Discretization of Three-Dimensional Aggregate Particles

Abstract

The design of concrete with specified properties became of increasing importance with the wide use of high-performance concretes (HPCs), such as pumpable concrete or self compacting concrete (SCC). Many concrete properties, starting from the mechanical properties as the compressive strength and modulus of elasticity, over the rheological properties influencing the workability of fresh concrete, up to physical properties as diffusivity and thermal and electric conductivity, for example, can be assessed by appropriate computational model representing concrete as a multiscale random composite material with realistically described aggregates. However, incorporation of three dimensional aggregate particles into computational code requires their proper discretization. This is not straightforward due to rather difficult mathematical characterization of aggregate particles of random shape.

Modern technologies as computer tomography (CT) or magnetic resonance tomography (MRT) offer a powerful nondestructive technique for digital representation of opaque solid objects. This voxel based representation can be then discretized using for example marching cubes algorithm [1]. The resolution of the resulting triangulation, however, is strongly dependent on the resolution of the digital representation which might be either too coarse (without important features being captured) or too fine (with unimportant features captured by excessive number of elements).

In the present work, the digital representation is first used to derive a smooth representation of aggregate particle using the expansion into spherical harmonic functions [2]. Although this representation is not universal it is suitable for almost all aggregates used in structural concrete. The significant advantage of this approach is that resolution of the smooth representation can be flexibly controlled by the number of terms in the expansion. In the next phase, the surface of aggregate particle is subjected to discretization using the advancing front technique. Although the representation of the surface is parameterized (by two spherical angles), the actual triangulation is performed directly on the surface in the real space [3] and not in 2D parametric space with subsequent mapping to the real space. The advantage of this procedure consists in the fact that the anisotropic meshing of the parametric space as well as the demanding calculations related to the reparameterization or the inverse mapping are avoided.