An analytical model of an elementary elliptical cell forming an alveolar elastic material under plane stress

Abstract

This paper analyzes the static behavior of alveoled materials that is about to be developed for dynamic optimization of structural panels. It deals precisely with materials made of elliptical thin cells, filled with polymer material. The main contribution of the paperconsists in elaborating an analytical approach describing the material. The considered problem represents an unidirectional stress, the goal being to calculate the elastic energy and strain globally obtained in the material. The wall of the elementary cell is represented in accordance with the classical BRESSE's theory of thin beams, with specific adaptation for elliptical shape. The polymer material filling the cell is modelized with ABSI!s method of equivalence, which allows a direct approximation of various continuous media by equivalent spring segments. This method is presented and discussed for the present configuration, with its specific adaptation. The final result obtained by these analytical approaches is then compared to results from a finite element model. In spite of local differences between the analytical results and numerical computation, it appears clearly that the precision obtained by the proposed analytical approach is better than 95%, which is sufficient for this kind of material. Thus, the proposed analytical calculation and methodology allows robust and quick determination of material characteristics for elementary cells of such alveoled materials. The resulting laws can then be introduced into global models of a grid of cells.