Reconstruction of structure of planar dispersions

The simulated annealing procedure is used to reconstruct the positions of continuous fibres as observed on transverse cross sections of a composite. The modified concept of a pair correlation function is used to define the objective function, which is identified as a sum of squared differences of nodal points of integral correlation function for a reference and optimised pattern. The optimisation process is subject to two constraints. The geometrical constraint of topological entropy introduces a measure of arbitrariness of the polygonal tessellation associated with the point pattern of fibre centres. The second constraint is related to maximal radial stresses calculated at the fibres interfaces. This constraint is expressed in terms of angular positions and distances from the reference fibre to its nearest neighbours. Thus the screening effect and local interactions are taken into account. The results show that reconstructed families of the fibres dispersion resemble the reference pattern and therefore can be used for a further analysis to describe overall properties of the underlying composite material. Financed by Statens Teknisk-Videnskabelige Forskningsråds Rammeprogram Structurally Graded Polymeric Materials.... (Bogdan Bochenek, Ryszard Pyrz)