Deformability and strength of compact bone tissue during tensioning

The deformability and strength characteristics of compact bone tissue of human tibia during tensioning along all three main anisotropy axes was determined experimentally. The character of change in the secant moduli of elasticity and specific energies of deformation during the loading process were studied. A correlation was established between the mechanical characteristics and the biochemical composition of the bone tissue.     

Degree of deformation and strength of compact bone tissue during torsion

This paper discusses the variation in the deformation and strength properties of compact bone tissue during torsion in various zones of the cross section of human tibia. A correlation has been found between the specific energy of deformation consumed during the loading process and the level of stress attained. The degree of correlation between the deformation and strength properties of the bone tissue has been studied as a function of the concentration of certain biochemical substances in its composition.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No.5, pp. 911–918, September–October, 1973.     

Lateral strain coefficients of human compact bone tissue

The values of all the lateral strain coefficients of the compact bone tissue of the human tibia have been experimentally determined. The variation of these coefficients in six zones of the cross section have been studied at various stress levels, including the ultimate strengths in the corresponding directions. It has been established that the bone tissue possesses orthotropy of the elastic properties. The change in the volume of the bone tissue during deformation has been studied. The bulk moduli for both uniaxial and hydrostatic loading have been determined. A bulk deformation parameter characterizing the strain energy expended in producing a volume change of 100% is introduced. The coefficients of the rank correlation between the lateral strain coefficients and bulk moduli, on the one hand, and the concentrations of a number of biochemical substances found in bone tissue, on the other, are analyzed.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 6, pp. 1089–1100, November–December, 1973.     

Experimental determination of the shear modulus of compact bone tissue

Various methods of experimentally determining the shear moduli G₁₂, G₁₃, and G₂₃ of compact human bone tissue have been examined. The results of the study confirm the previous view that compact tissue has properties similar to those of a transversally isotropic material. It has been established that the shear modulus along the diaphysis of the tibia at the level of girdles 9–24 does not change significantly. There is a definite difference in the rigidity characteristics with respect to the regions of the cross section. The highest values for the shear modulus were established in the angle regions of the cross section. There is a linear dependence of the shear stress ₁₂ on the torsional angle ₁ within the experimental range of stresses (₁₂90 kg/cm²).Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 4, pp. 697–705, July–August, 1972.     

Deformation properties of demineralized human compact bone tissue upon stretching

Conclusions 1. Demineralized human compact bone is a physically nonlinear material with a nonuniform distribution of deformation parameters over the bone cross section.2. At the initial moment of stressing (₁₁=0), the modulus of elasticity of demineralized tissue is 380 times less than that of normal tissue. The minimum value of this parameter is in zone 6 (3.32 kgf/mm²) and the maximum value is in zone 1 (7.12 kgf/mm²). With increasing stress, the tangential modulus of elasticity increases.3. The specific energy of deformation under the same stressing conditions ₁₁/*₁₁ expended is greater for demineralized bone than for normal bone.4. The parameter of cross-sectional deformation ₁₂ upon stressing (at ₁₁/*₁₁ from 0.1 to 0.3) increases for demineralized tissue by a factor of 1.56, while for normal tissue this increase is only by a factor of 1.01. The average values of ₁₂ ^0·1 and ₁₂ ^0·3 for demineralized tissue are 3.3 and 2.2 times, respectively, higher than for normal tissue.5. The greatest correlations for the deformation parameters were found between the internal and external layers of the cross-sectional zones for E ₁ ⁰ (0.94) and ₁₂ ^0·3 (0.87), though the discrepancies in the zones between the internal and external layers are insignificant (p>0.05).6. The changes in the deformation parameters over the cross section have a positive correlation (with the exception of U ₁ ^0.3 ) with the amount of ground substance in normal tissue (determined relative to hexosamine).7. The deformation parameters of demineralized tissue may be described by a multi-dimensional linear equation using quantitative indices of the major biochemical components (hydroxyproline, phosphorus, and hexosamine) of normal tissue, which characterize the amounts of collagen, mineral substance, and ground substance, respectively.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 1, pp. 101–108, January–February, 1978.     

Change in the mechanical properties of human compact bone tissue upon aging

The ultimate tensile strength σ_z, elastic modulus E, maximum deformation ?, and Brinell hardness H_B of human compact bone tissue were determined. The contents of the minerals calcium and phosphorus, nitrogen, and water (relative to mass and volume), as well as the density were studied in the same bone samples. It was found that all the characteristics studied changed with increasing age. It is emphasized that various types of destructive mechanisms are characteristics of different ages.     

Effect of moisture content on the microdeformation of compact bone tissue in tension

Conclusions The x-ray diffraction results indicate the following major features for the microdeformation of bone tissue. The total deformation in the elastic region is determined by the microdeformation of the mineral bone tissue component. The large yield of the mineral component indicates its relatively low elasticity modulus. The shape of the deformation curves for both dry and moist bone tissue is a factor of the combined deformation of the mineral and organic components. While the total deformation up to fracture in dry bone tissue is determined largely by microdeformation of the crystalline mineral phase, such behavior is found for moist bone tissue only in the first segment of the curve. Deformation in the second, more curved segment of the deformation curve is a factor largely of deformation of the organic bone-tissue component.Translated from Mekhanika Kompozitnykh Materialov, No. 3, pp. 530–535, May–June, 1983.     

Effect of the rate of deformation on the mechanical properties of compact bone tissue

Conclusions The results of this study show that the ultimate stress increases with increasing deformation rate from 10^–5 to 1 sec^–1 but the initial elasticity modulus remains virtually constant. A characteristic feature of bone tissue is the significant increase or even maximum in specific deformation energy for destruction in the range of deformation rates corresponding to normal physiological conditions for bone function. The deformation diagrams of human bone tissue for the same values of moisture content and deformation rate in tensile testing do not differ from the analogous curves for the bone tissue of cattle. Quantitatively, the ultimate stress ₁₁ and the initial elasticity modulus E₁ are 5–10% and 15–25% greater, respectively, than for cattle bone tissue, while the ultimate deformation eu is virtually the same. An increase in the moisture content of bone tissue leads to a more pronounced dependence of the mechanical parameters on the deformation rate.Translated from Mekhanika Kompozitnykh Materialov, No. 3, pp. 512–517, May–June, 1982.     

Variation of certain mechanical properties of human compact bone tissue with age

The nature of the variation of the moduli of elasticity, shear moduli, and flexural and torsional decrements of human compact bone tissue during biological aging has been investigated. It has been found that the moduli of elasticity and shear moduli increase sharply up to age 20–25 and then progressively fall; the distribution of the modulus of elasticity over the individual zones of the cross section of the tibia changes significantly with age. By investigating the changes in the logarithmic decrements by nondestructive methods it is possible to estimate the changes in the mechanical and structural properties of the bone.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 5, pp. 885–891, September–October, 1974.