**Bridging the gap between
random microstructure and 3-D meshing **

__Yang
Lu__ and Edward J.
Garboczi

There are different ways of mathematically representing 3-D heterogeneous material structures. But for each of these methods, usually the desired end result is a 3-D finite element mesh that will be used to investigate the mechanical properties of the material, including fracture. This paper focuses on concrete composed of a matrix of cement paste (hydrated cement) and sand and gravel inclusions (aggregates). However, the methods presented are effective for more general random composite materials. The mathematical representations of heterogeneous material structure considered here include 3-D digital image models, exemplified by the Virtual Cement and Concrete Testing Laboratory (VCCTL), X-ray computed tomography (CT) images stacked into a 3-D digital image, and real-shaped sand and gravel particles, represented by spherical harmonic series, randomly placed into a 3-D box to make a virtual concrete model. 3-D cubic meshes of brick (voxel) elements can already be generated for the X-ray CT structures, but this work describes how optimized meshes, more suitable for complex mechanical problems, including crack generation, can be implemented. The approach used involves the definition of a topological structure suitable for Stereo Lithography file (STL) representation and the development of algorithms for topology and geometry data processing in order to obtain a 3-D optimized mesh that incorporates the random material structure. Mesh optimization is obtained through a set of re-meshing tools. Non-manifold assembly technology is utilized to obtain matching surfaces between the aggregates and the paste. During the mesh generation procedure, we combine both the aggregates and the cement paste matrix to ensure perfectly coinciding nodes at their interface. Based on the proposed procedures, the complex geometries of heterogeneous systems can be generated with data consistencies (e.g. no overlapping, no gap at the interfaces), thus bridging the gap between heterogeneous microstructure and computer-aided engineering finite element analysis.