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

A quadtree-polygon scaled boundary finite element-based approach for image-based modelling of concrete fracture at the mesoscale is developed. Digital images representing the two-phase mesostructure of concrete, which comprises of coarse aggregates and mortar are either generated using a take-and-place algorithm with a user-defined aggregate volume ratio or obtained from X-ray computed tomography as an input. The digital images are automatically discretised for analysis by applying a balanced quadtree decomposition in combination with a smoothing operation. The scaled boundary finite element method is applied to model the constituents in the concrete mesostructure. A quadtree formulation within the framework of the scaled boundary finite element method is advantageous in that the displacement compatibility between the cells are automatically preserved even in the presence of hanging nodes. Moreover, the geometric flexibility of the scaled boundary finite element method facilitates the use of arbitrary sided polygons, allowing better representation of the aggregate boundaries. The computational burden is significantly reduced as there are only finite number of cell types in a balanced quadtree mesh. The cells in the mesh are connected to each other using cohesive interface elements with appropriate softening laws to model the fracture of the mesostructure. Parametric studies are carried out on concrete specimens subjected to uniaxial tension to investigate the effects of various parameters e.g. aggregate size distribution, porosity and aggregate volume ratio on the fracture of concrete at the meso-scale. Mesoscale fracture of concrete specimens obtained from X-ray computed tomography scans are carried out to demonstrate its feasibility

Approximate proper solutions in vector optimization with variable ordering structure

In this paper, we study approximate proper efficient (nondominated and minimal) solutions of vector optimization problems with variable ordering structures (VOSs). In vector optimization with VOS, the partial order-ing cone depends on the elements of the image set. Approximate proper efficient/nondominated/ minimal solutions are defined in different senses (Henig, Benson, and Borwein) for problems with VOSs from new stand-points. The relationships among the introduced notions are studied, and some scalarization approaches are developed to characterize these solutions. These scalarization results based on new functionals defined by elements from the dual cones are given. Moreover, some existing results are ad-dressed

Extending Lattice Discrete Particle Model of Concrete for Non-circular Aggregates

In this paper, Lattice-Discrete Particle Model (LDPM) of concrete has been extended in 2-D to account for the effect of non-circular aggregates. To this end, the flexible equation of super-ellipse is employed for generating aggregates in order to add the simulation possibility of a greater spectrum of aggregate samples in 2-D to lattice-Discrete particle Model. Alongside this extention, required procedures for the generation of aggregates, their packing in space, the determination of influencing region of each particle, the definition of interacting surfaces and computational points and the definition of strains are outlined. Finally, the effects of aggregates geometry on macro-scale compressive strength and softening curve and also cracking pattern of concrete under uniaxial compression are discussed