LIMITATIONS OF THE CONTINUUM ASSUMPTION IN CANCELLOUS BONE MECHANICS.

A fundamental, but rarely explicit, assumption made in all finite element analyses of natural synovial joints and their man-made replacements to date is that cancellous bone is a continuum. As a consequence, elastic moduli, yield criteria, volumetric density, stress, and strain are treated as continuum quantities without regard to whether these quantities are definable at a point. Continuum mechanics postualates a differential element which is large relative to intrinsic material dimensions. Hence in cancellous bone, where morphological dimensions can be 0. 5 mm in some regions, the validity of this assumption is open to serious question. However, little or no discussion of the limitations of this assumption has appeared in the biomechanics literature. This study establishes length scales over which the continuum assumption is valid in cancellous bone using the classical definition of continuum length and a new measure of microstructural orientation.