In the current paper, finite element method is employed for numerical simulations and the study of influential parameters on elastic modulus of polymer-matrix nano-composites. Effects of different key parameters including particle elastic modulus, interphase elastic modulus, matrix elastic modulus, interphase thickness and particle volume fraction on total elastic modulus of nano-composite materials are observed in order to shed some light on experimental parameters that are difficult to measure. To this end, a three phase (i.e. particle, interphase and matrix) unit cell is modelled and results compare with previously introduced theoretical model. It is found that interphase parameters such as elastic modulus and thickness strongly influences the elastic properties of the nano-composite and cannot be neglected.

The available analytical and finite element methods set the values of elastic modulus of nanocomposites more than the values obtained from the test. In this thesis, a new linear and continuous analysis method is used to determine the best and most similar value of elastic modulus for polymer nanocomposites to laboratory value is provided. For this purpose, the governing elasticity equations in polar coordinates have been solved for nanocomposite representative volume element (RVE) with shear-lag model by assuming perfect bond condition between CNT and matrix. Then, using the finite element modeling with Ansys software, elastic modulus of connectivity states of almost complete and half break between the two phases are calculated and finally the proposed new model that is modeling with spring in the states of almost complete connectivity and half break between the two phases are provided and elastic modulus is calculated. In this method, shear stress is also offering a new relationship between CNT and matrix areas that have been. To ensure the validity of the results of presented model to determine the elastic modulus, the obtained results are compared with laboratory method results of other researchers that in all cases the proposed elastic modulus is much closer to laboratory sample and finite element models and good agreement

Common carotid arterial stiffness can be assessed during carotid arterial ultrasonography, but its association with brachial stiffness, a well-defined cardiovascular risk factor, has not been clarified. The aim of this study was to examine the relationship between common carotid artery and brachial artery stiffness. The static pressure-strain elastic modulus of the common carotid and brachial arteries were evaluated in 40 men with 15 healthy carotids, 15 mild carotid stenoses, and 10 severe carotid stenoses, by B-mode and Doppler ultrasonography. The local elastic modulus was estimated by the measurement of the arterial strain; the static pressure was also measured based on the peak-systolic and end-diastolic velocity in each artery. The elastic modulus of the right common carotid artery (RCCA) and right brachial artery (RBA) increased linearly with the growth of atherosclerosis from 1772±566 Pa and 2639±1096 Pa for the normal subjects to 6168±1026 Pa and 5587±1592 Pa for the severe stenosis group, respectively. In the three groups; healthy, mild stenosis, and severe stenosis; there was a significant difference in the elastic modulus of the right common carotid artery between the groups and also for the right brachial artery, separately (p-value<0.05). The Pearson correlation analysis showed a significant correlation between the elastic modulus of the right common carotid artery and the elastic modulus of the right brachial artery. The brachial artery elastic modulus is associated with the common carotid elastic modulus. This study showed that atherosclerosis was a generalized process that might involve the entire vasculature. An evaluation of the elastic modulus of the RBA, however, showed that there were fundamental differences in the dynamic behavior of the brachial artery when compared to elastic arteries, such as the common carotid artery.

The main goal of this research is study on longitudinal elastic modulus of nanocomposites reinforced with Zigzag and Armchair carbon nanotubes in different volume fractions and aspect ratios with finite element simulation. A three-phase volumetric element was used to model the behavior of the nanocomposite and used nonlinear spring strain elements to model the interfacial phase interface and the effective force between the nanotube and the resin based on the Lenard-Jones potential. After evaluation and validation of the model, the elastic modulus and Poisson coefficient were extracted from nanocomposites reinforced with Zigzag and Armchair carbon nanotubes in different volume fractions and aspect ratios. By increasing the nanotube volume fraction and aspect ratio, the amount of the elastic modulus of the composite increases. In the same aspect ratio and volume fraction, the modulus of elastic composites reinforced with armchair nanotubes and the Poisson coefficient of composites reinforced with zigzag nanotubes is higher. Also, the results of the study showed that the elastic modulus of the composite is independent of the elastic modulus of intermediate phase.

In this research, stiffness of polymer-clay nanocomposites was simulated by Mori-Tanaka and two and three dimensional finite element models. Nanoclays were dispersed into polymer matrix in two ways, namely parallel and random orientations toward loading direction. Effects of microstructural parameters including volume fraction of nanoclays, elastic modulus of nanoclays and interphase, thickness of interphase, aspect ratio of nanoclays and random orientation of nanoclays on elastic modulus of the nanocomposite were investigated by finite element model. Comparing the simulation with experimental results showed that the Mori-Tanak simulation results were closer to the experimental results. Analysis of results showed that the volume fraction of nanoclay, elastic modulus of nanoclay, deviation of nanoclay layers with respect to loading direction, nanoclays aspect ratio, thickness of interphase and the elastic modulus of interphase had respectively the most to the least effect on elastic modulus of nanocomposite.

The purpose of this study is to calculate and investigate the effect of porosity on the elastic moduli in Kangan and Dalan Formations in the South Pars gas field of Iran. Compressional and shear wave velocities were calculated using travel times of compressional wave and travel times of shear waves, which are deduced from the Dipole Shear Sonic Imager (DSI) logs. Bulk modulus, Shear modulus, Young’s modulus, Lame parameter, Poisson’s ratio and the ratio of K/G were calculated using the relationship between the acoustic wave velocities, density and physical moduli. In this study, the relationship between porosity and elastic moduli were determined by real data and observed that elastic moduli are decreased by porosity increasing. Comparison of elastic moduli with porosity shows significant consistency between bulk modulus and porosity (compared to other moduli). Also, the ratios of Vp/Vs, K/G and Poisson’s ratio were examined. Result of this investigation showed that these ratios are slightly reduced by increasing the porosity.

The elastic parameters of the rock include the Young modulus, the Poisson ratio, the bulk modulus and the shear modulus. Young modulus with the unconfined compressive strength of rock, are two key parameters in the definition of intact rock. Elastic modulus represents the amount of rock rigidity and is known as the stress-strain chart slope. These parameters represent of rock strength to failure, are important parameters for the stability analysis of wellbore stability. According to the unavailability and cost of core data, and also attended to this fact that the data from the core are not continuous and not available at all points in the well, the uses of DSI logs is one of the best methods for calculating elastic modules. Using these logs, you can also study elastic moduli continuously in a well. In this study, elastic dynamic parameters were calculated using the DSI and density logs for the Dalan Formation. Attention to the fact that the calculated parameters using the velocity of the sound waves are of the type of dynamic parameters, these parameters were have converted to the static modules using appropriate empirical relationships. The rock strength Parameters were calculated using the experimental relationships commonly used in the oil industry to determine rock strength parameters. These parameters were calculated according to static elastic modulus as well as porosity and shale volume. Comparing the values of elastic modulus and rock strength parameters with porosity showed that porosity with elastic modulus and rock strength parameters has an inverse relationship, so that with increases the porosity, the elastic modulus and rock strength parameters have been reduced.

Polymer-clay nano-composite materials, in which nano-meter thick layers of clay dispersed in polymer matrix, have generally higher mechanical properties than normal polymeric materials. A new three-dimensional unit cell model has been developed for modeling three constituent phases including inclusion, interphase and matrix. The total elastic modulus of nano-composite is evaluated. Numerical results are in good agreement with the previous proposed theoretical modeling. Higher matrix and inclusion elastic modulus both can dramatically increase the total elastic modulus.

A new three-dimensional unit cell model has been developed for modeling three constituent phases including inclusion, interphase and matrix. The total elastic modulus of nano-composite is evaluated. Numerical results are in good agreement with the previous proposed theoretical modeling. Higher matrix and inclusion elastic modulus both can dramatically influence the total elastic modulus.

In finite deformation analysis¡ the use of constitutive equations in rate form is often required. In a spatial setting¡ elastic modulus tensor relates some objective rate of a spatial stress tensor to the rate of deformation. It is important to know that¡ the spatial elastic modulus tensors of a material in different constitutive equations differ and relation between them may be interest for some researchers. In this paper¡ a general explicit formulation between the spatial elastic modulus tensors of some constitutive equations expressed. This formulation is a function of left Cauchy-Green tensor and its eigenvectors.