Elastic modulus

About: Elastic modulus is a research topic. Over the lifetime, 33153 publications have been published within this topic receiving 810247 citations.

Bending elasticity and thermal fluctuations of lipid membranes. Theoretical and experimental requirements

Abstract: Thermal fluctuations of giant lipid vesicles have been investigated both theoretically and experimentally. At the theoretical level, the model developed here takes explicitly into account the conservation of vesicle volume and membrane area. Under these conditions, the amplitude of thermal fluctuations depends critically not only on the bending elasticity of the bilayer, but also on the membrane tension and/or hydrostatic pressure difference between the interior and exterior of the vesicle. At the experimental level, the determination of the bending modulus kc first requires the analysis of a large number (several hundred) of vesicle contours to obtain a significant statistics. Secondly, the contribution of the experimental error on the contour coordinates, which results in a white noise on the Fourier amplitudes, must be eliminated, and this can be done by using the angular autocorrelation function of the fluctuations. Finally, the amplitudes of harmonics having short correlation times must be corrected from the effect of the integration time (40 ms) of the video camera, which otherwise leads to an overestimation of kc. All these theoretical and experimental requirements have been considered in the analysis of the thermal fluctuations of 42 giant vesicles composed of egg phosphatidylcholine. The behaviour of this population of vesicles can be accounted for with a bending modulus kc equal to 0.4 - 0.5 x 10-19 J, and extremely low membrane tensions, ranging below 15 × 10-5 mN/m.

Effects of drying on the mechanical properties of bovine femur measured by nanoindentation.

Abstract: Effects of drying on the measurement of mechanical properties of bone by nanoindentation methods have been examined. Tests were conducted to measure the elastic modulus and hardness of two cross-sectional cortical specimens obtained from adjacent areas of bovine femur. One specimen was thoroughly dried in air prior to testing while the other was stored in deionized water. The properties of osteons and interstitial lamellae showed statistically significant differences (plt; 0.0001) and were therefore investigated separately. Drying was found to increase the elastic modulus by 9.7% for interstitial lamellae and 15.4% for osteons. The hardness was also found to increase by 12.2% for interstitial lamellae and 17.6% for osteons.

Polymeric-hydroxyapatite bone composite

Abstract: A method for the fabrication of three-dimensional macroporous polymer matrices for use as bone graft or implant material was developed. The composites are formed from a mixture of biodegradable, biocompatible polymer and hydroxyapatite (HA), a particulate calcium phosphate ceramic. The method leaves irregular pores in the composite between 100 and 250 microns in size. In a preferred embodiment, implants are composed of a 50:50 poly(lactide-co-glycolide) (PLGA) polymer and reinforced by hydroxyapatite. Mechanical and histological analysis showed the matrix fabricated by this method to be structurally and mechanically similar to cancellous bone. Prior to degradation, pure polymer specimens exhibited an elastic modulus of 293 MPa and specimens which were 50% HA by weight exhibited a modulus of 1459 MPa. After six weeks of degradation under physiological conditions, the reinforcing effect of ceramic loading had diminished. Modulus of polymer matrices at all HA load levels had decreased sharply to approximately 10 MPa. Mean macro- and micropore diameters of the polymer specimens were 100 μm and 20 μm respectively and remained constant throughout degradation.

High-temperature elasticity of iron-bearing olivines

Abstract: The first high-temperature data on the nine adiabatic elastic moduli for iron-bearing olivine are reported. These measurements are on two single-crystal specimens of natural olivine at ambient pressure and from room temperature to a maximum of 1500 K. The two specimens contain 8 and 9 modal percent fayalite, which required the oxygen fugacity be controlled at high temperature to preserve their chemical stability. The rectangular parallelepiped resonance apparatus was adapted to buffer the specimens from the atmosphere with a mixture of CO and CO2 gas. A small increase (∼1–2 GPa) in the adiabatic bulk modulus of each specimen, over that of end-member forsterite, was found. The data are high quality to extreme temperatures, with good agreement found when comparing the temperature derivatives of the elastic moduli of the two specimens. Neither specimen exhibits measurable nonlinear temperature dependence in the computed isotropic bulk and shear moduli, which is in contrast to published forsterite data. The temperature derivatives of the isotropic bulk modulus KS are (−1.69, −1.80) × 10−2 GPa K−1 for the two olivine specimens, and the shear modulus G derivatives are (−1.38, −1.36) × 10−2 GPa K−1. These derivatives are only slightly larger in magnitude than |(∂KS/∂T)P| = 1.56 × 10−2 and |(∂G/∂T)P| = 1.30 × 10−2 GPa K−1 found previously for iron-bearing olivine over a very small temperature range. There are also no significant differences between the temperature derivatives found here and the average derivatives of end-member forsterite from data retrieved over a slightly larger temperature range. Several dimensionless parameters have been calculated from these results and are discussed in view of systematics which bear on high-pressure phases in Earth's transition zone. One result from these systematics related to the seismic velocities in the Earth, and especially the shear wave velocities, is that an olivine content of less than 50% is implied at the 400-km discontinuity if Earth's upper mantle is isochemical. Furthermore, the substitution of almost 10% iron for magnesium at the forsterite end of the olivine solid solution series has little effect on the dimensionless parameters or on the temperature derivatives of the elastic moduli at high temperature.

Effect of Fiber Orientation and Strain Rate on the Nonlinear Uniaxial Tensile Material Properties of Tendon

Abstract: Tendons are exposed to complex loading scenarios that can only be quantified by mathematical models, requiring a full knowledge of tendon mechanical properties. This study measured the anisotropic, nonlinear, elastic material properties of tendon. Previous studies have primarily used constant strain-rate tensile tests to determine elastic modulus in the fiber direction. Data for Poisson's ratio aligned with the fiber direction and all material properties transverse to the fiber direction are sparse. Additionally, it is not known whether quasi-static constant strain-rate tests represent equilibrium elastic tissue behavior. Incremental stress-relaxation and constant strain-rate tensile tests were performed on sheep flexor tendon samples aligned with the tendon fiber direction or transverse to the fiber direction to determine the anisotropic properties of toe-region modulus (E0), linear-region modulus (E), and Poisson's ratio (v). Among the modulus values calculated, only fiber-aligned linear-region modulus (E1) was found to be strain-rate dependent. The E1 calculated from the constant strain-rate tests were significantly greater than the value calculated from incremental stress-relaxation testing. Fiber-aligned toe-region modulus (E(1)0 = 10.5 +/- 4.7 MPa) and linear-region modulus (E1 = 34.0 +/- 15.5 MPa) were consistently 2 orders of magnitude greater than transverse moduli (E(2)0 = 0.055 +/- 0.044 MPa, E2 = 0.157 +/- 0.154 MPa). Poisson's ratio values were not found to be rate-dependent in either the fiber-aligned (v12 = 2.98 +/- 2.59, n = 24) or transverse (v21 = 0.488 +/- 0.653, n = 22) directions, and average Poisson's ratio values in the fiber-aligned direction were six times greater than in the transverse direction. The lack of strain-rate dependence of transverse properties demonstrates that slow constant strain-rate tests represent elastic properties in the transverse direction. However, the strain-rate dependence demonstrated by the fiber-aligned linear-region modulus suggests that incremental stress-relaxation tests are necessary to determine the equilibrium elastic properties of tendon, and may be more appropriate for determining the properties to be used in elastic mathematical models.