Mesoscopic Homogenization And Cohesive Fracture Modelling Of Concrete Using SBFEM

As a heterogeneous, multiphasic composite material, concrete is composed of mortar, aggregate and pores. Its macroscopic mechanical properties and damage and fracture behavior are dependent upon random distribution, material properties, interfacial properties of these phases at micro/meso-scale. The difficulty in conducting experiments makes numerical simulations an important method for micro/mesoscopic mechanical research on concrete.The scaled boundary finite-element method (SBFEM) is a relatively new semi-analytical numerical method combining the advantages of both boundary element method (BEM) and finite element method (FEM). In the SBFEM, a domain is divided into several subdomains/polygons, and only boundaries of these subdomains are discretized so that the modelled spatial dimensions are reduced by one as the BEM with significant reduction in the degree of freedom; and no fundamental solutions are needed as the FEM. Moreover, the accuracy of results is guaranteed by the semi-analytical nature of displacement and stress fields inside the subdomains.In this study, two numerical algorithms based on the SBFEM and the random aggregate generation approach are developed considering the geometric characteristic of concrete meso-structures. The meso-models with randomly distributed aggregate and pores are first generated. The mortar is then triangularised using the Delaunay algorithm followed by Thiessen polygonisation, so that both the mortar and aggregates are modelled by SBFEM polygons. The resultant models are used for homogenization analysis. As the SBFEM polygons are much fewer than elements in FEM and the mean stress is analytically integrated along the radial direction in each polygon. This algorithm has much higher efficiency as well as accuracy than FEM. It is successfully implemented in MATLAB and validated by comparison with results from ABAQUS. In the second algorithm, the mortar is modelled by finite elements and the aggregates by SBFEM polygon. Cohesive interface elements are pre-inserted inside the mortar elements and on the mortar-aggregates interfaces, to model complicated nonlinear fracture in concrete. Compared with FEM, this algorithm used much fewer degrees of freedom with lower computational costs because only the boundaries of aggregates are discretized.