Compression induced intercellular shaping for some geometric cellular lattices

Abstract

The wall perimeter fraction, which contact neighboring cells, was named compression ratio (alpha). A zero compression ratio indicates maximum intercellular (air) volume (vG, v/v) and neglectable contact among cells, while alpha=1 indicates complete adherence between neighboring cells and no vG in the lattice. The maximum intercellular air volume (beta, v/v), when alpha=0, was 0.593 for triangular, 0.2146 for square and 0,0931 for hexagonal lattices. The equation alpha=1- (vG/beta)½ was derived to relate alpha, beta and vG in the studied lattices. The relation (P S=p/alpha) between cell turgor (P S) and the tissue aggregating pressure (p), defined as the compression to keep in place a layer of cells, was demonstrated using the compression ratio concept. Intercellular deformations of Ipomea batatas L. roots obtained with pressure chamber were used to test alpha, vG, p and P S as a function of compression. Volumetric and transversal elastic extensibilities and the lamella media tearing forces were obtained and alpha constancy was considered as a criteria of cellular shape stability.