Compression induced intercellular shaping for some geometric cellular lattices

Abstract

The wall perimeter fraction, which contact neighboring cells, was named compression ratio (a). A zero compression ratio indicates maximum intercellular (air) volume (vc, v/v) and neglectable contact among cells, while a=l indicates complete adherence behveen neighboring cells and no VG in the lattice. The maximum intercellular air volume (β, v/v), when a=0, was 0.593 for triangular, 0.2146 for square and 0,0931 for hexagonal lattices. The equation a=l- (vc/β)1/2 was derived to relate α, β and VG in the studied lattices. The relation (Ps=p/cc) between cell turgor (PS) 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 oflpomea batatas L. roots obtained with pressure chamber were used to test α, VG, p and PS as a function of compression. Volumetric and transversal elastic extensibilities and the lamella media tearing forces were obtained and a constancy was considered as a criteria of cellular shape stability.