consideration, are no need and impossible to coincide with all the experiment curves well. These empirical constitutive equations give a good prediction of stress-strain curve along the mean variation tendency against density.
gripping method, precondition procedure, and selection of test machine and proper strain measurement method due to the observed crash pattern of specimen during testing. The corresponding mechanical properties were obtained, which is meaningful as these data are not much for cancellous bone in vertebral bodies of human cervical spine.
The mean properties as well as overall average stress-strain curves were obtained for the employed compression or tension specimens respectively, which showed higher modulus/failure stress and lower ultimate strain in compression than in tension. Meanwhile, the experimental measured properties appeared scatter among each individual specimen. There may be many factors caused the experimental data scatter, such as specimen location within spine and cadaver particulars.
Density is a key macro parameter that reflects the porosity properties of cellular materials. Discussion on density measurement method was described; and the fresh bone density, apparent bone density, bone tissue density as well as porosity ratio are obtained for cancellous bone in human cervical spine. In this study, the measured data were only regressed to bone density, and influences of other factors on bone properties are supposedly embedded potentially by its effects on bone density, such as old age may result in lower density than the young. For example, the average density (standard deviation) was (rF ¼1.2 (0.085) g/cc; rA¼0.64 (0.15) g/cc) for specimens from the 47 years old cadaver, and was (rF¼0.653 (0.181) g/cc;rA¼0.293 (0.078) g/cc) for specimens from the 69 years old cadaver in this study.
Power or linear relationship was used to fit the variation trend of modulus, ultimate stress and strain against densityrFand rArespectively; and power law fitting is preferred as it has theoretical basis. The results show modulus and ultimate stress of compression increases fast with density than that of tension; and only beyond a certain density the compression data become larger than tension and their discrepancy increases against density. The ultimate strain of tension is larger than compression and both seem independent of density. Linear regression to the stress-strain curves was presented for simplification;
however, in this study emphasis was put on the nonlinear characteristics for both compression and tension stress-strain.
The empirical nonlinear constitutive equations againstrFor rAwere constructed for either compression or tension, and showed good predictions for their nonlinearity till mean ultimate strain. As the ultimate tensile strain is quite scattered out of order, the model can not predict stress-strain curve till ultimate point well with each experimental result. These fitted equations and nonlinear models gave a way to predict the mechanical properties of cancellous bone in human cervical vertebral bodies along the main variation tendency against parameter of density, instead of coinciding exactly with each scatted experimental results of this bio-tissue.
References
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Table 16.1 Power/linear regression of modulus/ultimate stress and the nonlinear constitutive equations for compression and tension Fresh bone densityrF(g/cc) Apparent bone densityrA(g/cc)
Power fit Linear fit Power fit Linear fit
Elastic modulus (Mpa) Compression E¼211.12rF^1.891 E¼436.39rF194.91 E¼530.29rA^1.248 E¼580.29rA49.10 Tension E¼117.87rF^0.540 E¼62.12rF+ 59.43 E¼163.34rA^0.436 E¼49.30rA+ 73.79 Ultimate stress (Mpa) Compression su¼5.18rF^2.151 su¼12.09rF6.19 su¼14.89rA^1.433 su¼14.44rA1.24 Tension su¼4.63rF^1.038 su¼5.56rF0.65 su¼9.38rA^0.922 su¼10.12rA0.13 Nonlinear models Compression s¼(rF/1.0680)^2.151fmc(e) (e<2.5) s¼(rA/0.5589)^1.433fmc(e) (e<2.5)
Tension s¼(rF/0.8847)^1.038fmT(e) (e<5.3) s¼(rA/0.4174)^0.922fmT(e) (e<5.3) Note: Stress unit is Mpa and strian unit is %; fmc/fmTis polynomial equation of mean compression/tension stress-strain curve as indicated in Eq.16.2; Apparent density for tensile specimen is driven value, not measurement value
16 Quasi-static Compressive and Tensile Tests on Cancellous Bone in Human Cervical Spine 117
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118 J.F. Liu et al.
Chapter 17
Utilizing Digital Image Correlation to Capture Strains in Dental Applications
Bradley W. LaCroix, Peter G. Ifju, Karl J. Soderholm, and Saulo Geraldeli
Abstract The objective of this study was to explore the usefulness of digital image correlation in determining deformations in teeth induced during polymerization of a restorative material. The teeth were initially prepared and coated with a spray paint speckle pattern while the prepared cavities were protected with a silicone insert. Each tooth was then attached to a workbench configured with two digital cameras. Once the tooth was secured, a reference image was taken before filling the cavity. Then additional images were taken at each stage of restorative material insertion and curing. Post-processing of the images consisted of calculating the full-field displacement of the side of interest in each of the three coordinate directions of the tooth. Measurements showed that the cusp tips were displaced toward one another by 10–20 mm during resin polymerization. Post-cure shrinkage was also exhibited and documented here-within. The degree of accuracy of the camera set-up in the in-plane and out-of-plane direction was experimentally determined through rigorous testing and post-processing.
Keywords Didital image correlation • Dental • DIC • Dental applications • Dental restoration • Carity • Dental composite
• Polymerization • VIC • Tooth • Filling • Teeth