Tanaka Method Research Articles

Estimation of salt intake from urinalysis as a prognostic indicator in patients with heart failure

Abstract Background Restricting sodium consumption by reducing salt intake is crucial in heart failure management. The average salt intake in Japan is approximately 10 g/day, which is significantly higher than that in other countries. Therefore, the Japanese guidelines for heart failure recommend a target salt intake of less than 6 g/day. Purpose Excessive salt intake is a well-known risk factor for heart failure, but it has also been reported that excessive salt restriction does not affect clinical outcomes in patients with heart failure. Moreover, although previous reports have mainly focused on clinically stable patients with chronic heart failure, appropriate salt intake management in patients with unstable heart failure immediately after hospital discharge remains unexplored. Therefore, this study aimed to investigate the effect of salt intake management on patients with heart failure in the early post-discharge period. Methods The study was conducted between April 2015 and March 2023, and included 395 of 4,292 patients (mean age: 72 y; sex: 63% male) who were hospitalized owing to heart failure and whose salt intake was measured at early post-discharge. Salt intake was estimated via the Tanaka Method, using spot urine samples. The patients were divided into four groups based on the estimated salt intake: very low (< 4 g/day) (n = 24), low (≥ 4 and < 7 g/day) (n = 109), high (≥ 7 and < 10 g/day) (n = 149), and very high (≥ 10 g/day) (n = 113). The primary endpoint was all-cause rehospitalization within 1 year of discharge. Results During a median follow-up period of 303 days, 153 rehospitalization occurred. 96 were heart failure rehospitalization; others included infection, arrhythmia, dehydration etc. Spline curve analysis for estimated salt intake and rehospitalization (Fig. 1) showed a significant nonlinear curve (P = 0.017). Cox regression analysis (Fig. 2) revealed a significantly higher number of rehospitalization in the very low group (hazard ratio [HR]: 2.29; 95% confidence interval [CI]: 1.24–4.25; P = 0.009), compared with the low group, and a similar trend was also observed in the very high group (HR: 1.51; 95% CI: 0.99–2.31; P = 0.056). Subgroup analysis (Fig. 3) showed that the impact of estimated salt intake on rehospitalization, as represented by a U-shaped curve, was more pronounced in patients who were not treated with loop or thiazide diuretics. Conclusion The results of this study suggest that both excessive salt intake and excessive restriction may increase the risk of rehospitalization in patients with heart failure during the early post-discharge period. Additionally, the results indicate that estimation of salt intake using the Tanaka method may be particularly useful for patients not undergoing diuretic treatment. Conversely, patients with very low salt intake, potentially indicative of inadequate oral intake due to an impaired general condition, may require careful follow-up.

Failure investigation of woven scarf-repaired laminates reinforced with nanoparticles: Experimental and numerical investigations

This study explores the efficacy of multi-walled carbon nanotubes (MWCNTs) and graphene nanoplatelets (GNPs) as nano-reinforcement for the epoxy adhesive layer in scarf joints and 3D scarf-repaired laminates subjected to tensile loading. Experimental characterization of pure epoxy and nanocomposite mechanical properties was validated using the Mori–Tanaka method (incorporating agglomeration effects). A 3D finite element model considering material non-linearity and strain-based damage was employed to investigate joint failure behaviour, validated for 0.5 vol% MWCNT and GNP concentrations. A subsequent parametric study explored the influence of scarf angle, nanoparticle concentration, and patch configuration on 3D repaired specimens. The results suggest a 2.86° scarf angle with a [(+45/−45)]4s patch configuration reinforced with 1 vol% MWCNTs and 0.5 vol% GNPs exhibits the highest tensile strength improvement.

Improved thermoelectric properties of graphene reinforced multiphase cement composites: experiments and modeling

Nanoscale graphene has demonstrated effectiveness in self-sensing cement composites and energy harvesting in buildings. However, the widespread application of graphene reinforced cement composites (GRCCs) in energy conversion is hindered by their low thermoelectric conversion efficiency. To address this limitation, multiphase cement composites with high Seebeck coefficient and low thermal conductivity are designed by using Cu2Se and ZnO. The increase in carrier mobility and enhanced phonon scattering lead to an order of magnitude improvement in the figure of merit (ZT) compared to GRCCs without incorporating Cu2Se/ZnO. A hybrid micromechanical model (HMM) based on effective medium theory and the Mori–Tanaka method is developed for predicting the electrical and thermal conductivity of the multiphase cement composites, which can be used to evaluate the thermoelectric performances of the composites. The combined experiments and modeling aim to provide guidelines for developing high-performance GRCCs with improved thermoelectric properties, potentially expanding their application in energy conversion technologies.

Serendipitous relationship between discrete distribution models representing random orientations of fillers in composite materials and the golden ratio

The purpose of this study is to establish simple discrete distribution models capable of expressing the two and three-dimensional random orientation states of fillers in composite materials. Initially, a new method is proposed to divide the elastic constants into isotropic and anisotropic parts. Employing this method, for the composite material containing ellipsoidal fillers with various orientations in the material, the macroscopic elastic constants and thermal expansion coefficients of the material are derived based on the Mori–Tanaka method. Subsequently, the analysis of the macroscopic properties is performed for fillers oriented two and three-dimensional discrete distributions. As a result, it is found that when both angular pitches of the azimuth angle and the rotational angle of the fillers in a plane are at most 72°, the macroscopic elastic constants and the thermal expansion coefficients of the material exhibit in-plane isotropy, leading to the realization of a two-dimensional random state. Furthermore, if the angular distribution of the zenith angle and azimuth angle corresponds to the vertices of the regular dodecahedron and icosahedron, and the angular pitch of the rotational angle of the fillers is at most 72°, the macroscopic properties of the material become isotropic, resulting in a three-dimensional random state. Notably, the angle of 72° and the orientation angles of the vertices of the regular dodecahedron and icosahedron are associated with the golden ratio. Therefore, this analysis suggests a serendipitous relationship between the golden ratio and the angular pitch that simplifies the random orientation distribution of fillers.

Micromechanical analysis for effective elastic moduli and thermal expansion coefficient of composite materials containing ellipsoidal fillers oriented randomly

In this study, we examine to derive the solutions of effective elastic moduli and thermal expansion coefficient for composite materials containing ellipsoidal fillers oriented randomly in the material using homogenization theories, which are the self-consistent method and the Mori–Tanaka method. This analysis is carried out by micromechanics combining Eshelby’s equivalent inclusion method for each theory. The solutions for effective elastic moduli and thermal expansion coefficient obtained on each theory are expressed by common coefficients composed of both the physical properties of the constituents of the composite material and geometrical factors depending upon the shape of the fillers. Moreover, these solutions enable us to calculate effective elastic moduli and thermal expansion coefficient for composite materials that contain randomly oriented fillers of various shapes and physical properties. By taking the limit of eliminating the existence of the matrix for these solutions, we can derive effective physical properties of polycrystalline materials. Using the obtained solutions, we investigate the effects of the shape of the fillers on the effective elastic moduli and thermal expansion coefficient. As a result, we confirm that these effective properties fall within the lower and upper bounds, and find that a characteristic result appears when the shape of the fillers is flake or oblate. Through comparisons between the analytical and experimental results, we confirm the practical usability of the solutions obtained in this analysis. Furthermore, we determine originally the shape factor for the filler and can show that this factor has the potential to provide guidelines for the optimal design of filler shape to improve the effective elastic properties of materials.

Effective thermal and electromagnetic properties of composite materials containing ellipsoidal-coated fillers oriented randomly

This study aims to derive explicit solutions for the effective thermal and electromagnetic properties of composite materials containing coated fillers oriented randomly. In this study, the coated fillers are modeled as double inhomogeneous inclusions with anisotropic properties and ellipsoidal shapes, without loss of generality. This model is analyzed by combining the double inclusion method with the self-consistent method or the Mori–Tanaka method. The derived solutions for the effective properties are expressed in explicit form by the physical properties of constituents and the difference in shape between the inner and outer regions of the coated fillers, and confirmed to be consistent in the limit of no coating layer. In addition, the solutions of effective properties are also derived for composite materials containing many kinds of coated fillers with different shapes and physical properties. The solutions allow the prediction of thermal conductivity, permittivity, electrical conductivity, and magnetic permeability of a wide range of composite materials by analogy with thermal and electromagnetic properties. These solutions are applied to the following two composites: diamond fillers coated with TiC/Al, and Co fillers coated with Co 3 O 4/Mg. The effect of the thickness of the coating layer on the effective thermal conductivity of these materials is investigated. As a result, our analytical results for these composite materials generally agree with the experimental results. Moreover, from the viewpoint of maximizing the thermal conductivity of diamond fillers coated with TiC/Al, the optimal combinations of the thickness of the coating layer and the shape of the diamond fillers are identified. For Co coated with Co 3 O 4/Mg, we find that the shape of Co fillers should be long fibrous from the viewpoint of giving high magnetic permeability while maintaining high thermal conductivity due to Mg. Thus, the analytical solutions are demonstrated to be powerful tools for designing composite materials containing coated fillers.

Laboratory investigation on physical and mechanical behaviors of granite after heating and different cooling rates

As an important formation of geothermal reservoirs, granite has very complex microstructure and strong heterogeneity which play an important role in the damage and failure mechanical behavior of granite under different temperatures and cooling rates. In order to better understand the influence of microstructure on the multiscale physical and mechanical properties of granite at evaluated temperatures and cooling rates, this paper conducted a series of macroscopic and microscopic experimental investigations on the granite samples after a heating with two cooling rates treatment. The results show that the failure mode changes from brittle to ductile at 400 °C which is the critical temperature for both macroscopic and microscopic properties. The physical and mechanical properties of specimen after air cooling treatment increase at 200 °C due to the transition of macropores into micropores. Transgranular cracks take place in feldspar at 400 °C and numbers of intergranular cracks develop inside all minerals at 500 °C. The number and width of microcracks in water-cooled samples are much greater than those of air-cooled simples. Based on these experimental investigations, a cross-scale characterization method of Young’s modulus is proposed by introducing a thermal damage factor into the Mori–Tanaka method to consider the thermal damage induced by the thermal treatment.

A micromechanical scheme with nonlinear concentration functions by physics-guided neural network

The mechanical behavior of heterogeneous materials has been reported to be significantly influenced by the nonlinear properties of both the matrix and interface. However, the micromechanical homogenization methods for predicting the effective properties are challenged in nonlinear problems due to the difficulties in solving the analytical form of the concentration tensors. In this study, we develop a nonlinear micromechanical scheme for heterogeneous materials with complex interfacial behaviors, where the key component, namely nonlinear concentration functions, is determined by the devised physics-guided neural network. In particular, the nonlinear Mori–Tanaka method (NMT) implemented within this new micromechanical scheme yields accurate solutions to axisymmetric nonlinear homogenization problems considering the effects of finite deformation, loading conditions, volume fraction, etc. Furthermore, the NMT is equivalent to the linear Mori–Tanaka method in the condition of the small deformation. Notably, this neural-network-based micromechanical scheme shows good generalization for different types of nonlinear interfaces, while the corresponding approach for generating training data via the finite element method (FEM) is cost-effective. This theoretical framework introduces a novel approach to nonlinear physical modeling, namely, not by the direct regression from the dataset but by deeply embedding neural networks in physical laws.

Analytical calculation model for elastic modulus and strength of foamed concrete

Foamed concrete has gained increasing attention for its excellent engineering performance. Endeavors have been made to experimentally and numerically elucidate the mechanism of foamed concrete, while few theoretical methods are used to analytically calculate mechanical properties. This paper proposes a theoretical framework to describe the elastic behavior of foamed concrete by combining Eshelby’s equivalent inclusion theory with the Mori–Tanaka method. In the analytical model, foamed concrete is regarded as a two-phase composite comprising a homogeneous cement matrix and randomly oriented ellipsoidal air void. During derivation, the elastic modulus, strength, bulk modulus, shear modulus, and Poisson ratio are measured. A good agreement is established between the proposed method and experimental data.

A macro-mesoscopic constitutive model for porous and cracked rock under true triaxial conditions

The complex mechanical and damage mechanisms of rocks are intricately tied to their diverse mineral compositions and the formation of pores and cracks under external loads. Numerous rock tests reveal a complex interplay between the closure of porous defects and the propagation of induced cracks, presenting challenges in accurately representing their mechanical properties, especially under true triaxial stress conditions. This paper proposes a conceptualization of rock at the mesoscopic level as a two-phase composite, consisting of a bonded medium matrix and frictional medium inclusions. The bonded medium is characterized as a mesoscopic elastic material, encompassing various minerals surrounding porous defects. Its mechanical properties are determined using the mixed multi-inclusion method. Transformation of the bonded medium into the frictional medium occurs through crack extension, with its elastoplastic properties defined by the Drucker–Prager yield criterion, accounting for hardening, softening, and extension. Mori–Tanaka and Eshelby’s equivalent inclusion methods are applied to the bonded and frictional media, respectively. The macroscopic mechanical properties of the rock are derived from these mesoscopic media. Consequently, a True Triaxial Macro-Mesoscopic (TTMM) constitutive model is developed. This model effectively captures the competitive effect and accurately describes the stress-deformation characteristics of granite. Utilizing the TTMM model, the strains resulting from porous defect closure and induced crack extension are differentiated, enabling quantitative determination of the associated damage evolution.

Piezoresistive Theory and Numerical Calculation for Carbon Nanotube Polymer Composite.

A three-dimensional theory has been established for the piezoresistivity of carbon nanotube (CNT) polymer composites. Based on the Mori-Tanaka method in meso-mechanics theory and considering quantum tunneling effect between CNTs, an approach to calculate equivalent electrical conductivity of composites was proposed. On this basis, a piezoresistive theory, which incorporates the effect of composites' geometric nonlinearity, was developed for CNT polymer composites. The theory is dependent only on some basic physical parameters of the materials. A finite element formula of the theory for the numerical calculation of piezoresistivity was presented from the analysis of both elastic and electric fields. Numerical simulations demonstrated that the results predicted by the theory were in good agreement with those of the experimental tests. Parameter sensitivity analysis revealed that when both the potential barrier height of the matrix and the initial average separation distance between CNTs increased, the piezoresistivity obviously increased. However, with the increase in aspect ratio and CNT conductivity, the piezoresistivity decreased gradually. A practical engineering application of this theory is also provided.

Comparative evaluation of three different regression-equation-based mixed dentition analysis of children for prediction of the mesiodistal width of permanent canine and premolars.

Dental malocclusion is common all over the world, and it is caused by a difference in arch length and tooth size. This necessitates mixed dentition analysis for early intervention treatment planning such as eruption guiding, serial extraction, space maintainer, space regainer, and jaw extension. The aim of the study is to comparatively evaluate three different regression equation based mixed dentition analysis of children for prediction of the mesiodistal width of permanent canine and premolars in population of Vidarbha region. This study comprised of 300 patients aged 13 to 16 years old. The impressions of patients were poured, and the mesiodistal width of their teeth was measured and documented. Three independent analyses were performed using the Ling and Wong method (L&W), the Bernabe and Flores-Mir method (B&F), and the Tanaka and Johnston method (T&J), and the results were compared to the sum of permanent canine and premolar teeth (SPCP). ANOVA with post hoc analysis was used to compare the predicted mesiodistal diameter (MDD) by analysis to the SPCP observed on cast. The mesiodistal width of SPCP of maxilla and mandibular teeth had statistically significant difference (P<0.001) with the predicted width by Ling and Wong method, Bernabe and Flores method and Tanaka and Johnston method for patients of Vidarbha region. The study concluded that all the three analysis overestimated the mesiodistal width of the sum of permanent canine and premolar in the patients. Tananka and Johnston analysis method was better in predicting the SPCP of the children of Vidarbha region.

Effective elastic properties of one-dimensional hexagonal quasicrystal composites with spring-type imperfect interfaces

Considering the spring-type imperfect interfaces, the effective elastic properties of one-dimensional (1D) hexagonal quasicrystal (QC) are investigated systematically. The spring-type imperfect interface between QC matrix and inclusion is an ultra-thin, soft and weakly conductive interface. The Mori–Tanaka method is presented to determine the effective elastic constants of phonon, phason and phonon–phason coupling field. The numerical results are provided to show that the existence of imperfect interfaces reduces the effective elastic constants to some extent. It indicates that the interface plays an important role in the elastic properties of QC composites. Besides, the effective elastic constants are also subject to the aspect ratio and the volume fraction of inclusions.

Characterization of solute-solvent interactions in liquid chromatography systems: A fast method based on Abraham's linear solvation energy relationships

The Abraham's solvation parameter model, based on linear solvation energy relationships (LSER), allows the accurate characterization of the selectivity of chromatographic systems according to solute-solvent interactions (polarizability, dipolarity, hydrogen bonding, and cavity formation). However, this method, based on multilinear regression analysis, requires the measurement of the retention factors of a considerably high number of compounds, turning it into a time-consuming low throughput method. Simpler methods such as Tanaka's scheme are preferred. In the present work, the Abraham's model is revisited to develop a fast and reliable method, similar to the one proposed by Tanaka, for the characterization of columns employed in reversed-phase liquid chromatography and particularly in hydrophilic interaction liquid chromatography. For this purpose, pairs of compounds are carefully selected in order to have in common all molecular descriptors except for a specific one (for instance, similar molecular volume, dipolarity, polarizability, and hydrogen bonding basicity features, but different hydrogen bonding acidity). Thus, the selectivity factor of a single pair of test compounds can provide information regarding the extent of the dissimilar solute-solvent interactions and their influence on chromatographic retention. The proposed characterization method includes the determination of the column hold-up volume and Abraham's cavity term by means of the injection of four alkyl ketone homologues. Therefore, five chromatographic runs in a reversed-phase column (four pairs of test solutes and a mixture of four homologues) are enough to characterize the selectivity of a chromatographic system. Tanaka's method is also analyzed from the LSER point of view.

Nonlinear active control of thermally induced pyro-coupled vibrations in porous-agglomerated CNT core sandwich plate with magneto-piezo-elastic facings

In this article, the damped nonlinear transient response of a smart sandwich plate (SSP) comprising of agglomerated CNT-reinforced porous nanocomposite core with multifunctional magneto-piezo-elastic (MPE) facesheets, subjected to the thermal environment, is numerically investigated. The synergistic influence of agglomeration, porosity and pyro-coupling on vibration control is studied for the first time under the finite element framework. The attenuation of the vibrations is caused by active constrained layer damping (ACLD) treatment. The kinematics of the plate is based on the layer-wise shear deformation theory and von-Karman’s nonlinearity. The viscoelastic properties of the ACLD patch and CNT agglomeration of the core are mathematically modelled using Golla–Hughes–McTavish and Eshelby–Mori–Tanaka methods, respectively. A comprehensive examination of the inter-related effects of different agglomeration states, porosity distributions and thermal loading profiles has been performed. The new insights on controlling pyro-coupled induced vibrations of smart sandwich plates by supplying control voltage directly to the MPE facesheets without ACLD treatment have been discussed thoroughly. The numerical analysis confirms the significant effects of pyro-coupling associated with active vibration control response of SSP.

Free Vibration Analysis of Carbon-Nanotube-Reinforced Beams Resting on a Viscoelastic Pasternak Foundation by the Nonlocal Eshelby–Mori–Tanaka Method

Free Vibration Analysis of Carbon-Nanotube-Reinforced Beams Resting on a Viscoelastic Pasternak Foundation by the Nonlocal Eshelby–Mori–Tanaka Method

A multiscale uncertainty propagation method for dynamic analysis of laminated FRP composite plates with hybrid random and interval uncertainties

In this paper, a multi-scale uncertainty analysis framework to deal with hybrid random and interval uncertainties is presented to analyse dynamic characteristics of FRP composite structures. The proposed method consists of a perturbation-based probabilistic analysis, particle swarm optimization interval analysis to address the hybrid uncertainties, and the Mori–Tanaka method based homogenization theory to propagate uncertainties from microscale to macroscale. The proposed numerical approach provides estimates of the natural frequencies of composite plates, with mean and standard deviation lower and upper bounds, at a low computational cost. Numerical examples are presented to demonstrate the feasibility of the proposed method for different forms of composite structures, and also to verify its effectiveness and accuracy in predicting natural frequencies. Results show that the proposed method is highly accurate in calculating the upper and lower frequency bounds for advanced composite laminates under complicated uncertainties.

A hybrid direct FE2 method for modeling of multiscale materials and structures with strain localization

Strain localization is a common phenomenon existing in various multiscale materials or structures, e.g., the bulking bands of thin-walled structures, the local collapse of porous materials, and the crack in solid materials, etc. However, this phenomenon cannot be captured by the conventional homogenization methods, such as mean-field homogenization (e.g., Mori–Tanaka method), first-order or high-order computational homogenization (e.g., the Finite Element Square method), etc., due to the high strain gradient associated with strain localization. Aiming at this, a hybrid Direct FE2 method is proposed by combining the D-FE2 (Direct FE2) and the traditional FE methods, while the multiscale structure is modeled using the D-FE2 method in the region exhibiting low deformation gradient, and the other region displaying high deformation gradient is modeled using the traditional FE method. Moreover, a node displacement constraint and an overall node displacement constraint derived from the multilevel equilibrium equations using the Gauss–Ostrogradsky theorem are respectively prescribed to the interface between the D-FE2 model and the FE model of the multiscale structure, to enforce the energy equilibrium and deformation continuity. The proposed hybrid D-FE2 method is then applied to predict the strain localization behavior of multiscale materials or structures, including local bulking of honeycomb structures, in-situ crack propagation, and localized plastic deformation in fiber reinforced composites, etc. Comparison of the simulation results obtained from the hybrid D-FE2 method and the traditional FE method validates the accuracy, efficiency and ease of numerical implementation of the proposed hybrid D-FE2 method.

Bending analysis of carbon nanotube coated–fiber multi-scale composite beams using the refined zigzag theory

The present work aims to investigate the bending analysis of sandwich and laminated carbon nanotube coated–fiber multi-scale composite (CFMC) beams employing the Refined Zigzag Theory (RZT). The model encompasses core fiber, surrounding carbon nanotube (CNT) coating region, and polymer matrix covering all scales from nano to macro-scale. Hierarchical multi-scale modeling is utilized where information is only transmitted from the fine-scale to the next coarser scale. The CNT coating region (CCR) consists of CNT, matrix, and non-bonded interphase whose mechanical properties are determined employing the Eshelby–Mori–Tanaka method and the equivalent continuum fiber approach. Considering different configurations of grown CNTs around the core fiber, two CCRs are constructed, comprising axially aligned (ACCR) and randomly oriented CCRs (RNCCR). The mechanical properties of the core fiber coated with the surrounding CCR are then obtained through the composite cylinder assemblage (CCA) method. Consequently, four RZT kinematic variables are acquired for the CFMC beams, and the effects of CNT volume fraction, coating thickness, and coating types are thoroughly investigated for various laminated and sandwich beams. The results reveal a substantial reduction in the maximum transverse displacements of the CFMC beams compared to the conventional composite beams, considering the low volume fraction of the CNTs in the coating region. Moreover, by employing a combination of ACCR and RNCCR for the layers in the sandwich CFMC beams, a pronounced decline in the transverse shear stress of the core medium is demonstrated, which can postpone the core shear failure in the sandwich structures. A great agreement is observed between the obtained results and the outcomes predicted by finite element analysis.

Efficient generation of random fiber distributions in fiber reinforced composites

This paper proposes a new algorithm to generate representative volume elements (RVEs) with random fiber distribution in fiber reinforced composites (FRC). The proposed algorithm is straightforward and easy to implement based on judging the maximum and minimum distances between a new fiber and existing fibers. The generation results demonstrate that the maximum fiber volume fraction gradually increases and oscillates violently before reaching 78.54% as the fiber radius rises. Moreover, with the increase of RVE size, the maximum fiber volume fraction changes gently when the fiber radius does not exceed 6.5 μm, but it changes dramatically at other fiber radii. Then, the fiber distributions of the generated RVEs are evaluated using the nearest neighbor distance, Ripley’s K function, and pair distribution function. The evaluation results indicate that the fiber distributions present randomness. Lastly, the effective elastic properties of the Carbon/Epoxy unidirectional FRC are predicted using the RVEs generated by the proposed algorithm, the RVEs generated by regularization, and the Mori–Tanaka method. It is found that the prediction using the RVEs generated by the proposed algorithm is more accurate than the regularization, compared with the Mori–Tanaka and experiment results. The proposed algorithm contributes to microstructure modeling in computational micromechanics.