- Lattice Geometry and the Structure of Cement and Concrete
In Chapters 2 and 3 we limited the discussion to situations where the material is assumed to be homogeneous and isotropic. If such a material is replaced by a lattice, the geometry of the lattice structure cannot be ignored because anisotropy may be introduced. The main question is now how can we simulate the behavior of real materials using a lattice model. Geomaterials such as concrete, rock, ice, clay, and so on all have a rather heterogeneous material structure. Other materials, such as metals and glass, are also heterogeneous, but at a much smaller size/scale. In normal continuum-based approaches the structure of the material is ignored and the average properties of the material are considered. For determining average properties it is important that a representative material volume is considered; that is, the volume has to be large enough. For small material volumes the scatter may become disproportionally large if the structure of the material is coarse. As an extreme example a dam concrete may be mentioned containing aggregates of up to 150-mm diameter. Obviously a sample volume of 100 mm3 would not sufªce. Every time a new sample is cut from a larger volume of material and the Young’s modulus is determined, the value may (in the extreme case) vary between the Young’s modulus of the matrix and that of the aggregate material, which may be a variation by a factor of 6 to 7 in the case of normal gravel concrete. For a better understanding of the situation it is necessary to discuss to some extent the material structure of concrete.