Young’s modulus of 2D cellular structures under periodic boundary conditions and subject to structural effects

Two-dimensional random cellular structures are generated by coupling Voronoi and Monte Carlo algorithms in order to study the effect of cell irregularities on the elasticity parameters of biopolymer cellular solids. Firstly, the Voronoi technique provides the tessellation of the 2D space without producing discontinuities. Secondly, Monte Carlo strategy allows cell curvature to be generated. The Voronoi/Monte Carlo technique is able to represent various structural effects: cell density, elongation, local concentration as well as cell gradient and presence of defects. These effects are discussed in this paper based on the theory of cellular solids and finite element calculation. These numerical results should provide quantitatively correlations between the studied structural effects and effective properties of several natural biopolymer systems.