Homogenization Analysis Model for Granule System by Introducing Shape Parameters
The macroscopic static analysis of granule system performance in Literature  considered the position, direction and scale of the connection between granules in the system and other relevant physical properties. Taylor linear expansion was adopted to analyze the geometric displacement of the connection formed by granules. However, for the more complex granular connection in the form of network, the geometric position of granular connection in the statistical domain is linearly approximated, which may result in considerable calculation errors. In the complex network structure formed by granular connection, the displacement of connectors is discrete and discontinuous. In the presence of certain interactions among granular connections, there is the possibility to form spatial granular chain, with increased heterogeneity of deformation in the statistical domain. The accuracy of analysis will be affected if linear approximation is adopted. Shape parameter-based method proposed in this paper is a more universal method, which considers the influence of both the parameter of geometric location distribution of connectors and structural morphology of networks formed by granules. The core idea of this method is to introduce a corrected shape parameter vector for the non-linear part on the basis of linear approximation, to correct the displacement of connectors in geometric space so that the original linear analysis will better adapt to non-linear problems such as the network of connection formed by granules.
Jimmy (C.M.) Kao, Wen-Pei Sung and Ran Chen
Z. H. Wei et al., "Homogenization Analysis Model for Granule System by Introducing Shape Parameters", Advanced Materials Research, Vols. 581-582, pp. 632-640, 2012