Effects of specimen load-bearing and free surface layers on the compressive mechanical properties of cellular materials.

The influence of load-bearing surface layers on Young's modulus was determined for cancellous bone and polyurethane foam specimens of three different heights cut from each material: 16, 9, and 5 mm for bone specimens (cross-sectional area A = 81 mm2) ranging in density from 0.04 to 0.32 g cm-3; 20, 10, and 5 mm for foam specimens (A = 100 mm2) ranging in density from 0.064 to 0.64 g cm-3. The compressive elastic modulus of the 5 mm bone specimens was significantly smaller (42%) than that of the 16 mm bone specimens. A similar change in elastic modulus was also observed for the foam specimens, but the height effect diminished in a relatively linear manner as the foam density increased. For a height change from 20 to 5 mm, the foam modulus difference ranged from a 41% decrease for the lowest density specimens (p = 0.064 g cm-3) to an insignificant change (< 1.8%) for the highest foam density specimens (p = 0.64 g cm-3). The specimen height effect on elastic modulus was hypothesized to result from a higher deformation (compliance) of the cellular materials in the load-bearing or contacting surface layer than in the bulk. A mathematical formula was derived to predict the variation in measured elastic modulus (E) caused by the contacting surface layer modulus (Ecs) to bulk modulus (Eb) ratio (Y = Ecs/Eb) and contacting surface layer height (hcs) to sample height (h) ratio (t = hcs/h): E/Eb = Y/[Y(1-t)+t]. Predicted differences in the measured modulus associated with graduated specimen heights were verified experimentally by regional strain measurements of the foam and bone samples using an optical microscope. The influence of free-surface layers was also determined for the foam specimens with cross-sectional areas 1.21 and 10 times the load-bearing area of a load platen, but the measured differences were small (< 10%) compared to that of the load-bearing surface layer influence. In future compressive mechanical testing of cellular materials, specimens < 10 mm in height should be avoided, particularly specimens with low bulk density or high porosity.