Cell Method Research Articles

Micromechanical modeling of thermal conductivities of unidirectional carbon fiber/epoxy composites containing carbon nanotube/graphene hybrids

This article deals with the micromechanical modeling of thermal conductivities of the unidirectional carbon fiber (CF)-reinforced composites with carbon nanotube (CNT)/graphene nanoplatelet (GNP)-enriched epoxy matrix. The thermal conductivity of epoxy-based nanocompounds enriched through the incorporation of CNT/GNP hybrids is estimated within the framework of micromechanics. The significant contribution of several microstructures, including the volume fraction, dimension, and straightness of nanofillers, thermal resistance at the interface of the nanofillers and epoxy matrix, and the percolation effect on the nanocomposite thermal conductivity is considered. Furthermore, the method of cells (MOC) is used to anticipate the axial and transverse thermal conductances of unidirectional composites featuring CFs integrated into the CNT/GNP-enriched polymer nanocomposite matrix. The results reveal that incorporating a combination of GNTs and CNTs into the polymer matrix significantly increases the transverse thermal conduction of the multiphase compound. Several factors contribute to improved thermal conductance of the transverse direction in CF/CNT/GNP composites: (i) higher nanofiller concentration, (ii) presence of straight nanofillers, and (iii) use of larger nanofillers. The predictions of micromechanical modeling give good agreement with available experiments. This study compares the transverse and axial thermal conductivity of unidirectional compounds predicted by MOC method with results obtained using the finite element method.

A Comparative Study of Micromechanical Analysis Models for Determining the Effective Properties of Out-of-Autoclave Carbon Fiber-Epoxy Composites.

This study aims to critically assess different micromechanical analysis models applied to carbon-fiber-reinforced plastic (CFRP) composites, employing micromechanics-based homogenization to accurately predict their effective properties. The paper begins with the simplest Voigt and Reuss models and progresses to more sophisticated micromechanics-based models, including the Mori-Tanaka and Method of Cells (MOC) models. It provides a critical review of the areas in which these micromechanics-based models are effective and analyses of their limitations. The numerical analysis results were confirmed through finite element simulations of the periodic representative volume element (RVE). Furthermore, the effective properties predicted by these micromechanics-based models were validated via experiments conducted on IM7/5320-1 composite material with a fiber volume fraction of 0.62.

A Novel Neural Network Cell Method for Solving Nonlinear Electromagnetic Problems (Adv. Theory Simul. 12/2021)

Numerical-Intelligent Coupled Model for Nonlinear Problems In article number 2100216, Longnv Li and co-workers propose a NNCM coupling neural network (NN) and cell method (CM) for the effective calculation of nonlinear electromagnetic fields in ferromagnetic regions. The NNCM model the nonlinearities with partially connected NNs and construct the linearities through CM to guarantee both the training and the computing efficiencies.

A Novel Neural Network Cell Method for Solving Nonlinear Electromagnetic Problems

AbstractEffective analysis of nonlinear electromagnetic fields is essential for the accurate modeling of electromagnetic devices, such as transformers, generators, and motors. This paper proposes a novel approach of coupled neural network (NN) and cell method (CM) or NNCM for solving nonlinear electromagnetic problems with ferromagnetic domains. While the topologically linear relations of the cell complexes are mathematically assembled through a transformation in the Tonti diagram by the CM, and the constitutive nonlinear magnetic relations are dealt with by partially connected NN for the fast prediction of the permeability distribution inside the ferromagnetic domain. Since the construction of NN is directly related to the grid connections, a partially connected NN structure with a small number of neurons can reduce the computational cost of the training process. By using a compact NN, the proposed NNCM can effectively eliminate the time consuming iterations for determining the nonlinear permeability distribution, and improve the computational efficiency significantly. The NNCM is employed to analyze the transient electromagnetic field distribution inside a cylindrical ferromagnetic core. The results are compared with those obtained by the traditional iterative CM, which determines the nonlinear permeability distribution by lengthy numerical iterations, to verify the feasibility and effectiveness of the proposed NNCM.

An effective educational tool for straightforward learning of numerical modeling in engineering electromagnetics

Abstract“Engineering Electromagnetics” is the “most familiar stranger” of college students who major in electrical engineering (EE). Through years of physics learning, the students have had a certain understanding of the basic theories of electromagnetic fields. However, during studying the course, especially the numerical modeling chapter, large‐scale mathematical derivations need to be conducted, which significantly enhance the difficulty for students. The cell method (CM) is a newly established numerical method based on the direct derivation of physical laws in cell‐complexes, and the physical meanings of the equations are clear and definite. By establishing and applying the education platform based on CM, the students' cognition and mastery of electromagnetic theories and numerical techniques can be deepened substantially. In this paper, the electromagnetic field is mathematically modeled based on CM, and the related transformations in the dual cell complexes are illustrated through the Tonti diagram in class. The simulation platform for electromagnetic fields based on CM is established by coding mathematical models. After teaching the methodologies, students are asked to numerically simulate two static field problems with simple geometric structures by using the methodologies, and the results show that they can better understand and perform in numerically related courses based on CM compared with the performances of former students taught with the finite element method. A questionnaire is utilized to survey the teaching effectiveness, and the students' satisfaction is validated by the questionnaire survey. Finally, the methodologies are employed to analyze the electric and magnetic field of two complex engineering cases, and the students can better understand the use of the numerical methods by analysis. Through the numerical simulations based on CM, the students' ability to apply numerical algorithms to solve complex engineering cases is cultivated, and teaching effectiveness of the numerical analysis chapter in Engineering Electromagnetics is enriched.

Optimizing the recovery of peripheral blood mononuclear cells trapped in leukoreduction filters - A comparison study

IntroductionThe isolation of captured peripheral blood mononuclear cells (PBMNCs) from leukoreduction filters (LRFs) can be of great importance in terms of bringing the lost cells back into use. ObjectiveThe aim of this study was to evaluate various methods based on their potential to recover the peripheral blood cells from LRFs with a focus on mononuclear cells (MNCs). MethodFor cell isolation from LRFs, three distinct methods (back-flushing, direct and vacuum pump) were compared through the calculation of the yield of isolated MNCs. The viability of extracted cells was determined by the flow cytometry technique. Moreover, the recovered MNCs were characterized regarding the presence of blood stem cell purification. The cell culture, microscopic observation, and immunophenotyping were employed to characterize the blood stem cells (hematopoietic, mesenchymal and progenitor endothelial stem cells). ResultsThe yield of isolation obtained in the back-flushing, direct and vacuum pump methods were 17.7 ± 1.28, 17.3 ± 0.96 and 21.2 ± 0.90 percent, respectively. Although the highest potential for total blood cell recovery belonged to the vacuum pump method, the lowest cell viability (85.73 ± 4.84%) was observed in this method. However, the isolation process of the back-flushing and direct methods had less effect on cell viability. The characterization of the isolated MNCs displayed that the dominant positive phenotype was for CD34/CD45, indicating hematopoietic stem cells. In addition, the endothelial stem/progenitor cells were significantly detected as CD31/CD133 positive cells. ConclusionAccording to our results and considering the safety and efficiency potential of each of the applied methods, the back-flushing in comparison with the other methods can be considered a suitable procedure for MNC isolation from LRFs.

DECM: A Discrete Element for Multiscale Modeling of Composite Materials Using the Cell Method.

This paper presents a new numerical method for multiscale modeling of composite materials. The new numerical model, called DECM, consists of a DEM (Discrete Element Method) approach of the Cell Method (CM) and combines the main features of both the DEM and the CM. In particular, it offers the same degree of detail as the CM, on the microscale, and manages the discrete elements individually such as the DEM—allowing finite displacements and rotations—on the macroscale. Moreover, the DECM is able to activate crack propagation until complete detachment and automatically recognizes new contacts. Unlike other DEM approaches for modeling failure mechanisms in continuous media, the DECM does not require prior knowledge of the failure position. Furthermore, the DECM solves the problems in the space domain directly. Therefore, it does not require any dynamic relaxation techniques to obtain the static solution. For the sake of example, the paper shows the results offered by the DECM for axial and shear loading of a composite two-dimensional domain with periodic round inclusions. The paper also offers some insights into how the inclusions modify the stress field in composite continua.

Short Review on the Advancement of Osteoarthritis Treatment with Cell Therapy

Osteoarthritis has huge impact on medical care system and finance as its large patient populations and its increasing contribution to the chronic disability in age population. Increasing effort to develop new treatment of osteoarthritis with cell therapy is being made. In this paper, we review cell sources, inclusion criteria and delivery methodof cell therapy for osteoarthritis in the current clinical studies, and discuss the possibility to improve the clinical outcome.

The Time-Domain Cell Method Is a Coupling of Two Explicit Discontinuous Galerkin Schemes With Continuous Fluxes

The cell method (CM) or discrete geometric approach (DGA) in the time domain, already introduced by Codecasa et al. in 2008 for the coupled Ampere-Maxwell and Faraday equations, is here recast as a Galerkin Method similar to the finite-element method (FEM). In particular, it is shown to be a mixed method comprising an explicit scheme and two discontinuous Galerkin (DG) FEM spaces formulated on dual meshes, in which each of the two function spaces provides a continuous numerical flux choice for its dual mesh counterpart. The implemented version is shown to compare favorably in terms of accuracy and efficiency with respect to the classic conforming FEM scheme using Whitney elements. When tested on the same tetrahedral mesh, the Courant-Friedrichs-Lewy (CFL) condition for the proposed approach is a factor of 2 less restrictive on the time step with respect to the curl-conforming FEM scheme.

Thermal Analysis of a Magnetic Brake Using Infrared Techniques and 3D Cell Method with a New Convective Constitutive Matrix.

In this work we analyse the temperature distribution in a conductor disk in transitory regime. The disk is in motion in a stationary magnetic field generated by a permanent magnet and so, the electric currents induced inside it generate heat. The system acts as a magnetic brake and is analysed using infrared sensor techniques. In addition, for the simulation and analysis of the magnetic brake, a new thermal convective matrix for the 3D Cell Method (CM) is proposed. The results of the simulation have been verified by comparing the numerical results with those obtained by the Finite Element Method (FEM) and with experimental data obtained by infrared technology. The difference between the experimental results obtained by infrared sensors and those obtained in the simulations is less than 0.0459%.

Applying a micromechanics approach for predicting thermal conducting properties of carbon nanotube-metal nanocomposites

Heat dissipation is a very important issue in the harsh thermal loads affecting the reliability of structures. In this study, the thermal conducting behavior of carbon nanotube (CNT)-reinforced metal matrix nanocomposites (MMNCs) has been analyzed using a micromechanical model based on the method of cell (MOC) approach. The critical role of interfacial thermal resistance between the CNT and metal matrix in the MMNC thermal conducting response has been extensively explored. Also, the effects of volume fraction, length, diameter and curvature of CNTs have been investigated. It has been found that forming a perfect CNT/matrix interface contact would enhance remarkably the overall thermal conductivities. Generally, the axial thermal conductivity of the CNT-reinforced MMNCs can be increased with (i) rising CNT length and (ii) using straight CNTs. Moreover, the transverse thermal conductivity of these nanocomposite materials are improved with (i) rising CNT diameter and (ii) using wavy CNTs. Besides, increasing CNT volume fraction leads to a significant increment in the effective thermal conductivities in the presence of a perfect bonding at the CNT/matrix interface. Effective thermal conductivities of the MMNCs estimated by the MOC approach have been compared with those predicted by the effective medium and Halpin-Tsai models. A quite good agreement has been observed between the predictions of the MOC approach and experimental data.

A 3-D Hybrid Cell Boundary Element Method for Time-Harmonic Eddy Current Problems on Multiply Connected Domains

A novel 3-D hybrid formulation for time-harmonic eddy current problems in multiply connected domains is presented. The interior problem (in conductive regions) is discretized by the cell method (CM) in terms of magnetic vector potentials a, whereas the exterior problem (in the unbounded air domain) is discretized by the boundary element method (BEM) in terms of reduced scalar potentials ${\varphi }_{r}$ . Novel topological constraints are derived from magnetostatic energy conservation by using a decomposition of the magnetic field which minimizes the support and the number of cohomology generators. A fast algebraic procedure to pre-compute source fields to handle efficiently current-driven coils is also proposed. The final matrix system can be solved in a limited number of iterations by transpose-free quasi-minimal residual method with symmetric successive over-relaxation preconditioning. Convergence tests show that numerical results are in a very good agreement with third-order finite element method (FEM) on a 2-D axisymmetric model. The CM-BEM with piecewise uniform approximation shows also to be very effective when analyzing fully 3-D test cases, since second-order FEM accuracy is attained even with coarse mesh refinements, by using, however, a much lower number of degrees of freedom compared to FEM.

A face-smoothed cell method for static and dynamic piezoelectric coupled problems on polyhedral meshes

Low-order discretization schemes are suitable for modeling 3-D multiphysics problems since a huge number of degrees of freedom (DoFs) is typically required by standard high-order Finite Element Method (FEM). On the other hand, polyhedral meshes ensure a great flexibility in the domain discretization and are thus suitable for complex model geometries. These features are useful for the multiphysics simulation of micro piezoelectric devices with a thin multi-layered and multi-material structure. The Cell Method (CM) is a low-order discretization scheme which has been mainly adopted up to now for electromagnetic problems but has not yet been used for mechanical problems with polyhedral discretization. This work extends the CM to piezo-elasticity by reformulating local constitutive relationships in terms of displacement gradient. In such a way, piecewise uniform edge basis functions defined on arbitrary polyhedral meshes can be used for discretizing local constitutive relationships. With the CM matrix assembly is completely Jacobian-free and do not require Gaussian integration, reducing code complexity. The smoothing technique, firstly introduced for FEM, is here extended to CM in order to avoid shear locking arising when low-order discretization is used for thin cantilevered beams under bending. The smoothed CM is validated for static and dynamic problems on a real test case by comparison with both second-order FEM and experimental data. Numerical results show that accuracy is retained even if a much lower number of DoFs is required compared to FEM.

On the Relationship between Primal/Dual Cell Complexes of the Cell Method and Primal/Dual Vector Spaces: an Application to the Cantilever Elastic Beam with Elastic Inclusion

Abstract The Cell Method (CM) is an algebraic numerical method based on the use of global variables: the configuration, source and energetic global variables. The configuration variables with their topological equations, on the one hand, and the source variables with their topological equations, on the other hand, define two vector spaces that are a bialgebra and its dual algebra. The operators of these topological equations are generated by the outer product of the geometric algebra, for the primal vector space, and by the dual product of the dual algebra, for the dual vector space. The topological equations in the primal cell complex are coboundary processes on even exterior discrete p−forms, whereas the topological equations in the dual cell complex are coboundary processes on odd exterior discrete p−forms. Being expressed by coboundary processes in two different vector spaces, compatibility and equilibrium can be enforced at the same time, with compatibility enforced on the primal cell complex and equilibrium enforced on the dual cell complex. By way of example, in the present paper compatibility and equilibrium are enforced on a cantilever elastic beam with elastic inclusion. In effect, the CM shows its maximum potentialities right in domains made of several materials, as, being an algebraic approach, can treat any kind of discontinuities of the domain easily.

Indirect Coupling of the Cell Method and BEM for Solving 3-D Unbounded Magnetostatic Problems

A novel hybrid approach for solving magnetostatic problems with an unbounded air domain is presented. The basic idea is to use augmented dual grids for interfacing the cell method (CM) and Boundary Element Method by indirect coupling, introducing equivalent surface field sources. The field problem in bounded domains is discretized by the CM in terms of integral variables, i.e., line integrals of the magnetic vector potential. Boundary integral conditions, formulated with the reduced magnetic scalar potential, are applied to avoid the air region meshing. A mixed final symmetric algebraic system, which can be solved by fast iterative solvers, such as Minimal Residual Method or SYMMLQ, is finally obtained. The magnetic field in the air region is then easily reconstructed from the equivalent sources. Numerical tests show that the hybrid method is accurate even by using a collocation approach for discretizing the boundary integral conditions.

The Cell Method: An Overview on the Main Features

Abstract The Cell Method (CM) is a computational tool that maintains critical multi-dimensional attributes of physical phenomena in analysis. This information is neglected in the differential formulations of the classical approaches of finite element, boundary element, finite volume, and finite difference analysis, often leading to numerical instabilities and spurious results. This paper highlights the central theoretical concepts of the CM that preserve a more accurate and precise representation of the geometric and topological features of variables for practical problem solving. Important applications occur in fields such as electromagnetics, electrodynamics, solid mechanics and fluids. CM addresses non-locality in continuum mechanics, an especially important circumstance in modelling heterogeneous materials.

Effective Thermal Conductivities of a Novel Fuzzy Fiber-Reinforced Composite Containing Wavy Carbon Nanotubes

This article deals with the investigation of the effect of carbon nanotube (CNT) waviness on the effective thermal conductivities of a novel fuzzy fiber-reinforced composite (FFRC). The distinctive feature of the construction of this novel FFRC is that wavy CNTs are radially grown on the circumferential surfaces of the carbon fibers. Effective thermal conductivities of the FFRC are determined by developing the method of cells (MOCs) approach in conjunction with the effective medium (EM) approach. The effect of CNT waviness is studied when wavy CNTs are coplanar with either of the two mutually orthogonal planes of the carbon fiber. The present study reveals that (i) if CNT waviness is parallel to the carbon fiber axis then the axial (K1) and the transverse (K2) thermal conductivities of the FFRC are improved by 86% and 640%, respectively, over those of the base composite when the CNT volume faction present in the FFRC is 16.5% and the temperature is 400 K, (ii) the effective value of K1 of the FFRC containing wavy CNTs being coplanar with the carbon fiber axis is enhanced by 75% over that of containing straight CNTs for the fixed CNT volume faction when the temperature is 400 K, and (iii) the CNT/polymer matrix interfacial thermal resistance does not affect the effective thermal conductivities of the FFRC. The present work also reveals that for a particular value of the CNT volume fraction, optimum values of the CNT waviness parameters, such as the amplitude and the wave frequency of the CNT for improving the effective thermal conductivities of the FFRC can be estimated.

Micromechanics of piezoelectric fuzzy fiber-reinforced composite

A novel continuous unidirectional piezoelectric fuzzy fiber reinforced composite (PFFRC) comprised of zig-zag single-walled carbon nanotubes and piezoelectric fibers as reinforcements embedded in a conventional polymer matrix has been studied. Effective piezoelectric and elastic properties of this composite have been determined by the method of cell (MOC) approach and the Mori–Tanaka (MT) method. It is found that the effective in-plane piezoelectric coefficient and elastic coefficients of the PFFRC are significantly improved over those of the existing 1–3 piezoelectric composite without reinforced with carbon nanotubes.

Effective thermal conductivities of a novel fuzzy carbon fiber heat exchanger containing wavy carbon nanotubes

A novel fuzzy carbon fiber heat exchanger (FFHE) is proposed in this study. The novel constructional feature of the FFHE is that the sinusoidally wavy carbon nanotubes (CNTs) are radially grown on the outer circumferential surface of the hollow cylindrical carbon fiber (HCF) heat exchanger. The effective thermal conductivities of the FFHE have been estimated by employing the method of cells (MOC) approach and the effective medium (EM) approach. The present study reveals that if the amplitudes of the radially grown sinusoidally wavy CNTs are parallel to the axis of the HCF then the effective axial thermal conductivity of the FFHE is significantly improved over that of the bare HCF heat exchanger (i.e., without CNTs). On the other hand, if the amplitudes of the radially grown wavy CNTs are transverse to the axis of the HCF, the effective transverse thermal conductivity of the FFHE is significantly improved over that of the bare HCF heat exchanger. It is also found that the CNT/polymer matrix interfacial thermal resistance does not affect the effective thermal conductivities of the FFHE. The present investigation suggests that exploiting the waviness of radially grown CNTs on the HCF a truly multifunctional and promising heat exchanger can be developed for advanced technological applications.

Refoundation of the Cell Method Using Augmented Dual Grids

In this paper, the cell method (CM) is reformulated using augmented dual grids. In this way, the boundary of the discretized spacial domain can be properly dealt with and energetic quantities can be introduced, overcoming the well-known drawbacks of the CM. The details are given for electromagnetic boundary value problems, whose discretization can severely suffer from such drawbacks of the CM.