Faculty Bibliography

The influences of heterogeneity, anisotropy and geometric irregularity on the unrestrained, linearly elastic torsional response of long bones are assessed. Longitudinal geometric variations contribute insignificantly to the torsional response for typical long bone geometries. Anisotropy, heterogeneity and transverse geometric irregularity significantly influence the torsional response. A procedure is discussed which uses an approximate means to characterize both heterogeneity and anisotropy in predicting the torsional response. The accuracy of circular and elliptical annulus models of the bone cross-sectional geometry are assessed by comparing the stress predictions of these simple models to those of finite element models of the bone geometry.

A technique is established which allows an effective torsional shear modulus to be determined for long bones, while remaining nondestructive to whole bone specimens. Strain gages are bonded to the diaphysis of the bone. Strains are then recorded under pure torsional loads. Theoretical stress predictions are combined with experimental strain recordings to arrive at a modulus value. Shear modulus calculations for four canine radii are reported using theoretical stress predictions from circular, elliptical and finite element models of the transverse bone geometry. The effective shear modulus, obtained from an average of the shear moduli determined at strain gage locations, serves to average the heterogeneous shear modulus distribution over the cross section. The shear modulus obtained is that associated with the "circumferential" direction in transverse planes.