finite element method

The hyperelastic behavior of the rubber compounds filled with reinforcing fillers (carbon black) is dependent on the filler content. The previous theories for the prediction of the mechanical behavior of these materials arebased on phenomenological relationships. In this research, a new approach based on the amplified strain theory is presented and its reliability and applicability are examined for a rubber compound reinforced with different carbon black contents

Six rubber compounds based on SBR reinforced with different carbon black contents (20, 30, 40, 50, and 60 phr) as well as the neat compound were prepared. The mechanical behavior of these compounds under uniaxial tension mode, volumetric changes, compression, and simple shear modes were experimentally determined. TheYeoh material model was selected for the neat compound and material constants were calibrated using the uniaxial and volumetric changes data. Two strain amplification relationships were selected including the Bergstrom-Boyce and our newly proposed models. The parameters of the latter model were determined using an optimization algorithm in which a new UHYPER subroutine was developed and linked to Abaqus main code. To assess the proposed model and comparing it with the Bergstrom Boyce model the simulation results obtained from the finite element model of the uniaxial, compression, and simple shear tests were compared with their corresponding experimental data.

The results showed that hyperelastic behaviors of the filled rubber compounds, predicted by our developed strain amplified model, are more accurate than those obtained by the Bergstrom-Boyce equation. It is also found that the combination of the Yeoh hyperelastic model with our proposed relationship can precisely predict the mechanical behavior under different modes of loadings..

Hypothesis:

 Determination of the parameters of the material models for rubber compounds is usually carried out under simple modes such as uniaxial tension. These models are typically consisted of hyper-viscoelastic and stress-softening equations. However, due to the complicated behaviors of rubbery materials, the effectiveness and accuracy of such models under combined loads of tension, compression, and shear should be verified.

Three rubber compounds were prepared based on SBR reinforced by three different amounts of carbon blacks and underwent uniaxial cyclic under two loading/unloading rates and volumetric tests. The experimental data were used for the determination of parameters of three complex material models using a nonlinear curve fitting method. These models were selected based on the results of our previous findings. We have verified the uniaxial condition of the chosen test method and sample size using finite element method. The computed parameters were employed to simulate cylindrical rubber samples prepared from the same compounds through the finite element method using Abaqus code under compressive-contact loads. The predicted results were next compared with their experimentally measured data.

The results showed that the effectiveness of a material model in the prediction of stress-strain or stress-time behavior of a rubber compound under a simple load case does not necessarily guarantee that the same level of accuracy is obtained for the other loading modes, especially for highly filled compounds.  It is shown here that to obtain accurate results in such cases, in addition to hyper-viscoelastic and stress softening equations, the material model should include proper terms to consider the effect of the filler-filler interactions into account, especially for highly carbon black-loaded compounds. It is found that the best model is the one in which the viscoelastic behavior of the filler-filler structure is independently included.

Well integration aims to protect human life and the environment by reducing the risk of uncontrolled oil and gas production release during its life cycle. Well integrity requires safe connections for the casing, tubing, and downhole equipment. In this research, using modeling and simulation software by finite element method, a premium connection has been designed, which is required for the current conditions of oil and gas wells. The connection was loaded according to the international standard ISO 13679 in a triaxial loading, including the axial loads of tension and compression with internal and external pressure. The analysis results were evaluated using the criteria of stress and sealability. The results showed that the designed connection fully meets the standard requirements. The amount of stress created at different loads is lower than the yield strength of the material, while the contact pressure of the sealing surfaces makes reliable sealability. It was found that design by finite element analysis can be a reliable and inexpensive tool and an alternative to physical experiments.

Well integrity is a necessity for separating the well from the fluid entering the adjacent formations and eliminating this integrity over the life of the well, causing problems such as excess water production in the production well, fluid leakage of adjacent formations, damage to equipment, and well erosion. It will cause manpower and damage to the environment, and if the problem is not resolved, we will see the well closed and capital lost. The loss of this integrity has several factors, including incomplete blocking operations, damage and deformation of the maintenance system, poor connection caused by the mud cake, fractures created in the blocker and formation, and the presence of ducts in the cement. The application of geomechanics in the oil and gas industry is evolving dramatically, determining the geomechanical properties of the rock, such as wellbore stability, and fluid flow coupling, are various applications of the geomechanical model during the development of a hydrocarbon field; the creation of shear and tensile stresses at the joint surfaces between the blocker and the maintenance system as well as the formation and blocker, pore pressure changes, mechanical stresses caused by injection or production can cause existing stresses to change near the well, thus which the loss of integrity will lead to wells. In this study, geomechanical modeling with hydromechanical approach for wells of a field in western Iran was performed using finite element method and considering this model, the integrity of the well was investigated at the well production stage.

Today, the technical and engineering applications of textiles have received much attention from engineering researchers. It can be said that the most attention in this area is focused on medical textiles. There is a special group of medical textiles called compression garments, the function of which is to apply pressure to the body and was used for the first time for Pressure Therapy. The most important applications of these garments are to treat burns and varicose veins. The principle of treatment in these garments is the amount and distribution of pressure on the body, which is determined by the physician. The dimensions and material of the pressure garments should be chosen in such a way that the desired pressure is applied to the patient's body. For this purpose, one of the best methods for predicting pressure is to use simulation using finite element methods. In this research, a three-dimensional model of contact and pressure between the pressure garment and the human body is presented using ABAQUS software. Initially, the model was designed as a cylinder and the values of pressure, strain and stress on the hand and the pressure garment as well as pressure distribution showed that the model was properly designed and implemented in software. Then, the modeling was performed conically using real body sizes and pressure garment and the results were compared with the experimental results. Comparison of experimental results and model results showed that this model well simulates the pressure distribution and contact between the hand and the pressure garment. The method used in this research is a simple and practical method for model validation.

Hypothesis:

The aim of this study was to propose a modified model for the prediction of a stress softening behavior (Mullins effect) in carbon black filled rubber compounds. A new equation was suggested for the calculation of the damage variable in the classical Ogden-Roxburgh model based on a previously developed kinetic equation. The parameters of the new model were assumed dependent on the first principal strain. The developed model was verified by comparison of the model predictions with experimental data

Four rubber compounds based on S-SBR and E-SBR reinforced by 40 and 60 phr carbon blacks were prepared and cured into rubber sheets. The rubber test specimens (ASTM D412 C) were cut and subjected to cyclic tensile tests at an extension rate of 500 mm/min. In order to show the stress softening behavior, three cycles were selected in a way that the maximum stretch at each cycle was increased consecutively. The volumetric tests were also carried out to determine the bulk modulus and Poisson's ratio. The finite element models of the mentioned tests were created for Abaqus code. The new model was implemented into Abaqus through a user-defined subroutine developed specifically for this research. An optimization algorithm developed in Isight code was employed to determine the parameters of themodel for the prepared compounds

Comparing the predicted force versus time and force versus displacement with their corresponding experimentally measured data and goodness of fitting for new model and classical Ogden-Roxburgh model revealed that the developed model has higher capability and accuracy in prediction of the mechanical behavior of the rubber compounds. Comparing the ratio of the computed errors between two models showed that the new model has higher accuracy with an average of 38%. Moreover it is found that there are good correlations between variation of the model parameters with rubber grades and filler contents.

Underground storage of natural gas is mainly accomplished by three methods storage in depleted oil and gas reservoirs, storage in aquifers, and storage in salt domes. Among these methods, underground storage (UGS) in aquifers is of much paramount due to more accessibility to metropolises and consumption markets, proper conditions, and ability to keep the gas for long period of time. So far, storage of natural gas in aquifers has been studied from various aspects, but from a geomechanical point of view, no studies have been conducted to date. So, in this study, in order to investigate the geomechanical parameters affecting the process of underground storage of natural gas in an aquifer, the process has been simulated by Finite Element Method (FEM) using ABAQUS software and the geomechanical parameters affecting this process have been studied. For this purpose, first, the impacts of gas injection and production on pore pressure and vertical displacement in different times and locations are thoroughly investigated after injection and production phases. Afterwards, the sensitivity analysis is done regarding to the input parameters of the model. The results showed that the ratio of horizontal stresses to initial vertical stress is considered to have the maximum impact on increasing the probability of tensile failure. Also, injection/production rate and the horizontal stresses to initial vertical stress ratio have the greatest influences on probability of shear failure respectively. Besides, injection/production rate and reservoir Young modulus have the highest impact on vertical displacement respectively. The highest vertical displacement after injection phase and after production phase are 8 at the injection location and 12 (mm) at the production location, respectively. In addition, the highest increase of pore pressure took place around injection wells one-year after injection start time which is equal to 534 KPa compared to the aquifer initial pressure.

Reduction of rolling resistance in tyres plays a crucial role in reducing global warming and CO2 emissions. Consequently, the prediction of energy dissipation in tyre tread compounds has received increasing interest from tyre manufacturers to design low dissipative compounds. In the present work, a triple model based on the Ogden hyperelastic equation, Bergstrom-Boyce nonlinear viscoelastic relationship in conjunction with a stress softening equation was proposed for the prediction of the force-displacement behavior of tread compounds. Two series of rubber blends compounds based on SBR/BR solution and SBR/BR emulation reinforced by two carbon black (CB) grades and a surface-modified silica were prepared. Each series was comprised of three blends with different filler contents. The total part of filler in each compound was kept constant as 80 phr.  The first compound contained 80 phr of CB without any silica, while the second and third compounds were prepared using 20 and 40 phr silica as replacement. The mechanical behavior of the cured compounds was determined using a tensile test carried out on a ribbon type sample with 2X11 cm dimension and ATM D-412 C test specimens. An optimization loop was designed in Isight code using three Abaqus, data matching and optimization components. The developed algorithm was used for the determination of the parameters of the mentioned model. It is shown that the proposed material model and the developed numerical algorithm can predict the mechanical behavior of the compounds during a loading/unloading cycle. The trends of the variations of the predicted parameters are in reasonable agreement with macro- and micro- structure of the SBR and filler type (CB or silica). It is also found that the addition of silica to rubber compound has 25-35% decreasing effect on energy dissipation. Moreover, solution SBR has approximately 50% more reduction effect on energy dissipation compared to emulsion SBR at equal filler type and content.

In the oil industry, production of sand particles or detached sand clumps together with the formation fluids is called sand production. Sand production in oil wells is usually related to two fundamental mechanisms. The first mechanism is mechanical instability and degradation of the rock in the vicinity of the wellbore and the other is hydrodynamical instability due to flow induced drag force on the degraded material. In this paper, considering both the mechanisms, a new numerical model for predicting the onset of sanding as well as the amount of sanding is proposed. Implementation of the model in an explicitly coupled flow and deformation finite element program is described. The proposed model by removing the elements that have satisfied the sanding criteria as well as isolated rock chunks from reservoir can capture cavity evolution associated with sand production. The model is calibrated and validated against published results of a sanding experiment in a perforated reservoir rock. Results of the model in terms of initiation and amount of sanding are compares well with the experimental observations which suggests it can be used for sanding analysis of oil wells.

This research work is devoted to the study of the thermal diffusivity of SBR/BR compounds used as the tread of radial tires. Three series of rubber compounds were prepared, in which two solution SBR grades (with and without extra oil) as well as an emulsion SBR were selected. Five compounds with different CB/silica ratios were designed for each of the three series. Moreover, three compounds without fillers were prepared as reference samples. Thermal diffusivities of the compounds were determined by a novel technique to solve an inverse heat transfer problem. Abaqus and Isight codes were used to carry out the finite element solution and optimization. It is shown that, in all the compounds the thermal diffusivities were reduced with increasing the temperature. In addition, the macro- and micro- structures of SBR as well as the CB/silica ratios greatly affected the variations in thermal diffusivities with temperature. The thermal diffusivity and its variabilities were studied and discussed by different structural and functional parameters such as intermolecular distance, molecular vibrational energy, difference between the thermal diffusivities of the polymer and filler, and the chemical bonds between the polymer and silica.

A theoretical and experimental study was conducted on the mechanical behavior of nanocomposites based on PA6/NBR thermoplastic elastomer reinforced by single wall carbon nanotubes (SWNTs). The selected samples include 60 and 40% NBR with 0. 5، 1. 0 and 1. 5% SWNT. The modeling methodology was based on the use of two-dimensional «representative volume elements» (RVE). The Abaqus/standard code was employed to carry out the non-linear finite element calculations. Plane stress elements were selected for discretization of the domain. Linear elastic and isotropic hardening elastic-plastic models were utilized to describe the mechanical behaviors of the carbon nanotubes and polymer matrix، respectively. The samples were simultaneously prepared using melt mixing method in a laboratory internal mixer. Different orientations including regular in both longitudinal and transverse directions and random were selected for the nanotubes in the matrix. Also، two structural forms including hollow and solid for the carbon nanotubes were chosen. The highest and lowest predicted moduli were obtained from models with regular orientation in longitudinal and transverse directions، respectively. On the other hand، comparison between the predicted elastic modulus and elastic-plastic behaviors of the samples with their corresponding experimental data revealed that the random orientation in conjunction with hollow structural form gives the best results. Moreover، the selected material model for the thermoplastic elastomer i. e.، isotropic hardening can precisely describe the mechanical behavior in both tension and compression modes. It is also concluded that the main source of error in this modeling methodology can be attributed to the effects of interface between polymer and nanotubes and orientation in perpendicular directions.

This research work is devoted to the simulation of a steel-belted radial tire under different static loads. The nonlinear finite element calculations were performed using the MSC. MARC code، installed on a computer system equipped with a parallel processing technology. Hybrid elements in conjunction with two hyperelastic models، namely Marlow and Yeoh، and rebar layer implemented in surface elements were used for the modeling of rubbery and reinforcing parts، respectively. Linear elastic material models were also used for the modeling of the reinforcing elements including steel cord in belts، polyester cord in carcass and nylon cord in cap ply section. Two-dimensional axisymmetric elements were used for the modeling of rim-mounting and inflation and three-dimensional models were developed for the application of the radial، tangential، lateral and torsional loads. Different finite element models were developed، in which both linear and quadratic elements were used in conjunction with different mesh densities in order to find the optimum finite element model. Based on the results of the load deflection (displacement) data، the tire stiffness under radial، tangential، lateral and torsional loads were calculated and compared with their corresponding experimentally measured values. The comparison was verified by the accuracy of the measured radial stiffness. However، due to the neglecting of the stiffness in shear and bending modes in cord-rubber composites، modeled with rebar layer methodology، the difference between computed values and real data are not small enough so that a more robust material models and element formulation are required to be developed.

In this study، a three-dimensional model of a single fuel cell is considered. This modeling is done for a cathode half-fuel cell and consists of a parallel flow field، namely a cathode gas diffusion layer and a polymer membrane; it includes mass transfer at gas diffusion layer، electrochemical reaction at catalyst layer، and charge transfer in all the parts of fuel cell. Shoulder is considered in this model and thus concentration profile and charge distribution are more delicate. Governing equations are solved by FEMLAB software through the finite element method. This modeling could predict the behavior of fuel cell at different operation conditions by minimum cost. The performance of fuel cell is evaluated by different activation energies and، by comparing the results، the optimum operation condition is concluded.