Cell Method modelling of complex structure materials

The Cell Method has been used to predict the behaviour of materials characterized by a complex structure, in which the spatial arrangement of the constituents determines the material mechanical properties. In industrial applications, microstructure heterogeneities can derive from the manufacturing process, as in sintered alloys. In other cases, as in injection moulded short fibre composites, the final mechanical properties depend on the resulting fibre pattern within the matrix. Unlike the Finite Elements (FEM) and other methods, the Cell Method is a numerical method based on a direct discrete formulation of equilibrium equations, so that no differential formulation is needed to write the balance equations. When approaching the analysis of complex structure materials, a relevant aspect in the FEM approach is that special elements and a very large number of degrees of freedom must be employed because of the discontinuities and large gradients encountered. One of the consequences of the Cell Method direct discrete approach is that no restriction is imposed by differentiability conditions so that the characteristic length of the elementary cell in the discretization may be of the same order of magnitude as the heterogeneities of the structure. Therefore, the Cell method appears to be particularly suitable to assess the mechanical behaviour of complex structure heterogeneous materials. In this paper, plane models in the elastic and plastic field have been applied to predict the behaviour of sintered alloys, showing a good agreement with experimental data, and 3D models of short glass fibre reinforced polyamide, in which micro-structures are identified by tomographic techniques, have been used to investigate the relationships between the morphological and elastic properties deriving from the complex fibre orientation patterns induced by the manufacturing process.