Elastic modulus

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

Elastic modulus measurements of human liver and correlation with pathology.

Abstract: Viral hepatitis causes fibrosis in the liver and may change mechanical properties of the liver. To evaluate the impact of fibrosis on elastic properties of human liver and to investigate potential benefits of ultrasonic elasticity imaging, 19 fresh human liver samples and 1 hepatic tumor (focal nodular hyperplasia) sample obtained during operations were studied. Simple 1-D estimates based on the cyclic compression-relaxation method were performed. Elastic modulus values were derived from the predetermined strain (controlled by a step motor system) and the stress values (measured by an electronic balance). Each specimen subsequently received histologic examination and a grade of liver fibrosis was scored from 0 to 5. Results show that the elastic modulus values were on the order of several hundreds to thousands of Pascals. The elastic modulus generally increased with the fibrosis grade, although some discrepancies existed at the middle grades of fibrosis (scores 1 to 3). The correlation between the fibrosis score and the elastic modulus was significant (p < 0.01) based on the statistical analysis using the Pearson correlation method. In addition, the relation between the elastic modulus and the fibrosis grade generally exhibited a quadratic trend. It was concluded that severity of fibrosis had a good correlation with stiffness of the liver. Results also indicated that the elasticity imaging of the liver may provide significant clinical values if the elastic modulus can be accurately measured. (E-mail: paichi@cc.ee.ntu.edu.tw)

Mechanical properties of silicones for MEMS

Abstract: This paper focuses on the mechanical properties of polydimethylsiloxane (PDMS) relevant for microelectromechanical system (MEMS) applications. In view of the limited amount of published data, we analyzed the two products most commonly used in MEMS, namely RTV 615 from Bayer Silicones and Sylgard 184 from Dow Corning. With regard to mechanical properties, we focused on the dependence of the elastic modulus on the thinner concentration, temperature and strain rate. In addition, creep and thermal aging were analyzed. We conclude that the isotropic and constant elastic modulus has strong dependence on the hardening conditions. At high hardening temperatures and long hardening time, RTV 615 displays an elastic modulus of 1.91 MPa and Sylgard 184 of 2.60 MPa in a range up to 40% strain.

Elastic properties of single-walled carbon nanotubes

Abstract: Analytical expressions for the velocities of the longitudinal and the torsional sound waves in single-walled carbon nanotubes are derived using Born's perturbation technique within a lattice-dynamical model. These expressions are compared to the formulas for the velocities of the sound waves in an elastic hollow cylinder from the theory of elasticity to obtain analytical expressions for the Young's and shear moduli of nanotubes. The calculated elastic moduli for different chiral and achiral ~armchair and zigzag! nanotubes using force constants of the valence force field type are compared to the existing experimental and theoretical data. vibration amplitude of several isolated MWNT's was ana- lyzed in a transmission electron microscope to eventually obtain 1.8 TPa for the average Young's modulus. Later on, this technique was applied to measure Young's modulus of isolated SWNT's in the diameter range 1.0 21.5 nm and an average value ^Y&51.2520.35/10.45 TPa was derived. 7 In another experimental approach 8 the MWNT's were pinned to a substrate by conventional lithography and the force was measured at different distances from the pinned point by atomic force microscope ~ATM!. The average Young's modulus for different MWNT's with diameters from 26 to 76 nm was found to be 1.2860.59 TPa. Recently, Young's and shear moduli of ropes of SWNT's were measured by sus- pending the ropes over the pores of a membrane and using ATM to determine directly the resulting deflection of the rope. 9 The theoretical estimation of the elastic moduli was accomplished exclusively by numerical second derivatives of the energy of the strained nanotubes. In the calculation of the elastic moduli of various SWNT's within a simple force- constant model 10 it was found that the moduli were insensi- tive to tube size and helicity and had the average values of ^Y&50.97 TPa and ^G&50.45 TPa. In several works, molecular-dynamics ~MD! simulation algorithms using the Tersoff-Brenner potential for the carbon-carbon interactions were implemented to relax the strained nanotubes and calcu- late their energy. 11-13 For tubes of diameter of 1 nm values for Y of 5.5 TPa ~Ref. 12! and 0.8 TPa ~Ref. 13! were ob- tained. A non-orthogonal tight-binding ~TB! scheme was ap- plied to calculate Young's modulus of several chiral and achiral SWNT's yielding an average value of 1.24 TPa. 14 Recently, the second derivative of the strain energy with re- spect to the axial strain, calculated with a pseudopotential density-functional-theory ~DFT! model for a number of SWNT's, 15 was found to vary slightly with the tube type and to have the average value of 56 eV. In this paper, we choose a different approach to the cal- culation of the elastic properties of SWNT's. Namely, we derive analytical expressions for the elastic ~Young's and shear! moduli of SWNT's using a perturbation technique due to Born 16 within a lattice-dynamical model for nanotubes. 17 This scheme has the advantage that the elastic moduli are consistent with the lattice dynamics of the nanotubes and that each of these moduli is obtained in one calculational step only. The essential features of a model of the lattice dynamics of SWNT's based on the explicit accounting for the helical symmetry of the tubes 17 are summarized in Sec. II A. This model is applied to study of the long-wavelength vibrations in nanotubes using Born's perturbation technique 16 and to obtain analytical expressions for the velocities of the longi- tudinal and the torsional sound waves in SWNT's ~see Sec. II B!. The comparison of these expressions with the formulas from the theory of elasticity for the velocities of these waves in an elastic hollow cylinder allows one to determine the Young's and shear moduli of the nanotubes. The calculated phonon dispersion of a (10,10) nanotube and elastic moduli for various chiral and achiral ~armchair and zigzag! nano- tubes using force constants of the valence force field ~VFF! type 18 are presented in Sec. III and discussed in comparison with the existing experimental and theoretical data.

Crack‐Growth Resistance of Microcracking Brittle Materials

Abstract: A mechanics model of microcrack toughening is presented. The model predicts the magnitude of microcrack toughening as well as the existence of R-curve effects. The toughening is predicated on both the elastic modulus diminution in the microcrack process zone and the dilatation induced by microcracking. The modulus effect is relatively small and process-zone-size-independent. The dilatational effect is potentially more substantial, as well as being the primary source of the R curve. The dilatational contribution is also zone-size-dependent. The analysis demonstrates that microcrack toughening is less potent than transformation toughening.