FEM) and the scaled boundary finite element method (SBFEM) for crack propagation modelling in brittle and quasi-brittle materials. A very simple yet flexible local remeshing procedure, solely based on the FE mesh, is used to accommodate crack propagation. The crack-tip FE mesh is then replaced by a SBFEM rosette. This enables direct extraction of accurate stress intensity factors (SIFs) from the semi-analytical displacement or stress solutions of the SBFEM, which are then used to evaluate the crack propagation criterion. The fracture process zones are modelled using nonlinear cohesive interface elements that are automatically inserted into the FE mesh as the cracks propagate. Both the FEM’s flexibility in remeshing multiple cracks and the SBFEM’s high accuracy in calculating SIFs are exploited. The efficiency of the hybrid method in calculating SIFs is first demonstrated in two problems with stationary cracks. Nonlinear cohesive crack propagation in three notched concrete beams is then modelled. The results compare well with experimental and numerical results available in the literature. [Copyright &y& Elsevier]

Abstract: This study develops a method coupling the finite element method (FEM) and the scaled boundary finite element method (SBFEM) for fully-automatic modelling of cohesive crack growth in quasi-brittle materials. The simple linear elastic fracture mechanics (LEFM)-based remeshing procedure developed previously is augmented by inserting nonlinear interface finite elements automatically. The constitutive law of these elements is modelled by the cohesive/fictitious crack model to simulate the fracture process zone, while the elastic bulk material is modelled by the SBFEM. The resultant nonlinear equation system is solved by a local arc-length controlled solver. The crack is assumed to grow when the mode-I stress intensity factor K I vanishes in the direction determined by LEFM criteria. Other salient algorithms associated with the SBFEM, such as mapping state variables after remeshing and calculating K I using a “shadow subdomain”, are also described. Two concrete beams subjected to mode-I and mixed-mode fracture respectively are modelled to validate the new method. The results show that this SBFEM–FEM coupled method is capable of fully-automatically predicting both satisfactory crack trajectories and accurate load–displacement relations with a small number of degrees of freedom, even for problems with strong snap-back. Parametric studies were carried out on the crack incremental length, the concrete tensile strength, and the mode-I and mode-II fracture energies. It is found that the K I ⩾0 criterion is objective with respect to the crack incremental length. [Copyright &y& Elsevier]

Abstract: In the scaled boundary finite element method (SBFEM), the analytical nature of the solution in the radial direction allows accurate stress intensity factors (SIFs) to be determined directly from the definition, and hence no special crack-tip treatment, such as refining the crack-tip mesh or using singular elements (needed in the traditional finite element and boundary element methods), is necessary. In addition, anisotropic material behaviour may be handled with ease. These advantages are used in this study, in which a newly-developed Frobenius solution procedure in the frequency domain for solving the governing differential equations of the SBFEM, is applied to model transient dynamic fracture problems. The complex frequency–response functions are first computed using the Frobenius solution procedure. The dynamic stress intensity factors (DSIFs) are then extracted directly from the response functions. This is followed by a fast Fourier transform (FFT) of the transient load and a subsequent inverse FFT to obtain the time history of DSIFs. Benchmark problems with isotropic and anisotropic material behaviour are modelled using the developed frequency-domain approach. Excellent agreement is observed between the results of this study and those in published literature. The effects of the mesh density, the material internal damping coefficient, the maximum frequency and the frequency interval determining the frequency–response functions on the resultant accuracy and the computational cost are also discussed. [Copyright &y& Elsevier]

This study develops an efficient numerical homogenisation approach for meso-scale concrete samples with randomly generated and packed aggregates and pores. A simple algorithm is devised to discretize samples into meshes consisting of semi-analytical scaled boundary finite element (SBFE) polygons only. As each aggregate is modelled by one SBFE polygon and only polygonal boundaries are discretized into nodes, the degrees of freedom of a model is significantly reduced compared with conventional finite element models. The volumetrically averaged stress inside a SBFE polygon is semi-analytically integrated, leading to high accuracy in the homogenised elastic properties. The effects of model size and porosity are statistically studied by extensive Monte Carlo simulations. A size effect law taking porosity into account is proposed to predict effective elastic moduli in good agreement with experimental data up to 200 mm model size. The meso-models are found statistically homogeneous when the size is about 4.5 times the maximum aggregate size. [ABSTRACT FROM AUTHOR]

Abstract: An efficient methodology for automatic dynamic crack propagation simulations using polygon elements is developed in this study. The polygon mesh is automatically generated from a Delaunay triangulated mesh. The formulation of an arbitrary n-sided polygon element is based on the scaled boundary finite element method (SBFEM). All kind of singular stress fields can be described by the matrix power function solution of a cracked polygon. Generalised dynamic stress intensity factors are evaluated using standard finite element stress recovery procedures. This technique does not require local mesh refinement around the crack tip, special purpose elements or nodal enrichment functions. An automatic local remeshing algorithm that can be applied to any polygon mesh is developed in this study to accommodate crack propagation. Each remeshing operation involves only a small patch of polygons around the crack tip, resulting in only minimal change to the global mesh structure. The increase of the number of degrees-of-freedom caused by crack propagation is moderate. The method is validated using four dynamic crack propagation benchmarks. The predicted dynamic fracture parameters show good agreement with experiment observations and numerical simulations reported in the literature. [Copyright &y& Elsevier]

Abstract: An automatic cohesive crack propagation modelling methodology for quasi-brittle materials using polygon elements is presented. Each polygon is treated as a subdomain that is modelled by the scaled boundary finite element method (SBFEM). Generalised stress intensity factors (SIFs) based on matrix power function solutions of singular stress fields obtained from the SBFEM following standard finite element stress recovery procedures is used to evaluate the crack propagation criterion and determine the crack propagation direction. Interface elements model the fracture process zones and are automatically inserted into the polygon mesh as the crack propagates. A shadow domain procedure couples the polygons and interface elements. It computes the load–displacement response and crack propagation criterion, taking into account the cohesive tractions on the crack edges that are modelled as side-face tractions in the SBFEM. Cracks are propagated using a simple, yet flexible local remeshing procedure that can remesh any arbitrary polygon. Only minimal changes are made to the global mesh structure each time the remeshing algorithm is called. Five cohesive crack propagation benchmarks are modelled to validate the developed method and demonstrate its salient features. [Copyright &y& Elsevier]