Efficient meso-scale homogenisation and statistical size effect analysis of concrete modelled by scaled boundary finite element polygons

A Brief Review on Polygonal/Polyhedral Finite Element Methods

“…Various applications of PSBFEM can be seen in literature such as in linear elasticity [83], crack propagation [84][85][86][87][88], applications within geotechnical structures [89], dynamic fracture simulation [90], analysis of cracked functionally graded materials [91], polygonal mesh creation , elastoplastic analysis of structures [92], prediction of structural responses with randomly distributed material properties [93], simulation of crack surface contact problems 8 Mathematical Problems in Engineering [94], and analysis of mesoscale concrete samples [95]. Extension of the method to 3D can be seen in the literature [96][97][98].…”

A comparative study of numerical approaches for the computation of effective properties of micro‐heterogeneous materials

“…Moreover, QT meshes can be created automatically from digital images and converted into SBFE models following an approach presented in [1]. According to [2], the volume-averaged stress is expressed using SBFEM in 2D as in Eq. (1), where the constants c i , eigenvalues λ i and stress modes Ψ σi result from the semi-analytical solution procedure of the SBFEM.…”

A quadtree-polygon-based scaled boundary finite element method for image-based mesoscale fracture modelling in concrete

“…A mesh fragmentation process is then applied so that zero-thickness interface elements can be inserted along the cell boundaries. This approach diers from that developed by Huang et al [17] and Wang et al [49] in which a single SBFEM is employed to discretise the aggregates whereas the mortar is discretised with standard nite elements [17] or polygonal scaled boundary nite elements [49]. Instead, a quadtree decomposition in combination with polygon meshes within the framework of the SBFEM [26] is adopted.…”