DOI: 10.5061/dryad.2ngf1vhvr
title: Pneumatic elastostatics of multi-functional inflatable lattices: Realization of extreme specific stiffness with active modulation and deployability

description: Supplementary codes and data: Elastostatics of multi-functional inflatable
 lattices: Realization of extreme specific stiffness with active modulation
 and deployability
description: # **Pneumatic elastostatics of multi-functional inflatable lattices:
 Realization of extreme specific stiffness with active modulation and
 deployability** ***Descriptions of supplementary codes and data*** Note:
 The MATLAB files are hosted on Zenodo and the Excel files are on Dryad. *
 The Matlab code file E1_inflatable presents the variation in
 non-dimensionalized elastic moduli *E1/E* of hexagonal lattices with
 non-dimensionalized internal pressure *p/E*. It generates data for the
 Equation 24 of the paper which is then used to plot the Figure 5(A-D).
 Each subplot in Figure 5, i.e., Figure 5 (A-D) considers different
 combinations of cell configurations (i.e., different values of cell angle
 θ) for a particular value of *h/l*. * The Matlab code file
 E1_inflatable_rl presents the variation in non-dimensionalized elastic
 moduli *E1/E* of hexagonal lattices with non-dimensionalized internal
 pressure *p/E*. It generates data for the Equation 24 of the paper by
 considering different values of ratio of radius and length, i.e., *r/l*,
 which is then used to plot the Figure 5(E-F). The Figure 5(E-F) considers
 a particular value of *h/l* and cell angle θ. * The data set generated in
 the file E1.xlx corresponds to Figure 5A and the data set generated in the
 file E1_rl.xlx corresponds to Figure 5F. * The Matlab code file
 E2_inflatable presents the variation in non-dimensionalized elastic moduli
 *E2/E* of hexagonal lattices with non-dimensionalized internal pressure
 *p/E*. It generates data for the Equation 32 of the paper which is then
 used to plot the Figure 5(A-D). Each subplot in Figure 6, i.e., Figure 6
 (A-D) considers different combinations of cell configurations (i.e.,
 different values of cell angle θ) for a particular value of *h/l*. * The
 Matlab code file E2_inflatable_rl presents the variation in
 non-dimensionalized elastic moduli *E2/E* of hexagonal lattices with
 non-dimensionalized internal pressure *p/E*. It generates data for the
 Equation 32 of the paper by considering different values of ratio of
 radius and length, i.e., *r/l*, which is then used to plot the Figure
 6(E-F). The Figure 6(E-F) considers a particular value of *h/l* and cell
 angle θ. * The data set generated in the file E2.xlx corresponds to Figure
 6B and the data set generated in the file E2_rl.xlx corresponds to Figure
 6E. * The Matlab code file G12_inflatable presents the variation in
 non-dimensionalized elastic moduli *G12/E* of hexagonal lattices with
 non-dimensionalised internal pressure *p/E*. It generates data for the
 Equation 53 of the paper which is then used to plot the Figure 5(A-D).
 Each subplot in Figure 7, i.e., Figure 7 (A-D) considers different
 combinations of cell configurations (i.e., different values of cell angle
 θ) for a particular value of *h/l*. * The Matlab code file
 G12_inflatable_rl presents the variation in non-dimensionalized elastic
 moduli *G12/E* of hexagonal lattices with non-dimensionalized internal
 pressure *p/E*. It generates data for the Equation 53 of the paper by
 considering different values of ratio of radius and length, i.e., *r/l*,
 which is then used to plot the Figure 7(E-F). The Figure 7(E-F) considers
 a particular value of *h/l* and cell angle θ. * The data set generated in
 the file G12.xlx corresponds to Figure 7C and the data set generated in
 the file G12_rl.xlx corresponds to Figure 7E. * The Matlab code files
 E1_inflatable_reldensity and G12_inflatable_reldensity present the
 variation of the ratio of the elastic moduli and relative density with
 internal pressure, (as shown in Figure 8 of the paper), at different
 values of *r/l* along with the variation of *t/l* ratio, with the
 assumption of thin honeycomb cell walls (*t/l* ~
 ![](file:///C:/Users/mukho/AppData/Local/Temp/msohtmlclip1/01/clip_image002.png)).  The Figure shows that the specific properties of the inflatable structures are quite high and the stiffness by weight ratio for inflatable beams can increase up to a thousand times when compared with that of solid circular beams. The Matlab code E1_inflatable_reldensity is used to plot the Figure 8 (A-B) and the Matlab code G12_inflatable_reldensity is used to plot the Figure 8 (C-D) by considering different values of ratio of radius and length, i.e., *r/l* for a particular value of *t/l*. The results are presented in non-dimensional forms considering (*E1*/*ρ*) / ![](file:///C:/Users/mukho/AppData/Local/Temp/msohtmlclip1/01/clip_image004.png), (*E2/ρ*) / ![](file:///C:/Users/mukho/AppData/Local/Temp/msohtmlclip1/01/clip_image006.png) and (*G12*/*ρ*) / ![](file:///C:/Users/mukho/AppData/Local/Temp/msohtmlclip1/01/clip_image008.png) for the elastic moduli and *p/E* for the internal pressure. In the Figure, the subscript *s* denotes the properties that correspond to that of a solid circular beam. * The data set generated in the file E1_reldensity.xlx corresponds to Figure 8A and the data set generated in the file G12_reldensity.xlx corresponds to Figure 8D. ***Descriptions of the figures mentioned above:*** * Figure 5: Longitudinal effective Young's modulus for hexagonal inflatable lattices under the influence of air pressure. * Figure 6: Transverse effective Young's modulus for hexagonal inflatable lattices under the influence of air pressure. * Figure 7: In-plane effective shear modulus for hexagonal inflatable lattices under the influence of air pressure. * Figure 8: Comparative assessment of specific elastic properties of inflatable lattices with respect to conventional solid lattices. (Note: For further details regarding the above figures, please refer to the paper titled: Pneumatic elastostatics of multi-functional inflatable lattices: Realization of extreme specific stiffness with active modulation and deployability)