Validation and Investigation on the Mechanical Behavior of Concrete Using a Novel 3D Mesoscale Method

The mechanical performance of concrete is strongly influenced by the geometry and properties of its components (namely aggregate, mortar, and Interfacial Transitional Zone (ITZ)) from the mesoscale viewpoint, and analyzing the material at that level should be a powerful tool for understanding macroscopic behavior. In this paper, a simple and highly efficient method is proposed for constructing realistic mesostructures of concrete. A shrinking process based on 3D Voronoi tessellation was employed to generate aggregates with random polyhedron and grading size, and reversely, an extending procedure was applied for ITZ generation. 3D mesoscale numerical simulation was conducted under a quasi-static load using an implicit solver which demonstrated the good robustness and feasibility of the presented model. The simulated results resembled favorably the corresponding experiments both in stress–strain curves and failure modes. Damage evolution analysis showed that the ITZ phase has profound influence on the damage behavior of concrete as damage initially develops from here and propagates to mortar. In addition, it was found that tensile damage is the principal factor of mortar failure while compressive damage is the principal factor of ITZ failure under compression.

Environmental density of galaxies from SDSS via Voronoi tessellation

The aim of our work was to determine the environmental density of galaxies from SDSS DR9 using the Voronoi tessellation. We constructed the 3D Voronoi tessellation for the volume-limited galaxy sample within 0.02 <z<0.1 and -24 Mr-20.7 using an inverse volume of Voronoi cell as a parameter describing the local environmental density of a galaxy. It allowed us to inspect the morphology - density relation. We obtained that the early type galaxies prefer to reside in the Voronoi cells of smaller volumes (i.e. dense environments) than the late type galaxies, which are located in the larger Voronoi cells (i.e. sparse environments).

Applying and Practicing of MATLAB Programing for Voronoi Tessellation

Three-dimensional (3D) Voronoi tessellation diagrams are generated by compiling program in MATLAB software. According to these 3D Voronoi cells, crystal structure, even the disorder structure, can be geometrically described and tessellated into the regular object, reflecting the atomic structural parameters, such as the coordination numbers (CN) and the atomic separation. Studying the characteristic of these tessellations, we can find the rule of atomic packing in real space. This Voronoi diagram is also useful in materials structure teaching curriculum and it is the significant basis to realized the atomic structure of the materials. By programing with MATLAB, the abstract concept of Voronoi tessellation are transformed into the lively and understandable computer animation, which can be easily recognized and mastered.