Paws, pads and plants: the enhanced elasticity of cell-filled load-bearing structures

Abstract

Paws, fat pads and plants share a remarkable structure made up of closed cells with elastic cell walls capable of supporting large loads and deformations. A key challenge is to understand how the function of these structures is enhanced by their geometric and material design. To do so, we compare different elastic models operating in large strain deformation when the cells are empty or filled with an incompressible liquid or solid core. We demonstrate theoretically, for three different cell geometries, that the elastic modulus in a direction associated with the change of curvature in the cell wall (i) is greater when the cell is filled; (ii) increases as the internal cell pressure increases; and (iii) increases also as the thickness of the cell wall increases or when the wall is multi-layer. As these results do not depend on the choice of the strain-energy function describing the cell-wall material, they are valid for a wide range of structures made from different elastic materials. For multiple cells deforming together due to external forces, the increase in elastic modulus of the cell walls under increasing core pressure is found numerically throughout the structure.