Determination of the Modulus of Elasticity by Bending Tests of Specimens with Nonuniform Cross Section

Abstract

BackgroundBending tests offer technical advantages when material testing is performed to determine the modulus of elasticity. In biomechanical studies, beam-like cortical bone specimens subjected to flexural loading are usually characterized by nonuniform cross-sectional properties along the beam axis and a comparatively large spatial variation of the local material properties.ObjectiveA suitable evaluation method for determining the average modulus of elasticity within the volume of beam-like specimens with nonuniform cross section was to be identified.MethodsA total of 138 samples of human pelvic cortical bone were extracted and tested under flexural loading. Different methods, all based on the linear-elastic flexural theory of beams, were applied to determine the average modulus of elasticity on the basis of measured deformations, and the results were compared. Some of these methods utilized the measured midspan deflection, and others used the elastic curve obtained by digital image correlation.ResultsThe results showed that it was not appropriate to determine the average modulus of elasticity from only the measured midspan deflection. The consideration of deflections at multiple points along the beam axis is recommended.ConclusionsAn evaluation method based on the fitting of the analytically determined elastic curve of the beam with its nonuniform cross-sectional properties to the measured deflections is considered the most appropriate method for determining the average modulus of elasticity of the specimen.