Expansion behavior of cellular solids

The expansion behavior of cellular materials is especially attractive for potential applications such as design and development of bio-inspired adaptive materials since most of biological materials have a cellular microstructure at least at one of their hierarchical levels. Wood, bone, bamboo, ice plant and honeybee combs are examples of such natural materials.

The thermal expansion or hygro-expansion (sometimes referred to as swelling coefficient) of cellular solids are not studied to the same extent as mechanical properties such as elastic behavior, strength, buckling, etc. Lakes and co-workers proposed different configurations of cellular materials with extreme thermal expansions. These models are mainly composed of bi-layer cell walls with contrasting expansion ratio which induces a non-affine deformation in the structure under uniform temperature increase. Inspiring from anisotropic swelling behavior of wood cells, we recently investigated with finite element based homogenization the effective (hygro-)expansion of honeycombs and some interesting trends are captured:

http://dx.doi.org/10.1016/j.compstruct.2012.08.017

http://dx.doi.org/10.1016/j.mechmat.2012.08.002

The degree of anisotropy is dependent on the geometry and also the material properties of the cell wall. We can control the anisotropic expansion of cellular materials by tuning the material properties of the cell wall which is promising for stimuli-responsive actuation devices. The cell walls might be intrinsically anisotropic or composed of different isotropic layers with contrasting expansion behavior.

So far, similar to those relations proposed by Ashby and Gibson for elastic moduli of honeycombs and other cellular solids are not available for thermal or hygro-expansion coefficients. Development of analytical models will enable us to improve our understanding of the expansion behavior of cellular solids.