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This paper presents the computations of fracture parameters including stress intensity factors and T-stress of three-dimensional cracks and notches by the scaled boundary finite element method. The singular stress field along the crack front is approximated by a singularity at a point through a semi-analytical solution. The solution is expressed as a matrix power function which allows direct extraction of the fracture parameters based on their definitions. No singular element or asymptotic solution is required for the extraction process. The numerical examples presented which include bimaterial interface cracks and V-notches illustrate the accuracy and versatility of the proposed approach. [ABSTRACT FROM AUTHOR]

• Automatic image-based octree meshes for efficient modelling of composites. • Extension of scaled boundary finite element method (SBFEM) for homogenisation in 3D. • Use of piece-wise polynomial functions on the surface of a polyhedral element. • Implementation of periodic boundary conditions in SBFE analysis. • Computation of homogenised material properties for piezoelectric composites. The determination of effective material properties of composites based on a three-dimensional representative volume element (RVE) is considered in this paper. The material variation in the RVE is defined based on the colour intensity in each voxel of an image which can be obtained from imaging techniques such as X-ray computed tomography (XCT) scans. The RVE is converted into a numerical model using hierarchical meshing based on octree decompositions. Each octree cell in the mesh is modelled as a scaled boundary polyhedral element, which only requires a surface discretisation on the polyhedron's boundary. The problem of hanging (incompatible) nodes – typically encountered when using the finite element method in conjunction with octree meshes – is circumvented by employing special transition elements. Two different types of boundary conditions (BCs) are used to obtain the homogenised material properties of various samples. The numerical results confirm that periodic BCs provide a better agreement with previously published results. The reason is attributed to the fact that the model based on the periodic BCs is not over-constrained as is the case for uniform displacement BCs. [ABSTRACT FROM AUTHOR]

• The field of temperature and heat flux are derived in SBFEM. • SBFEM is first used to solve heat transfer problems with cracks or inclusions. • Hybrid quadtree mesh is adopted without dealing with hanging nodes. • Only a single S-element is required on the crack tip. • The fiber inclusion problem can be solved expediently. In this paper, a hybrid quadtree mesh is utilized to solve two-dimensional transient heat conduction problems with cracks or inclusions. The current approach developed based on the scaled boundary finite element method (SBFEM) is able to alleviate the hanging node issues typically encountered in the conventional finite element method when using quadtree mesh. Moreover, the present method does not require fundamental solutions, unlike the boundary element method. The formulas of temperature and temperature gradient fields are derived systematically for the insulated crack and the inclusions of different materials with temperature and heat flux boundary conditions. Several examples are presented to demonstrate the validity and stability of SBFEM when solving models with complex geometry and cracks or inclusions. [ABSTRACT FROM AUTHOR]

A novel and effective approach within the framework of the scaled boundary finite element method (SBFEM) is proposed for the damage analysis of structures in three dimensions. The integral-type nonlocal model is extended to SBFEM to eliminate the mesh sensitivity concerning the strain localization. In order to reduce the number of degrees of freedoms (DOFs), an automatic mesh generation algorithm using octree decomposition is employed to refine the localized damage process zone (DPZ), but no extra effort is required to deal with hanging nodes existing between adjacent subdomains with different sizes. A double-notched tension beam is simulated with two different meshes to illustrate the mesh-independence. Three benchmarks are modelled to further verify the effectiveness and robustness of the proposed approach. It is shown that the proposed computational approach is capable of accurately capturing the damage evolution under complicated boundary conditions, and the results agree well with the experimental observations and prior numerical simulations reported in the literatures. [ABSTRACT FROM AUTHOR]

• A nonlocal approach is proposed for dynamic damage modelling by using SBFEM. • Multiphase domains are automatically meshed by image-based quadtree decomposition. • The computational efficiency is accelerated by utilizing the features of SBFEM. • The mesh dependence is well eliminated by using an integral-type nonlocal model. • Benchmarks demonstrate the efficiency, robustness and variability of this method. In this contribution, a nonlocal approach is proposed to model the dynamic damage of quasi-brittle composites within the framework of the scaled boundary finite element method (SBFEM). The image-based quadtree decomposition is used to automatically achieve multi-level mesh of a domain with geometric as well as material discontinuities. By enforcing a 2:1 balanced condition, only limited types of S-domains are used. Owning to the salient capability of the SBFEM in constructing polygons with arbitrary edges and nodes, there is no extra burden on dealing with hanging nodes between neighbouring S-domains in different sizes. Furthermore, the strain modes and the original stiffness matrix of each S-domain and the weighting matrix for nonlocal formulation are all pre-computed initially and extracted in subsequent time steps. Consequently, the computational efficiency of the proposed approach is considerably accelerated. The mesh dependence is well eliminated by using an integral-type nonlocal model. Several benchmarks are simulated to demonstrate the efficiency, robustness and variability of the proposed approach for macroscale and mesoscale problems. It is found that the proposed method can model multiple crack propagation and crack branching as well. Compared with the case under static load, the failure mode of quasi-brittle materials under dynamic load depends not only on the strength of each component but also on the propagation of stress wave. [ABSTRACT FROM AUTHOR]

Point-cloud-based geometry acquisition techniques have seen an increased deployment in recent years and can be used in many branches of science and engineering. Different from conventional computer aided design (CAD) models, point-cloud data can be directly obtained by applying surveying technology, such as laser scanning devices. This opens a pathway to an efficient and highly automatic acquisition of the geometric model. However, in order to perform numerical analysis on point-cloud models using conventional finite element approaches, a surface reconstruction is required, which is both time consuming and error-prone. Therefore, a direct numerical analysis framework based on point-cloud data in conjunction with polyhedral element techniques is developed in this contribution. To this end, a robust and efficient meshing paradigm based on the direct use of point-cloud data (without surface reconstruction) is proposed. From the geometric model, a trimmed octree mesh containing only a limited number of master elements (element patterns) is directly generated, which is highly suitable for pre-computation techniques and parallelization (high-performance computing–HPC). By computing the element stiffness and mass matrices from pre-computed master elements via scaling, a fully automatic HPC framework is developed. By means of six numerical examples, we demonstrate the robustness, versatility, and efficiency of the developed methodology in handling (geometrically) complex engineering problems. • Point cloud-based direct structural analysis of geometrically complex domains. • Automatic mesh generation (i.e., no user intervention) from point cloud models. • Highly efficient pre-computation technique based on octree discretizations. • Parallel explicit dynamic analysis exploiting octree element patterns. [ABSTRACT FROM AUTHOR]

This paper introduces an automatic way of performing 3D static and dynamic elastoplastic analyses in the framework of the scaled boundary finite element method (SBFEM), which only requires the boundary discretization and thus can provide high flexibility in automatic mesh generation. The input models in this paper are described by Standard Tessellation Language (STL) format due to its simplicity and popularity in computer-aided design. The automatic mesh generation from any input geometry is achieved by utilizing the octree decomposition algorithm and boundary trimming. An efficient approach for 2D static image-based elastoplastic analysis based on SBFEM is extended to 3D static and dynamic elastoplastic analyses in this present work. In this improved approach, the return mapping algorithm is only required to be performed at the scaling center of each subdomain in the yield zone. Constant elastoplastic constitutive matrix and internal stresses are used within each yielded subdomain as well. This will greatly simplify the implementation of elastoplastic formulation and reduce the costs involved in the elastoplastic analysis as the return mapping algorithm is computationally expensive. Meanwhile, stabilization matrix is also introduced in the elastoplastic stiffness matrix to eliminate the spurious modes. Numerical examples are presented in this paper to show the feasibility and accuracy of the proposed approach as well as its capability of modelling complex structures in practical applications. [ABSTRACT FROM AUTHOR]