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The potential of paper and paperboard as fiber-based materials capable of replacing conventional polymer-based materials has been widely investigated and evaluated. Due to paper's limited extensibility and inherent heterogeneity, local structural variations lead to unpredictable local mechanical behavior and instability during processing, such as mechanical forming. To gain a deeper understanding of the impact of mechanical behavior and heterogeneity on the paper forming process, the Finite Element Method (FEM) coupled with continuum modeling is being explored as a potential approach to enhance comprehension. To achieve this goal, utilizing experimentally derived material parameters alongside stochastic finite element methods allows for more precise modeling of material behavior, considering the local material properties. This work first introduces the approach of modeling heterogeneity or local material structure within continuum models, such as the Stochastic Finite Element Method (SFEM). A fundamental challenge lies in accurately measuring these local material properties. Experimental investigations are being conducted to numerically simulate mechanical behavior. An overview is provided of experimental methods for material characterization, as found in literature, with a specific focus on measuring local mechanical material structure. By doing so, it enables the characterization of the global material structure and mechanical behavior of paper and paperboard. [ABSTRACT FROM AUTHOR]

Transport of volatile organic compounds (VOCs) through porous media with active surfaces takes place in many important applications, such as in cellulose-based materials for packaging. Generally, it is a complex process that combines diffusion with sorption at any time. To date, the data needed to use and validate the mathematical models proposed in literature to describe the mentioned processes are scarce and have not been systematically compiled. As an extension of the model of Ramarao et al. (Dry Technol 21(10):2007–2056, 2003) for the water vapor transport through paper, we propose to describe the transport of VOCs by a nonlinear Fisher–Kolmogorov–Petrovsky–Piskunov equation coupled to a partial differential equation (PDE) for the sorption process. The proposed PDE system contains specific material parameters such as diffusion coefficients and adsorption rates as multiplication factors. Although these parameters are essential for solving the PDEs at a given time scale, not all of the required parameters can be directly deduced from experiments, particularly diffusion coefficients and sorption constants. Therefore, we propose to use experimental concentration data, obtained for the migration of dimethyl sulfoxide (DMSO) through a stack of paper sheets, to infer the sorption constant. These concentrations are considered as the outcome of a model prediction and are inserted into an inverse boundary problem. We employ Physics-Informed Neural Networks (PINNs) to find the underlying sorption constant of DMSO on paper from this inverse problem. We illustrate how to practically combine PINN-based calculations with experimental data to obtain trustworthy transport-related material parameters. Finally we verify the obtained parameter by solving the forward migration problem via PINNs and finite element methods on the relevant time scale and show the satisfactory correspondence between the simulation and experimental results. Article Highlights: A mathematical model to describe transport of polar volatile organics through paper is proposed. Based on experimental data, the deep learning method of physics-informed neural networks (PINNs) is used to solve the inverse problem of finding the sorption time constant. Solutions for the forward problem are obtained by the standard finite element method (FEM) and PINN methods. These solutions are compared with each other as well as with the experimental data to verify the model. [ABSTRACT FROM AUTHOR]

A computationally efficient method to study the in-plane and out-of-plane dimensional instability of thin paper sheets under the influence of moisture changes is presented. The method explicitly resolves the bonded and the free segments of fibers in the sheet, capturing the effect of anisotropic hygroexpansion at the fiber level. The method is verified against a volumetric model. The importance of longitudinal fiber hygroexpansion is demonstrated in spite of the absolute value of longitudinal hygroexpansion being an order of magnitude lower than the transverse hygroexpansion component. Finally, the method is used to demonstrate the formation of macroscopic sheet curl due to a moisture gradient in structurally uniform sheets in the absence of viscoelastic or plastic constitutive behavior and through-thickness residual stress profiles. [ABSTRACT FROM AUTHOR]

• An attempt to characterize thin, low impedance paper at various high strain-rates. • The creation of a digital twin of the physical Split Hopkinson Test bench. • To demonstrate that there can be distortions of the transmitted measuring signal. This work deals with the high strain-rate characterization of paper under uniaxial tension using a Split Hopkinson test bench. An aluminum bar system featuring a highly sensitive hollow transmission bar was used. Paper tests were performed in a strain-rate range between approximately 60 s−1 and 210 s−1. The experimental tests showed that the breaking strength appears to decrease with increasing strain-rate. To verify these results, a digital twin of both the paper specimen and the entire test rig was created in an explicit Finite Element method environment. The numerical model was then used to perform a parameter study with different types of transmission bars. It was shown that the system is quite sensitive to additional masses caused by the specimen fixtures, as well as to drastic reductions in the cross section of the transmission bar. As a result, the transmitted measuring signal can be distorted and may need to be corrected using the digital twin. [ABSTRACT FROM AUTHOR]

Understanding heat transfer in corrugated fibreboard is important to the design of more effective packaging for industries which involve the freezing and chilling of food. In this work the thermal conductivity of papers which compose corrugated fibreboard were measured and used to validate finite element models of heat transfer in fibreboard. The results showed paper to be highly anisotropic, with thermal conductivity in the machine and cross machine directions being almost an order of magnitude larger than in the thickness direction. The finite element models showed good agreement with experimental results and demonstrated that the majority of heat transfer in corrugated fibreboard is though the fluted medium. Based on the finite element models, simple models for the prediction of the thermal performance of corrugated board were evaluated and shown to be very effective in reproducing the results of the more complex finite element methods. These simple methods can be used to perform corrugated fibreboard design calculations, and the models with and without radiation can be used to provide estimates of the lower and upper bounds of the thermal resistance for a given board design. [ABSTRACT FROM AUTHOR]

The article analyses the effects of paper moisture content on energy absorbed during its tensile testing in the range of moisture equilibrium obtained during paper air conditioning at a temperature of 23 °C. To predict changes in breaking energy caused by changes in moisture content, two calculation methods were proposed. The methods were verified on the basis of laboratory tests and calculation results, and their practical usefulness was confirmed. [ABSTRACT FROM AUTHOR]

A fully printed piezoelectric based touch sensor device has been successfully fabricated on flexible polyethylene terephthalate (PET) and paper substrates using screen printing technique. The device, consisting of a 4 × 4 array of printed sensors and interconnect lines, was fabricated using silver (Ag) ink. Screen printed polyvinylidene fluoride (PVDF), as a piezoelectric layer, was sandwiched between the printed Ag top and bottom electrode metallization layers. A linear relationship between the sensor response and varying applied forces to the device was obtained through finite element analysis (FEA) method simulation. X-ray diffraction (XRD) analysis was performed to verify the formation of the β-phase crystals in the PVDF layer during the curing process. The effective polarization of the printed piezoelectric layer was analyzed using capacitance-voltage analysis. A sensitivity of 1.2 V/N and 0.3 V/N, with correlation coefficient of 0.9954 and 0.9859, was obtained for the PET and paper based printed touch sensors, respectively. The piezoelectric-voltage analysis demonstrated that the printed sensors can be used for both touch and force based applications. [ABSTRACT FROM AUTHOR]

The present paper explores the short span compression tester (SCT) as a means to experimentally determine the transverse shear moduli of paper. These moduli, which are known to be difficult to determine by any other means, are of importance for the behavior of paper during tissue manufacturing and in the converting and embossing of paperboard. Testing was conducted on paper of two different grammages both in MD and in CD. By applying the Timoshenko–Engesser theory for buckling of shear compliant materials, estimates of the transverse shear moduli were obtained through the measured SCT values and standard measurements of the Young’s modulus and the thickness. These estimates were evaluated by detailed FE-analyses of the SCT setup incorporating initial geometrical imperfections representative for real test conditions. It was found that the Timoshenko–Engesser theory gives estimates of the transverse shear moduli that are within an accuracy well applicable for most engineering purposes. The results suggest that the method is at least as accurate as any other, more involved, method that could be used for the purpose. [ABSTRACT FROM AUTHOR]

The mechanical response of three different structural core sandwich panels in out-of-plane compression and shear has been analyzed. Specific core shapes examined are arc-tangent, wavy trapezoidal and hemispherical. Unit cells consisting of representative elements of the core attached to face sheets were selected for analysis. Both face sheets and core were assumed made from paper. Finite element analysis employing large deformation and rotations and orthotropic elastic–plastic behavior was used. The results show that the arc-tangent and trapezoidal cores are prone to collapse by extensive bending and buckling, whereas the hemispherical core behaved more stably in compression and shear. Core sheets with a hemispherical shape were prepared from copy paper sheets in a specially designed forming machine. Sandwich test specimens were prepared from this core and tested in out-of-plane compression, and the load-displacement response was compared to predictions from finite element simulations. The experimental and finite element results were consistent. [ABSTRACT FROM AUTHOR]

A moisture-dependent and temperature-dependent constitutive model for paper materials was proposed and implemented into a finite element model of the paper hydroforming process. Experimental hydroforming was conducted at temperatures of 23°C and 110 °C and moisture contents of 6.9 and 10.6 (respectively corresponding to 50 and 80% relative humidity). The proposed model, which also included the effects of drying, captured the extent of forming of all experimental results within reasonable accuracy. For the moisture content and temperature conditions in this study, the phenomenon of drying was found to be the reason why the application of temperature had a much greater effect on the degree of forming than hydroforming at various moisture contents. A simulation-based parametric study was conducted in order to identify the importance of various process and material parameters. This parametric study confirmed many previous empirical findings and was capable of quantifying the extent to which these process and material parameters affect the three-dimensional formability of paper. The coefficient of friction was identified as one of the most important factors when determining the extent of forming. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The tensile response of dense fiber-based materials like paper or paperboard is mainly dependent of the properties of the fibers, which store most of the elastic energy. In this paper, we investigate the influence of geometrical and material parameters on the mechanical response of the pulp fibers used in paper manufacturing. We developed a three-dimensional finite element model of the fiber, which accounts for microfibril orientation of cellulose fibril, and the presence of lignin in the secondary cell wall. The results showed that the change in the microfibril orientation upon axial straining is mainly a geometrical effect, and is independent of the material properties of the fiber, as long as the deformations are elastic. Plastic strain accelerates the change in microfibril orientation and thus makes it material-dependent. The results also showed that the elastic modulus of the fiber has a non-linear dependency on microfibril angle, with elastic modulus being more sensitive to the change of microfibril angle around small initial values of microfibril angles. Based on numerical results acquired from a 3D fiber model supported by available experimental evidence, we propose an anisotropic-kinematic hardening plasticity model for a fiber within a beam framework. The proposed fiber model is capable of reproducing the main features of the cyclic tensile response of a pulp fiber, such as stiffening due to changing microfibril angle. The constitutive model of the fiber was implemented in a finite-element model of the fiber network. By using the fiber network model, we estimated the level of strain that fiber segments accumulate before the typical failure strain of the entire network is reached. [ABSTRACT FROM AUTHOR]

The iso-margin method based on the classical analytical equations is widely used in the development of extra high voltage (EHV) bushing. Therefore, its effectiveness and feasibility have been fully validated. However, with the theoretical formula, it is difficult to evaluate the influence of stray capacitance and temperature on the internal electric stress of the ultra high voltage (UHV) bushing. It?s necessary to further improve the traditional iso-margin method. Firstly, the basic principle of iso-margin method has been briefly described. After that, the E-field distribution of condenser bushing was investigated on the Finite Element Method (FEM) computing platform. Then, the mathematical model of the advanced equal margin design method was established. Furthermore, this paper presents the program flow of optimization which combines the simulation of electro-thermal coupling process and the particle swarm optimization (PSO) algorithm. The proposed methodology was applied to the design of the prototype of the UHV resin impregnated paper (RIP) oil-SF6 bushing, which realizes the uniform axial E-field distribution of the bushing condenser. Meanwhile, the partial discharge margin between adjacent foils can be equal. Moreover, the hot-spot temperature is lower than the operation limiting temperature of the RIP material. The bushing condenser was fabricated according to the optimal structure design. The prototype of bushing has passed through all the type tests. In this paper, the FEM electro-thermal coupling simulation and the advanced equal margin design method were applied to the inner insulation structure optimization of the UHV RIP oil-SF6 bushing. Meanwhile, the proposed methodology provides some theoretical guidelines for the future research and development of other types of bushing on the UHV level. [ABSTRACT FROM AUTHOR]

The work is built on a previous research by Wiryana and Berg, in which wicking into four wet-formed paper stripes, consisting of cellulose fibers and four different percentages of the powdered carboxymethyl cellulose (CMC) superabsorbent, was studied experimentally. Because of the swelling of cellulose fibers and CMC powder on contact with water, the wicking was accompanied by a swelling of the matrix. A finite element/control volume (FE/CV)-based computer program is used for the first time to model the wicking in such swelling porous medium. The simulation used a novel form of continuity equation, which included the effects of liquid absorption and matrix swelling, in conjunction with the Darcy's law to model the single-phase flow behind a clearly defined liquid-front. A new method of estimating the time-varying permeability of the paper, based on the absorbed liquid-mass vs. time plots, is also proposed. Later, this time-dependent permeability is used in the numerical simulation to change the permeability in elements behind the moving liquid-front as a function of the time that the element has been wetted by the liquid, since the passage of the liquid-front. The numerical prediction of the wicking-front location as a function of time compares well with the reported experimental data. © 2011 American Institute of Chemical Engineers AIChE J, 58: 2536-2544, 2012 [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a method to predict the through-thickness moisture content distribution and associated induced deformations of paper and cardboard sheets as they are subjected to relative humidity changes. The transient moisture diffusion problem is solved using a “natural” analytic approach that has previously been applied for solving transient heat conduction in multi-layer solids. The deformation behaviour of the sheet during the moisture diffusion process is predicted using a semi-analytical approach based on a Rayleigh–Ritz minimization of the total potential energy. Geometrically nonlinear effects are taken into account. Curvatures of the originally flat sheet are predicted as a function of time, as are the shapes of the sheet for steady-state condition. As multiple solutions exist, stability is studied. The developed model was used to study the deformation behaviour of one paper and two cardboard sheets. Comparisons with finite-element results demonstrate that the developed model provides accurate results. The displacements obtained for steady-state conditions are within +6%. Comparisons with previous steady-state analyses reveal important differences in the shape of one cardboard sheet. This suggests that the moisture diffusion process may influence the configuration assumed by the sheet at steady-state equilibrium. Hence, it may be necessary to take the moisture diffusion into account in the analysis to accurately predict the hygro-mechanical behaviour of paper or cardboard sheets. [Copyright &y& Elsevier]

Abstract: Non-crimp fabric (NCF) composites are constituted by differently oriented layers of ideally unidirectional fibre tows. However, a slight waviness always appears in the tows. The applicability of the general laminate theory (GLT) to obtain the stiffness properties of NCF laminates is elucidated in this paper. For this purpose, a 3D finite element (FE) model of the representative unit cell (RUC) of a single NCF lamina has been carried out to obtain its apparent stiffness properties, which are employed, along with the GLT, to determine the stiffness properties of the laminate. These properties are compared with those obtained from the FE model of the RUC of the whole laminate for several configurations with different stacking sequences, fibre contents and crimp angles. Finally, predictions are compared with existing experimental results. The numerical results achieved validate the use of the GLT in NCF composites, once the lamina properties have been calculated taking into account the internal structure of these materials. [Copyright &y& Elsevier]

In this paper a smoothing procedure is suggested for the 3D beam-to-beam contact. A smooth segment is defined basing on current position vectors of three nodes limiting two adjacent finite elements. The approximated fragment of a beam axis as a 3D curve spans between the centre points of these elements. The curve is described parametrically using three Hermite polynomials. The four boundary conditions necessary to determine the coefficients for each of these polynomials involve co-ordinates and slopes at the curve ends. The slopes are defined in terms of the element nodal co-ordinates, too. There is no dependence on nodal rotations so this formulation can be embedded in a beam analysis using any type of beam finite element. This geometric representation of the curve is incorporated into the 3D beam-to-beam frictional contact model with the penalty method used to enforce contact constraints. The residual vector and the corresponding tangent stiffness matrix are determined for the normal part of contact and for the stick or slip state of friction. A few numerical examples are presented to show the performance of the suggested smoothing procedure in the cases featuring large frictional sliding. [ABSTRACT FROM AUTHOR]

In this paper, a finite element procedure is used to study the dynamic behaviour of a paper web in a free span between two rollers, including effects of transport velocity and surrounding air. The paper web is modelled as a three-dimensional orthotropic structure. The influence of air is accounted for by utilizing fluid–solid interaction analyses based on acoustic theory. The contribution of transport velocity is included through gyroscopic matrices and forces. The structural response on harmonic excitations has been studied using linear and non-linear models. Results show that air significantly reduces eigenfrequencies of the web. So called “edge-flutter” is nothing but the result of skew tension profile. Excessive web vibration can be eliminated by adjusting the web tension. [Copyright &y& Elsevier]

Abstract: The creep of paper is accelerated by moisture cycling. This effect is known as mechano-sorptive creep. It is assumed that this is an effect of transient stresses produced during moisture content changes in combination with non-linear creep behaviour of the fibres. The stresses produced by the moisture content changes are often much larger than the applied mechanical loads. If this is the case, the mechanical loads are only a perturbation to the internal stress state, and it will appear as if the mechano-sorptive creep is linear in stress. It is possible to take advantage of this feature. In the present report the pure moisture problem is first solved. The mechanical load is then treated as a perturbation of the solution to the moisture problem. Using this strategy, it is possible to linearize a non-linear network model for mechano-sorptive creep and to formulate a continuum model. As a result, the number of variables in the model is reduced. This is a significant improvement as it will be possible to use the linearized model to describe the material in a finite element program and solve problems with complicated geometries. [Copyright &y& Elsevier]

Abstract: A multisymplectic integrator for the periodic nonlinear Schrödinger equation is presented in this paper. Its accuracy is proved. By introducing a norm, we investigate its nonlinear stability. We also discuss the relationship between this multisymplectic integrator and two variational integrators which are derived by using the discrete multisymplectic field theory and the finite element method. [Copyright &y& Elsevier]

Abstract: This paper presents a flexural analysis of I-shaped laminated composite beams. A general analytical model applicable to thin-walled I-section composite beams subjected to vertical load is developed. This model is based on the shear-deformable beam theory, and accounts for the flexural response of the thin-walled composites for arbitrary laminate stacking sequence configuration, i.e. unsymmetric as well as symmetric. Governing equations are derived from the principle of the stationary value of total potential energy. Numerical results are obtained for thin-walled composites under vertical loading, addressing the effects of fiber angle and span-to-height ratio of the composite beam. [Copyright &y& Elsevier]

Abstract: The rolling of a cylindrical drum on a stack of separate paper sheets is studied using the finite element method. A two-dimensional model under plane strain conditions is considered. The material of the sheets is modelled by a linearly elastic orthotropic constitutive law. The friction between the various contacting surfaces is modelled by the conventional Coulomb''s law. As a result of the FEM-calculations, the time development of the displacements, stresses and strains of the paper layers is obtained. The slip behaviour at the various contacting surfaces is presented. The micro-slip pattern of the contacting surfaces in the nip area and, particularly, at the trailing edge of the nip, seems to be the main reason for the tightening effect of the nip. The results are compared to the corresponding results for a solid elastic block under the rolling cylinder. [Copyright &y& Elsevier]

Upon application of water based coating onto silicone-coated paper and during the subsequent drying process, the water permeates through the silicone layer into the paper substrate. At the same time, water evaporates from both the surface of the coated layer and throughout the paper layer. Initially, the evaporation rate from the wet coating surface may be dominant, but at longer times the bulk evaporation from the paper can dominate. Here a three-layer diffusion model for such a system is developed. Solutions obtained by Galerkin's method with finite element basis functions show that the hygroscopic nature of the paper leads to low drying rates at low moisture contents. Further, the model predicts that initially the coating dries to a moderately low residual moisture concentration faster than a coating applied on an impermeable substrate. However, at longer times, the predicted residual moisture of coatings applied on silicon-coated paper is higher than for a coating applied on an impermeable substrate. [ABSTRACT FROM AUTHOR]

In this paper, the revolutions of wafer and pad were considered the same and the force forms including the pressure exerted on the top of wafer surface and the carrier back pressure were axisymmetric distributed, a 2D axisymmetric quasi-static model for chemical mechanical polishing process (CMP) was first established. Based on the principle of minimum total potential energy, a 2D axisymmetric quasi-static finite element model with a carrier back pressure compensation for CMP was then established. In this model, the four-layer structures including wafer carrier, carrier film, wafer and pad are involved. The effect of a given carrier back pressure on the stress components and von Mises stress on wafer surface was analyzed and the effect of different carrier back pressures on the von Mises stress and nonuniformity on wafer surface was investigated. The findings indicated that the axial stress was the dominant factor to the von Mises stress distribution on wafer surface. Because that the back pressure had the maximum affect on the axial stress and it made the axial stress increased along the −z direction. Thus, while applying a back pressure, the von Mises stress distribution increased. In addition, the changes of back pressure had the trend to be proportional to the von Mises stress variation and to be inversely proportional to the nonuniformity variation. The result showed obviously that during the CMP process, it could achieve the purpose to improve the planarization of wafer surface by compensating the different carrier back pressures. [Copyright &y& Elsevier]

Asperity flattening study plays an important role in predicting the friction behavior at the interface and the surface roughness transfer during sheet metal-forming process. This paper presents a comparison of asperity flattening activities under 1-wavelength, 2-wavelength and 3-wavelength finite-element models developed based on a power spectral density (PSD) analysis of measured data on steel sheet surfaces. First, a proper asperity thickness for the modeling has been determined by the investigation of plastic strain distribution along the depth of asperity. The comparison then examines the evolution of real contact area, surface roughness, contact pressure distribution and variation of friction force at the interface between a tool and a workpiece drawn from different wavelength simplification models under various friction conditions. It is concluded that 3-wavelength model has closer results to experimental measurements and introduces less contact area and more local pressure concentrations than those from the other two models. [Copyright &y& Elsevier]

In this paper, we use a prevalent finite element analysis software, MARC, to simulate the process for a subject material undergoing equal channel angular extrusion (ECAE), as well as calculating the strain conditions. For a single ECAE pass, the transversal strain distribution in the deformed body will be analyzed to investigate the influences from channel angle, friction between die and pressed material, and curved joining channels. Simulations involving double passes of the subject material were also conducted, something that has not been previously pursued much elsewhere. [Copyright &y& Elsevier]