Quantifying the Accuracy of Euler-Bernoulli and Timoshenko Beam Theories for Long Bones in Three- and Four-Point Bend Tests with Finite Element Analysis
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Authors
Zojaji, Mahsa
Date
Type
thesis
Language
eng
Keyword
Bone Flexural Rigidity , Bone Stiffness , Biomechanics , Bone , Timoshenko Beam Theory , Euler-Bernoulli Beam Theory
Alternative Title
Abstract
Mechanical assessment of long bones is of importance for predicting the risk of fracture in bone diseases such as osteoporosis. These assessments are applied in pre-clinical research to assess the efficacy of osteoporosis treatments. Biomechanical methods used in bone mechanical assessments include mechanical testing and image-based finite element analysis (FEA). Euler-Bernoulli (EB) beam theory is commonly used to estimate the elastic modulus of bone from three- and four-point bend tests. However, the assumptions of EB lead to the underestimation of elastic modulus. In this study, I hypothesized that Timoshenko (TI) beam theory could be used to predict bone surrogate flexural rigidity (EI) more accurately than EB. I used a bone surrogate of the porcine femur to avoid errors due to the misassumption of homogeneity and linearity of material properties. Therefore, I was able to quantify the magnitudes of error associated with applying EB and TI beam theories to EI predictions from mechanical testing and computer-aided design (CAD)-and computed tomography (CT)-based FEAs. I employed the digital image correlation (DIC) method to validate the results from FEAs and a good agreement was found between the results from DIC and FE models. In four-point bend tests, using TI instead of EB beam theory decreased the error of stiffness measurements from machine crosshead displacement from -33% to -24%. TI beam theory provided an accurate estimation of EI from DIC measurements with only a 1% error. The errors associated with employing EB beam theory in flexural rigidity calculations were -58% to -49% from machine crosshead measurements, in three- and four-point bend tests, respectively. The results of this study found that the TI beam theory reduced the error of EI estimation from machine crosshead displacement to -41% to -16% in three- and four-point bend tests, respectively. The bland-Altman analysis found a bias in EI between EB and TI beam theories varied from 34% to 64% using different deflection measurements. Therefore, stiffness and flexural rigidity cannot be compared across the different methods of measurement. Despite some limitations of this study such as the sample size and simplicity of the bone surrogate geometry and mechanical properties, I showed that TI improves the estimation of bone stiffness and flexural rigidity in three- and four-point bend tests.
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ProQuest PhD and Master's Theses International Dissemination Agreement
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Copying and Preserving Your Thesis
This publication is made available by the authority of the copyright owner solely for the purpose of private study and research and may not be copied or reproduced except as permitted by the copyright laws without written authority from the copyright owner.
Attribution-ShareAlike 3.0 United States