Eshelby Mori Tanaka Approach Research Articles

Active vibration control of metal foam reinforced agglomerated graphene nanoplatelets nanocomposite truncated conical shells with piezoelectric layers

This study examines active vibration control (AVC) in a truncated conical shell composed of metal foam reinforced with agglomerated graphene nanoplatelets and integrated with piezoelectric layers functioning as sensors and actuators. Both complete and partial agglomeration states are considered based on the Eshelby–Mori–Tanaka approach, and the mechanical properties of the porous core are characterized using a closed-cell metal foam model. The governing equations of motion are derived using Hamilton’s principle, based on the two-dimensional axisymmetric elasticity theory, and solved through the finite element method coupled with the Newmark method. Vibration mitigation is achieved using a fractional-order fuzzy proportional–integral–derivative (PID) controller. A comprehensive parametric study is conducted, examining the effects of geometric dimensions, various boundary conditions, reinforcement parameters (including weight fraction, distribution patterns, and agglomeration parameters), and porosity parameters (including pore size, and porosity pattern) on the vibration properties of the shell. Numerical simulations are performed to assess the effectiveness of the proposed AVC system in reducing structural vibrations compared to a constant velocity feedback control approach. The velocity feedback controller reduced central deflection from 12.65 to 5.089 μ m , while a fractional-order fuzzy PID controller further improved it to 2.348 μ m , representing a 53.86% enhancement over the velocity feedback controller.

Nonlinear Optimized PID Vibration Control of Thermal-Dependent FG Composite Porous Plates Reinforced by Agglomerated CNTs

This research study aims to delve into the effects of carbon nanotubes (CNTs) agglomeration on the dynamic characteristics of smart functionally graded (FG) porous sandwich plates. The structure of the sandwich plate comprises a core layer that incorporates dispersed CNTs within a polymer matrix. In addition, two layers are equipped with piezoelectric sensors and actuators. The agglomeration of CNTs is mathematically modeled using the Eshelby–Mori–Tanaka approach, accounting for both complete and partial agglomeration states. Moreover, the study takes into account the thermal-dependent behavior of CNTs. Subsequently, an optimal nonlinear proportional-integral-derivative (PID) control scheme based on the Bat optimization algorithm is applied to mitigate vibrations within the composite structure. Unlike the fixed gains of the classical PID, the nonlinear version dynamically adjusts its parameters in real time, ensuring enhanced responsiveness and stability. Furthermore, a comprehensive numerical investigation is conducted to assess the impact of several parameters on the natural frequencies in the frequency domain. These parameters encompass porosity distributions, porosity coefficients, reinforcement patterns, weight fractions of nanofillers, temperature, and the agglomeration of CNTs. The vibration attenuation performance of both nonlinear and classical PID controllers is evaluated through numerical simulations. The findings indicate the robustness and rapid disturbance rejection of the proposed control scheme.

Effects of non-uniformity in thickness and volume fraction of agglomerated CNTs on the dynamics of a spinning CNT-reinforced nanocomposite truncated conical shell

In the presented work, the free vibration analysis of a rotating truncated conical shell whose thickness varies in the meridional direction is examined. The material that the shell is made of is a polymeric matrix (epoxy) enriched with carbon nanotubes (CNTs) whose volume fraction varies in the meridional direction. CNTs agglomeration is considered and the density and elastic constants of such a two-phase nanocomposite are calculated sequentially based on the Eshelby–Mori–Tanaka approach alongside the rule of mixture. The conical shell is modeled using the first-order shear deformation theory (FSDT) including the relative acceleration, Coriolis acceleration, and centrifugal acceleration along with the initial hoop tension, and the governing equations are obtained utilizing Hamilton’s principle. The solution of governing equations is performed via the combination of an analytical solution in the circumferential direction and a numerical one in the meridional direction via the differential quadrature method (DQM). The impacts of several parameters on the forward and backward natural frequencies of such a rotating shell are studied such as chirality, mass fraction and dispersion pattern of the CNTs, thickness variation parameters, and boundary conditions. It is observed that higher natural frequencies and critical rotational speeds can be achieved for CNT-reinforced conical shells when the volume fraction of the CNTs and the thickness of the shell increase from its small radius to the large one.

Vibrational characteristics of fastening of a spherical shell with a coupled conical-conical shells strengthened with nanocomposite sandwiches contained agglomerated CNT face layers and GNP core under spring boundary conditions

The following paper is prepared to compute the Natural Frequency Parameters (NFPs) linked to the Fastened Spherical-Conical-Conical Shell (FSCCS) structures composted of Nanocomposite Sandwich (NS) materials under the effects of springs as Boundary Conditions (BCs). To explain, the NS material implemented here is made of three layers covering Top Face Layer (TFL), Bottom Face Layer (BFL), and Core Layer (CL). In addition, the TFL and BFL are composed of Carbon Nano Tube (CNT) nano-fillers with agglomeration characteristics, while the CL benefits from Graphene Nano Platelet (GNP) nano-materials. For more information, the mechanical values related to the Agglomerated Carbon Nano-Tube Nanocomposite (ACNTN) material composer the TFL and BFL (ACNTN-TFL and ACNTN-BFL) are carried out by the Eshelby-Mori-Tanaka Approach (EMTA). At the same time, the Halpin-Tsai Approach (HTA) is used to extract these values for GNP-CL. To add more, four different sandwich models are implemented by considering the compatibility between layers. Moreover, the First Order Shear Deformation Theory (FOSDT) and Donnell's Shell Theory (DST) are exploited to obtain the primary relationships of the FSCCS segments. Hamilton's strategy is also operated to derive the Governing Differential Equations (GDEs) of the FSCCS's components. Further, the well-systematized computational meshless method tagged the Generalized Differential Quadrature (GDQ) program is carried out to discrete the GDEs coupled with the structure's segments. Furthermore, the calculation of the eigenvalues is implemented to compute the NFPs of the FSCCS structure. After that, to credit the submitted program, the outputs related to the FSCCS calculated by the present framework are analogized with the responses linked to the FE-based commercial software. In the last, multiple examples are styled and computed to point to the influences of the different material, geometric, and BCs forms on the NFPs of the NS-FSCCS structures, including 12 different geometry types related to the NS-FSCCS.

Active control of nonlinear coupled transient vibrations of multifunctional sandwich plates with agglomerated FG-CNTs core/magneto-electro-elastic facesheets

This article investigates the controlled nonlinear transient response of sandwich plates made of magneto-electro-elastic (MEE) facesheets and agglomerated carbon nanotube (ACNT) core. The control is achieved by active constrained layer damping (ACLD) treatment which consists of piezoelectric (PE) and viscoelastic (VE) layers. The agglomeration is mathematically modelled using the Eshelby–Mori–Tanaka approach. The governing equations are derived under the framework of finite element (FE) methods using Hamilton’s principle and condensation technique. The VE patch of the ACLD treatment is modelled through the Golla–Hughes–McTavish method. This evaluation has considered two states of agglomerations, such as complete and partial agglomeration. The proposed FE model facilitates the integration of the three-field (magnetic, electric and elastic) coupling with the agglomeration and electromagnetic circuit effects, which makes this work interesting. It acts as a ready tool for the realistic design of a smart structure and system. In addition, the computational efforts and efficiency of the proposed FE model prove to be better than the commercial numerical software. Extensive numerical examples are solved to assess the influence of CNT distributions, electromagnetic circuits, coupling, mechanical boundary conditions, thickness configuration and ACLD patch position. This work serves as a novel benchmark solution for further research on the active control of agglomerated CNT structures.

Bending response analysis of a laminated, tapered, curved, composite panel made from an agglomerated and wavy MWCNT–glass fiber–polymer hybrid

The work investigates the influence of multiwalled carbon nanotubes (MWCNTs) on the bending behavior of laminated, spherical, cylindrical, hyperbolic, and elliptical tapered composite panels made from a MWCNT–glass fiber–polymer hybrid and subjected to transverse loading conditions. The deflection and stress behavior of the composite panels were studied by developing a mathematical model based on high-order shear deformation theory using finite element (FE) formulation. In this context, the agglomeration and waviness of MWCNTs were modeled and characterized using the Eshelby–Mori–Tanaka approach and a continuum mechanics based 3-D representative volume element (RVE), respectively. Subsequently, glass fiber was introduced as a reinforcement phase, and the elastic properties of the three-phase hybrid composite material were obtained using the Chamis model. The developed FE formulation was validated theoretically and experimentally. Further, detailed parametric studies were performed to examine the influence of micromechanical and structural characteristics such as weight fraction of MWCNTs, weight fraction of fiber, type of load, taper configuration, curved geometry, curvature ratio, and length to thickness ratio of the panel on the bending behavior of the composite panels. The effective laminated tapered curved composite panel, TC-3, tailored with improved MWCNT characteristics, can substantially resist the stresses from a bending load.

Damage Modeling of Solid Oxide Fuel Cells Accounting for Redox Effects

This paper applies a multiscale mechanistic damage model developed for porous brittle ceramics and implemented in finite element analysis (FEA) packages [1] to study progressive damage in solid oxide fuel cells (SOFC) subjected to thermomechanical loading under operating and shutdown states. The damage model captures the micromechanics of stiffness reduction due to material porosity change and microcracking and integrates the as-obtained stiffness reduction law into a continuum damage mechanics (CDM) formulation for the evolution of microcracks up to fracture. An Eshelby-Mori-Tanaka approach (EMTA) [2-3] is first used to model the ceramic containing pores and aligned microcracks regarded as inclusions with negligible stiffness. The stiffness of the actual porous ceramic is obtained from the EMTA solution averaged over all possible microcrack orientations using an orientation averaging method. The evolution of microcracking damage is described by a CDM formulation derived from our previous model [4]. Apart from the operating and shutdown states, additional damage that may occur due to reduction and re-oxidation (redox cycling) of Ni/YSZ anodes is also studied. The reduction of NiO into Ni leads to changes in volume and porosity of the anode layer that consequently change its physical and thermomechanical properties. The volume change or volumetric “swelling” during redox cycling may affect the structural integrity of the anode and may cause fracture of the electrolyte under high tensile stresses leading to operational failure for SOFCs. In the constitutive relations, volumetric swelling is treated in a similar way to thermal expansion using the models developed in Refs [5-6] for fusion energy ceramic materials. However, while thermal expansion vanishes if temperature change tends to zero, swelling is irreversible and significantly contributes to degrade SOFC stacks during redox cycling.This damage model was implemented in the commercial FEA software ABAQUS© and ANSYS© via user subroutines. First, it has been validated through predictions of strength and stress-strain response for the typical SOFC ceramic materials. Figs 1(a) and 1(b) show the predicted stress-strain responses as a function of temperature for dense NiO/YSZ and Ni/YSZ, respectively. These figures also illustrate the predicted responses at 750°C with prescribed initial values of porosity. The damage model predicts significant reductions in strength and elastic modulus with higher initial porosity and higher temperatures, and the predicted trends are in good agreement with the experimental findings [7-8].Next, the damage model was applied to predict the potential for degradation in a generic planar SOFC stack with large active area cells modeled in ANSYS. Stack models with single and multi-cells were simulated in both co-flow and counter-flow configurations. The thermomechanical loads representing the operating and shutdown conditions were simulated. The realistic thermal gradients that occur in an operating stack were imposed in the models by solving the electrochemistry under various operating conditions using the in-house SOFC multiphysics code (SOFC MP-3D) [9-10]. In addition to the operating and shutdown conditions, a constant temperature redox cycle was also simulated to capture overall cell electrode damage due to volumetric swelling of the Ni/YSZ anode in the anode supported cells. The results from single cell stack models showed little damage at operating and shutdown conditions which could be attributed to enough out-of-plane support for the PEN assembly. The results from the multicell stacks (Fig. 2) showed higher damage in counter-flow configuration. Within the stack, the top cells experienced the highest damage and the middle cells experienced the lowest. Overall, no significant damage that may lead to total failure of the cells was observed in the multicell stack models with the operating conditions considered in this study.

Optimization of CNT/polymer/fiber laminated truncated conical panels for maximum fundamental frequency and minimum cost

This paper is presented to study the free vibration analysis and optimization of CNT/polymer/fiber laminated truncated conical panels. Each layer of the panel is composed of a polymeric matrix reinforced with oriented fibers along with uniformly distributed and randomly oriented agglomerated carbon nanotubes (CNTs). The panel is modeled based on the first-order shear deformation theory (FSDT) and the effective mechanical properties are estimated using the Eshelby–Mori–Tanaka approach, Hahn’s homogenization method, and the rule of mixture. The governing equations are derived utilizing Hamilton’s principle and are solved numerically via the differential quadrature method (DQM). An optimization problem is provided via particle swarm optimization (PSO) and the optimum orientations of the fibers and best values of weight fractions of the CNTs and fibers are found to increase the fundamental frequency and reduce the relative cost of such structure. It is concluded that the optimum design of the panel is strongly affected by the chirality of the CNTs and the boundary conditions.

A predictive modeling tool for damage analysis and design of hydrogen storage composite pressure vessels

In this paper, a predictive modeling tool is developed for damage analysis and design of hydrogen (H2) storage composite pressure vessels. It integrates micromechanics of matrix cracking into a continuum damage mechanics (CDM) description for damage evolution, and three-dimensional (3D) finite element (FE) modeling of the vessel structural response. At the scale of the composite layer (mesoscale), the temperature-dependent stiffness reduction law in terms of the damage variable for transverse matrix cracking is computed using an Eshelby-Mori-Tanaka approach (EMTA) for the initial composite thermoelastic properties and a self-consistent model for the stiffness reduction as a function of the damage variable. While transverse matrix cracking obeying a damage evolution relation can progressively evolve from an initiation to a saturation state, fiber failure is predicted by a micromechanical fiber rupture criterion that accounts for the fiber strength and matrix stress that can be computed within EMTA. The implementation of this integrated multiscale modeling model into a 3D FE formulation enables damage analysis and design of H2 storage composite pressure vessels. The developed tool is illustrated through 3D damage analyses of a cryogenically compressed H2 storage vessel model subjected to thermomechanical loadings to investigate effects of the helical layer fiber orientation and loading scenario on damage development, vessel integrity and burst pressure.

An Assessment of Thick Nanocomposite Plates’ Behavior under the Influence of Carbon Nanotubes Agglomeration

The influence assessment of carbon nanotubes (CNTs) agglomeration on CNT-reinforced composite (CNTRC) thick plates’ behavior is the main aim of the present work. CNTs are known to agglomerate into clusters even for relatively low volume fractions, which imposes the need to characterize the effects this may introduce in structures behavior, also knowing that recent works have concluded that neglecting agglomeration phenomenon may lead to an overestimation of the mechanical properties of nanocomposites. Hence, it matters to understand how the arising of these clusters may affect the static and free vibrational behaviors of low side-to-thickness nanocomposite plates. To this purpose, the nanocomposite plate properties’ estimation is performed by using the two-parameter model of agglomeration based on the Eshelby–Mori–Tanaka approach, while for behavioral analyses one considers a Higher-order Shear Deformation Theory (HSDT) based on the displacement field of Kant, implemented through the finite element method. The analyses developed consider a set of parametric studies involving the assessment of the influence of side-to-side ratios, side-to-thickness ratios, boundary conditions, and CNTs’ distributions along the thickness. The results obtained allow concluding that the transverse deflections and fundamental frequencies of these structures are significantly influenced by the CNTs’ agglomeration.

A Study on the Effect of Carbon Nanotubes’ Distribution and Agglomeration in the Free Vibration of Nanocomposite Plates

The present work aimed to characterize the free vibrations’ behaviour of nanocomposite plates obtained by incorporating graded distributions of carbon nanotubes (CNTs) in a polymeric matrix, considering the carbon nanotubes’ agglomeration effect. This effect is known to degrade material properties, therefore being important to predict the consequences it may bring to structures’ mechanical performance. To this purpose, the elastic properties’ estimation is performed according to the two-parameter agglomeration model based on the Eshelby–Mori–Tanaka approach for randomly dispersed nano-inclusions. This approach is implemented in association with the finite element method to determine the natural frequencies and corresponding mode shapes. Three main agglomeration cases were considered, namely, agglomeration absence, complete agglomeration, and partial agglomeration. The results show that the agglomeration effect has a negative impact on the natural frequencies of the plates, regardless the CNTs’ distribution considered. For the corresponding vibrations’ mode shapes, the agglomeration effect was shown in most cases not to have a significant impact, except for two of the cases studied: for a square plate and a rectangular plate with symmetrical and unsymmetrical CNTs’ distribution, respectively. Globally, the results confirm that not accounting for the nanotubes’ agglomeration effect may lead to less accurate elastic properties and less structures’ performance predictions.

An analytical study on the nonlinear forced vibration of functionally graded carbon nanotube-reinforced composite beams on nonlinear viscoelastic foundation

This paper deals with the nonlinear forced vibration of nanocomposite beams resting on a nonlinear viscoelastic foundation and subjected to a transverse periodic excitation. It is considered that the functionally graded carbon nanotubereinforced composite (FG-CNTRC) beam is made of an isotropic matrix reinforced by either aligned- or randomly oriented-straight single-walled carbon nanotubes (SWCNTs) with four types of distributions through the thickness direction of the beam. Both the Eshelby–Mori–Tanaka approach and extended rule of mixtures are used to predict the effective material properties of the FG-CNTRC beams. The mathematical model of the beam is developed based on the Euler–Bernoulli beam theory together with von Karman assumptions. Subsequently, the accurate analytical solutions of the governing equation are obtained through applying the variational iteration method (VIM). Several examples are verified to have higher accuracy than those available in the literature. In addition, a comprehensive investigation into the effect of carbon nanotubes (CNTs) distribution, CNTs volume fraction, end supports, vibration amplitude, and foundation coefficients on the vibrational characteristics of the nanocomposite beam is performed and some new results are presented.

Application of smart electro-rheological dampers in semi-active control of electro-rheological sandwich plates with nanocomposite facesheets rested on orthotropic visco-Pasternak foundation

In this research, semi-active control of sandwich plates with electro-rheological (ER) core and carbon nanotubes-reinforced composite facesheets using smart ER dampers is studied. Sandwich plate is subjected to the external electric field and rested on orthotropic visco-Pasternak foundation. The material properties of ER core and nanocomposite facesheets are obtained by Yalcintas model and Eshelby–Mori–Tanaka approach, respectively. The governing equations of motion are solved by a combination between finite element and Newmark methods for clamped and simply supported boundary condition. The effects of various parameters such as applied voltage, controlled electric field and initial gap of the electrodes on the vibration suppression time are discussed. The results show that the settling time of system introduced in this work is much less than previous researches in this field which is a very important advantage.

Electric field effect on dynamic analysis of smart porosity-dependent nanocomposite sandwich plate resting on silica aerogel foundation considering carbon nanotubes agglomeration

In this study, the influence of carbon nanotubes agglomeration is investigated on the electroelastic dynamic behavior of a sandwich plate. The smart sandwich plate consists of functionally graded porous layer as the core and piezoelectric layers as the face sheets, which is subjected to the harmonic electrical loading. In order to take into account the continuum model for the silica aerogel foundation of the smart structure, the modified Vlasov’s model is applied. The porosity distribution of the core layer varies non-uniformly throughout the thickness due to the non-uniform function. The equivalent material properties of nanocomposite core layer are determined using the Eshelby–Mori–Tanaka approach, in which the influence of carbon nanotube agglomeration is considered. For modeling the electroelastic fact sheets behavior, the piezoelasticity theory is adopted. On the basis of non-polynomial shear and normal deformation theory, the governing equations of motion are inferred applying the Hamilton’s principle and the obtained equations are solved by an iterative procedure. The verification is accomplished through the available results in the literature and the influences of carbon nanotube agglomeration, different geometrical parameters, porosity index, and applied voltage are assessed on the dynamic deflection of nanocomposite sandwich plate.

Nonlinear vibration and modal analysis of FG nanocomposite sandwich beams reinforced by aggregated CNTs

In the present work, by considering the aggregation effect of single‐walled carbon nanotubes (SWCNT), the nonlinear vibration of functionally graded (FG) nanocomposite sandwich Timoshenko beams resting on Pasternak foundation are presented. The material properties of the FG nanocomposite sandwich beam are estimated using the Eshelby–Mori–Tanaka approach and differential quadrature method (DQM) is used to obtain natural frequency. The nonlinear governing equations and boundary conditions are derived using the Hamilton principle and von Kármán geometric nonlinearity. The higher order nonlinear governing equations and boundary conditions are calculated using the Hamilton principle. A direct iterative method is employed to determine the nonlinear frequencies and mode shapes of the beams. It is shown that the mechanical properties and therefore vibration of functionally graded carbon nanotube reinforced (FG‐CNTR) sandwich beams are severely affected by CNTs aggregation. A detailed parametric study is carried out to investigate the influences of Winkler foundation modulus, shear elastic foundation modulus, length to span ratio, thicknesses of face sheets on the nonlinear vibration of the structure. POLYM. ENG. SCI., 59:1362–1370 2019. © 2019 Society of Plastics Engineers

Vibrational analysis of sandwich sectorial plates with functionally graded sheets reinforced by aggregated carbon nanotube

In the present work, by considering the agglomeration effect of single-walled carbon nanotubes, free vibration characteristics of functionally graded nanocomposite sandwich sectorial plates are presented. The volume fractions of randomly oriented agglomerated single-walled carbon nanotubes are assumed to be graded in the thickness direction. To determine the effect of carbon nanotube agglomeration on the elastic properties of carbon nanotube-reinforced composites, a two-parameter micromechanical model of agglomeration is employed. In this research work, an equivalent continuum model based on the Eshelby–Mori–Tanaka approach is considered to estimate the effective constitutive law of the elastic isotropic medium (matrix) with oriented straight carbon nanotubes. The two-dimensional generalized differential quadrature method as an efficient and accurate numerical tool is used to discretize the equations of motion and to implement the various boundary conditions. The proposed sectorial plates are simply supported at radial edges, while all possible combinations of free, simply supported, and clamped boundary conditions are applied to the other two circular edges. The benefit of using the considered power-law distribution is to illustrate and present useful results arising from symmetric and asymmetric profiles. The effects of agglomeration, geometrical, and material parameters together with the boundary conditions on the frequency parameters of the sandwich functionally graded nanocomposite plates are investigated. It is shown that the natural frequencies of structure are seriously affected by the influence of carbon nanotubes agglomeration. This study serves as a benchmark for assessing the validity of numerical methods or two-dimensional theories used to analyze the sandwich sectorial plates.

Big data in nanocomposites: ONN approach and mesh-free method for functionally graded carbon nanotube-reinforced composites

Abstract In this paper, the concept of big data in composite materials for design purpose with focus on functionally graded carbon nanotube reinforced composites (FG-CNTRC) has been addressed through mesh-free method and an optimized neural network (ONN) approach. With this regard, mesh-free method as a robust technique was used to analyze the FG-CNTRC for vibrational frequency. The applied nanocomposite is made of aggregated single-walled carbon nanotubes (CNTs) that are embedded in an isotropic polymer as matrix. The material properties are estimated based on the Eshelby–Mori–Tanaka approach. Then a new multi-step approach was used to find optimized neural network for accurate modeling of the nanocomposite which can be used for later goals of optimization and design. Computational time and accuracy of various algorithms were investigated and compared for big data modeling of nanocomposite to come up with the optimal model. Comparative study of the results was carried out to examine and compare the accuracy of the developed ONN model relative to mesh-free method. Furthermore, a comprehensive parametric study was also performed to investigate the effect of geometrical dimensions, CNT distribution and volume fraction on vibrational frequency of the nanocomposite. Highlights Big data in nanocomposites. Analysis of nanocomposite through mesh-free method. Optimized neural network (ONN) for big data mining. Multi-step approach for finding an optimized model. Efficiency of ONN to handle big data.

Bending analysis of agglomerated carbon nanotube-reinforced beam resting on two parameters modified Vlasov model foundation

The present work deals with bending behavior of nanocomposite beam resting on two parameters modified Vlasov model foundation (MVMF), with consideration of agglomeration and distribution of carbon nanotubes (CNTs) in beam matrix. Equivalent fiber based on Eshelby–Mori–Tanaka approach is employed to determine influence of CNTs aggregation on elastic properties of CNT-reinforced beam. The governing equations are deduced using the principle of minimum potential energy under assumption of the Euler–Bernoulli beam theory. The MVMF required the estimation of γ parameter; to this purpose, unique iterative technique based on variational principles is utilized to compute value of the γ and subsequently fourth-order differential equation is solved analytically. Eventually, the transverse displacements and bending stresses are obtained and compared for different agglomeration parameters, various boundary conditions simultaneously and variant elastic foundation without requirement to instate values for foundation parameters.

Free vibration analysis of nanocomposite sandwich plates reinforced with CNT aggregates

AbstractIn this article, free vibration analysis of simply supported sandwich plates with a flexible core and two functionally graded nanocomposite face sheets resting on two‐parameter elastic foundation is carried out using Navier's solution. The nanocomposite face sheets are reinforced by randomly oriented and aggregated carbon nanotube (CNT). The material properties of the nanocomposites plates are graded along the thickness and are estimated though the Eshelby–Mori–Tanaka approach. In the proposed theory, 3‐D elasticity theory and first order shear deformation theory are used for core and face sheets, respectively. Also, Hamilton's variational principle is used to derive the equations of motion.

Three-dimensional analysis of a faulted CO2 reservoir using an Eshelby-Mori-Tanaka approach to rock elastic properties and fault permeability

This work develops a three-dimensional (3D) multiscale model to analyze a complex carbon dioxide (CO2) faulted reservoir that includes some key geologic features of the San Andreas and nearby faults southwest of the Kimberlina site. The model uses the STOMP-CO2 code for flow modeling that is coupled to the ABAQUS® finite element package for geomechanical analysis. A 3D ABAQUS® finite element model is developed that contains a large number of 3D solid elements with two nearly parallel faults whose damage zones and cores are discretized using the same continuum elements. Five zones with different mineral compositions are considered: shale, sandstone, fault damaged sandstone, fault damaged shale, and fault core. Rocks' elastic properties that govern their poroelastic behavior are modeled by an Eshelby–Mori–Tanaka approach (EMTA), which can account for up to 15 mineral phases. The permeability of fault damage zones affected by crack density and orientations is also predicted by an EMTA formulation. A STOMP-CO2 grid that exactly maps the ABAQUS® finite element model is built for coupled hydro-mechanical analyses. Simulations of the reservoir assuming three different crack pattern situations (including crack volume fraction and orientation) for the fault damage zones are performed to predict the potential leakage of CO2 due to cracks that enhance the permeability of the fault damage zones. The results illustrate the important effect of the crack orientation on fault permeability that can lead to substantial leakage along the fault attained by the expansion of the CO2 plume. Potential hydraulic fracture and tendency for the faults to slip are also examined and discussed in terms of stress distributions and geomechanical properties.