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### Browsing by Author "Rahman, Rezwanur"

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Item Damage evolution in composite materials under environmental ageing: a stochastic model with experimental validation(University of Alabama Libraries, 2009) Rahman, Rezwanur; Haque, Anwarul; University of Alabama TuscaloosaShow more This work emphasizes on predicting probability density function of damages or "number density of damage" in graphite/epoxy polymer matrix composite materials (PMC) under hygrothermal aging condition. A coupled Forward-Backward Stochastic Differential Equation (FBSDE) is proposed as a mathematical model to predict number density of damages. The FBSDE consists of damage nucleation and annihilation rate in terms of Brownian motion. The uncertainty in damage nucleation and annihilation rate is noticed by proposing these two terms as "Brownian motion with drift". In order to verify the proposed model, a quantitative analysis was carried out on a limited number of graphite/epoxy specimens manufactured by VARTM process. The specimens were kept in a hygrothermal condition with room temperature cycling. A rigorous quantitative analysis of damages was done by optical microscopic inspection at different stages of aging period. The damages were classified based on the criteria of their size. Finally, the experimentally collected data for number density of damages were verified by using the proposed FBSDE. A detail parametric study was carried out using FBSDE and best possible predicted data was validated with the experimental observation. A reasonable estimation was observed from the model output.Show more Item Molecular dynamics modeling and characterization of graphene/polymer nanocomposites(University of Alabama Libraries, 2012) Rahman, Rezwanur; Haque, Anwarul; University of Alabama TuscaloosaShow more The current work focuses on the characterization of graphene based nanocomposites using molecular dynamic simulation and multiscale modeling approaches. Both graphene-epoxy and graphene-cellulose nanocomposites were considered in this study. A hierarchical multiscale modeling approach has been proposed using peridynamics and molecular dynamics simulation. Firstly, the mechanical properties of crosslinked graphene/epoxy (G-Ep) nanocomposites were investigated by molecular mechanics (MM) and molecular dynamics (MD) simulations. The influence of graphene's weight concentration, aspect ratio and dispersion on stress-strain response and elastic properties were studied. The MD models were further analyzed through the radial distribution function (RDF), molecular energy and atom density. Both the amorphous and the layered structures of G-Ep nanocomposites were considered in order to study the effect of graphene dispersion on elastic properties. A polymer consistent force field (pcff) was used throughout the analysis. Each of the G-Ep system underwent an NVT (constant number of atoms, volume and temperature) and an NPT (constant number of atoms, pressure and temperature) based equilibration followed by finite deformation. The stress-strain responses were evaluated from MD simulations for both amorphous and layered-graphene unit cells in order to determine elastic constants. Moreover, MM was also used to calculate Young's modulus and shear modulus. The results show significant improvement in Young's modulus and shear modulus for the G-Ep system in comparison to the neat epoxy resin. It appears that the RDF, molecular energy and aspect ratios are influenced by both graphene concentrations and aspect ratios. The graphene concentrations in the range of 1-3% are seen to improve Young's modulus and shorter graphenes are observed to be more effective than larger ones. In addition, the dispersed graphene system is more promising in enhancing in-plane elastic modulus than the agglomerated graphene system. The cohesive and pullout forces versus displacements data were plotted under normal and shear modes in order to characterize interfacial properties. The cohesive force is significantly improved by attaching the graphene with a chemical bond at the graphene-epoxy interface. The elastic constants determined by molecular modeling showed a good agreement with the nanoindentation test results. In the second part of the work, cellulose was considered to study the mechanical properties of graphene-cellulose bionanocomposite. Multiple number of cellobiose repeat units were connected together to obtain long cellulose chains. Similar to the previous study, the effect of graphene's weight concentration, aspect ratio and dispersion was studied by considering the amorphous and the layered graphene-cellulose systems. Each unitcell was equilibrated using the NVT and NPT molecular dynamics. Uniaxial deformation was applied in order to obtain stress-strain response. The Young's modulii were calculated from the linear portion of the stress-strain responses. Similar to graphene-epoxy systems, the effect of graphene dispersion and agglomeration were studied in the stress-strain plots of graphene-cellulose system. A pcff forcefield was used to define intermolecular and intramolecular interactions. The effect of graphene's aspect ratio and weight concentration on the structural property of each unitcell was analyzed in terms of the radial distribution function (RDF), molecular energy, pairwise bond stretch and angle bending. The interfacial properties between graphene and cellulose were studied by analyzing both cohesive and pullout separation of graphene from cellulose matrix. Finally, the Young's modulii calculated from the MD simulation was compared with the tensile test data. The MD results showed a reasonable agreement with the tensile test results. It was addressed that incorporating graphane in cellulose matrix enhances the mechanical property of the cellulose based bio-polymer systems. In the third part of the work, a hierarchical multiscale modeling framework was established between peridynamics and molecular dynamics simulation using an intermediate coarse grained atomic model. The peridynamics formulation is based on continuum theory implying nonlocal force based interaction. It means, continuum points are separated by a finite distance and exert force upon each other. Peridynamics applies integral equations rather than partial differential equations as used in the classical continuum mechanics. Hence, the peridynamics (PD) and the molecular dynamics (MD) have similarities since both use a nonlocal force based interaction. In this work PD based continuum model of graphene-epoxy (G-Ep) nanocomposite is defined by the Lagrangian PD particles. Atomistic model is coupled with PD model through a hierarchical multiscale framework. The PD particles at a coarse scale interact with the fine scale PD particles by transferring pressure, displacements and velocities among each other. Based on the same hierarchical coupling method, a fine scale PD model is seamlessly interfaced with the atomistic model through an intermediate mesoscale region i.e. coarse-grain model. At the end of this hierarchical downscaling, the information such as the deformation, energy and other important parameters were captured in the atomistic region under the applied force at micro and macro regions. The change in atomistic domain is used to update the coarser PD models by introducing a hierarchical upscaling formulation. A simple two dimensional plate of neat epoxy was considered for a complete demonstration of such multiscale simulation platform. Displacements at different scales were analyzed in order to show the validity of the proposed multiscale model. Afterward, the model was applied to a graphene-epoxy plate with an edge crack. The region near the crack tip is interfaced with atomistic model by applying proposed hierarchical coupling method. The crack opening displacements were discussed at different scales. Finally, the multiscale framework was demonstrated with a 3D nanoindentation problem. The displacements at different scales during nanoindentation were compared. A benchmark analysis was also carried out to determine crack opening displacement (COD) in an edge cracked graphene sample using FEA, PD and MD simulation. The results showed good agreement between PD and MD simulation but FEA results addressed to have comparatively higher COD values. The results from peridynamic based framework for hierarchical multiscale modeling showed reasonable agreement between PD and atomistic models.Show more