The behaviour of ceramics, and more generally of brittle materials, depends strongly upon the microstructural features that determine the initiation and propagation of cracks. Therefore, the generation of numerical models representative of real microstructures, necessary for the correct simulation of the micromechanics, is of fundamental importance for modelling the macroscopic behaviour of the material.
The work presented illustrates the implementation of the algorithm for the generation of numerical models statistically representative of a wide range of polycrystalline materials, recently integrated into the commercial software LS-PrePost.
The algorithm, based on the Laguerre-Voronoi tessellation, provides a high level of control over the grain size distribution by introducing the definition of “weight” of each cell. The versatility of the formulation, obtained by increasing the number of degrees of freedom (i.e. weights), however, comes at the cost of a non-univocal relationship between cells and nuclei. To avoid the occurrence of degenerated tessellations, a conditioning method to assign values of weight that allows an accurate reproduction of the desired microstructural topology is implemented.
The algorithm allows the discretisation of the tessellation with hexahedral finite elements (i.e. structured mesh), with the possibility to insert cohesive interfaces (e.g. elements, contacts) along the grain boundaries, thus providing the capability to simulate crack initiation and propagation within the microstructure.
Examples of possible applications of the models generated to simulate the behaviour of ceramic materials under different loading conditions, combining both inelastic deformation and crack propagation mechanism at the grain scale, are presented.
Finally, the potentiality of the use of algorithm to model macroscopic structures within a more generic (hierarchical or concurrent) multiscale approach are illustrated.