A New Numerical Simulation Method for Three-Dimensional Mesoscale Analysis of Concretes

This paper presents a method for generating a region with a lot of randomly distributed ellipsoids. Using the parametric expression of an ellipsoid, the criterion for determining if a spatial point is in the interior or exterior of the ellipsoid is established. Then the computation of the distance between a point and the ellipsoid is converted into finding the solution to an optimization problem, which can be efficiently approximated by the searching method. Based on these facts, the proposed method is able to make the distance between generated ellipsoids very small and then successfully improve the content of ellipsoids grains in the region. Numerical results show that the proposed method can generate simulation of specimens in which the content of ellipsoids is higher than 55% according to four-graded aggregates, 50% according to three-graded aggregates, and 45% according to two-graded aggregates, respectively, in relatively short time.