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Made available in DSpace on 2022-04-29T08:31:12Z (GMT). No. of bitstreams: 0 Previous issue date: 2021-10-01 Organization and planning of reverse logistics networks make sustainable processes more efficient. Thus, an important sector for connecting the collection and waste paper recycling echelons is the intermediate center. In this study, a Mixed Integer Linear Programming model, which is multi-objective, multi-product, multi-level and multi-period, was developed to optimize the waste paper logistics processes of intermediate centers. The formulation includes the following echelons: collection, considering vehicle routing with different capacities; inventory of non-baling materials; baling sorted waste and inventory of bales; selling bales; disposal of non-recyclable waste. The aims of the model include: maximizing the collected waste; minimizing distances; maximizing both the production and sale of bales, and minimizing costs. According to research carried out in the literature, the developed model is a new proposal and to implement it, the Weighted Goal Programming and Revised Multi-Choice Goal Programming approaches were used to deal with multiple objectives and incorporate uncertainty into the quantity of waste available for collection. To analyze the proposed model, computational tests were executed with instances based on real data from a Brazilian company in the sector. For all performed tests, General Algebraic Modeling System 23.6.5 modeling language and CPLEX 12.2.0.2 solver were used for modeling and optimization. The results show that this study presents formulation and technological approaches that represent real situations and provide competitive solutions to the problem. Sáo Paulo State University “Júlio de Mesquita Filho” [Universidade Estadual Paulista Júlio de Mesquita Filho] School of Engineering of Guaratinguetá [Faculdade de Engenharia de Guaratinguetá] Production Department, Av. Ariberto Pereira da Cunha, 333, Portal das Colinas Agulhas Negras Military Academy [Academia Militar das Agulhas Negras] Rodovia Presidente Dutra, km 306, s/n Escola Preparatória de Cadetes do Exército Avenida Papa Pio XII 350 Jardim Chapadão Campinas - SP Brazil, Avenida Papa Pio XII, 350, Jardim Chapadão, Campinas - SP Sáo Paulo State University “Júlio de Mesquita Filho” [Universidade Estadual Paulista Júlio de Mesquita Filho] School of Engineering of Guaratinguetá [Faculdade de Engenharia de Guaratinguetá] Production Department, Av. Ariberto Pereira da Cunha, 333, Portal das Colinas

The paper drying process has the highest level of energy consumption in the pulp and paper production process. Analysis and optimization of the energy system during the paper drying process is critical for improving the energy efficiency of the entire paper mill. In the existing model for the paper drying process, the solution requires accurate boundary conditions such as the air temperature and humidity of the pocket area and the cylinder surface temperature, which are very difficult to obtain in the papermaking process. This can result in significant deviations between the model solution and the actual production process. This paper focuses on the single-tier dryer cylinder-based paper drying process that has been widely used with high-speed papermaking machines in recent years. A mathematical model is proposed based on real-time data. The verification via industrial production demonstrates that the proposed model is reliable for the paper drying process. Based on the simulation results, two optimization operations have been proposed. The energy consumption decreases from 1.51 t steam/t paper to 1.44 t steam/t paper, 4.6% of the steam and 1.26 × 106 RMB can be saved for a medium-scale paper mill with the annual production capacity of 105 t paper.

Cellulose fibers come in a wide range of shapes and sizes. The heterogeneity of the fiber length, width, wall thickness, curl and external fibrillation is detrimental to the mechanical performance of products such as paper and paperboard. Although micro-mechanical models of these materials sometimes incorporate features of this heterogeneity, so far there is no standardized method of fully incorporating this. We examine a large number of industrial mechanical fiber pulps to determine what information such a standardized method would have to have. We find that the method must allow for both non-Gaussian distributions and dependence between the variables. We present a method of characterizing mechanical pulp under these conditions that views the individual fiber as outcome of a sampling process from a multivariate distribution function. The method is generally applicable to any dataset, even a non-Gaussian one with dependencies. Using a micro-mechanical model of a paper sheet the proposed method is compared with previously presented methods to study whether incorporating both a varying fiber size and dependencies is necessary to match the response of a sheet modeled with measured characterization data. The results demonstrate that micro-mechanical models of paper and paperboard should not neglect the influence of the dependence between the characteristic shape features of the fibers if the model is meant to match physical experiments. © 2022 The Authors

In fibrous paper materials, an exposure to a variation in moisture content causes changes in the geometrical and mechanical properties. Such changes are strongly affected by the inter-fibre bonds, which are responsible for the transfer of the hygro-mechanical response from one fibre to its neighbours in the network, resulting in sheet-scale deformation. Most models developed in literature assume perfect bonding between fibres. In the 3D reality, there is some flexibility in the bond region, even for the perfectly bonded fibres, because of the possibility of deformation gradients through the fibre thickness. In earlier 2D idealizations, perfectly bonded fibres were assumed, implying full kinematic constraint through the entire thickness of the sheet. The purpose of the present study is to assess the effect of this assumption. Using a homogenization approach, a random network of fibres is generated with different coverages and modelled using finite elements. In order to understand the role of bonding between fibres on the hygro-expansive behaviour of a network, a bond model is developed. In this model, the fibres are modelled using 2D regular bulk finite elements and the bonds are represented by interfacial elements of finite stiffness, which are introduced between each pair of fibres bonded in the network. These embedded interfacial elements form a connection between two respective fibres, allowing relative displacements between their mid-planes. The hygro-elastic response of networks obtained with this bond model is investigated by varying the bond stiffness and the network coverage under the application of mechanical loading and changes in moisture content. Furthermore, the bond model is used to analyse the influence of inter-fibre bonds on the anisotropic response of the paper fibre network., Comment: 26 pages, 16 figures

The European Transport White Paper 2011 sets high modal shift targets from road freight to rail 50% by 2050. The objective of this paper is to determine the rolling stock fleet size and type up to the year 2050 and associated challenges for stakeholders. Considering the White paper targets, three scenarios are considered; a) Business as usual or Reference Scenario – extrapolation of current trends without major policy change; b) White Paper 2011 Low Scenario (WPL) based on a partial implementation of the modal shift targets and c) White Paper 2011 High Scenario (WPH) based on the full implementation of modal shift targets. To determine the future fleet size, the current paper also conducts a sensitivity analysis assuming 60% productivity level as a base line. The study finds, among others, that significantly more rolling stock (in particular flat wagons, covered wagons and covered hopper wagons) as well as improved asset utilisation will be vital to facilitate the transport of increased freight volume. A unified rail freight system starting with nine Rail Freight Corridors and cooperation among the rail freight operators, wagons manufacturers and companies involved in leasing and hiring wagons will be very important to achieve the modal shift.

This paper proposes an agent-based simulation model to study and analyse the performance of various procurement and production policies in the recycled paper industry. The proposed model includes the recycled pulp production process, as well as the waste paper inventory and procurement processes. A detailed simulation model developed in partnership with a large recycled pulp producer in North America was developed in order to emulate the procurement manager's behaviour. Therefore, based on the observed behaviour of the procurement manager, a procurement behaviour model, which takes both market price and inventory requirement into account, is introduced. This paper also introduces a waste paper market model that simulates a market price and enables the control of price forecast accuracy. Two series of experiments were carried out in order to study the performance of procurement and production policies in several productions contexts. Results show that production Volume Flexibility has a negative impact on costs, inventory and quality. However, it is possible to partially reduce these issues with the introduction of contracts with Volume Flexibility, although only a limited effect has been observed in our experiments. A more significant strategy to improve costs consists in reducing production rate to the minimum level required to meet demand.

A number of problems associated with dimensional stability of paper products have to do with hygroexpansion in response to changes in humidity or moisture content. The main underlying mechanism of hygroexpansion in paper is the effect of the change of fiber cross-sections transferred through fiber bonds. In fact, the transverse expansion of fibers can be an order of magnitude greater than the longitudinal expansion. Addressing such problems using modeling on the microscale is associated with large computational costs since both the bonds and the fibers need to be resolved. We present a method for modeling the hygro or thermal expansion of interconnected fiber networks modeled with beam elements and connected through beam-to-beam contact. Being a line structure, beams can only support pointwise contact, which poses a challenge for modeling the force transfer induced by the deformation of the cross-sections at the contact point. The idea of implementing the stress transfer is to use a concurrent multiscale approach in which the bond level is resolved in detail using the configuration of the fibers and the computed strains are passed over to the beam elements. We verify and prove the applicability of this approach by comparing it with continuum models. We demonstrate the advantage of using this approach in terms of its tremendous saving in time. The use of beam models for modeling the hygro- or thermal expansion of fiber networks enables considering relevant sizes in the problems involving dimensional stability, in particular those associated with embedded inhomogeneities. We will show the applicability of the model by providing insights into published experimental observations on the hygroexpansion properties of paper products. Finally, we will demonstrate that the use of a 2D model to simulate the inter-fiber bonds in a network, not only leads to underestimation of out-of-plane deformations, but also to overestimation of the contribution of the transverse deformation of fibers to the in-plane dimensional change of the network.

Recently, metapopulation models for rock-paper-scissors games have been presented. Each subpopulation is represented by a node on a graph. An individual is either rock (R), scissors (S) or paper (P); it randomly migrates among subpopulations. In the present paper, we assume victory rates differ in different subpopulations. To investigate the dynamic state of each subpopulation (node), we numerically obtain the solutions of reaction-diffusion equations on the graphs with two and three nodes. In the case of homogeneous victory rates, we find each subpopulation has a periodic solution with neutral stability. However, when victory rates between subpopulations are heterogeneous, the solution approaches stable focuses. The heterogeneity of victory rates promotes the coexistence of species.

We discuss cutting stock problems (CSPs) from the perspective of the paper industry and the financial impact they make. Exact solution approaches and heuristics have been used for decades to support cutting stock decisions in that industry. We have developed polylithic solution techniques integrated in our ERP system to solve a variety of cutting stock problems occurring in real world problems. Among them is the simultaneous minimization of the number of rolls and the number of patterns while not allowing any overproduction. For two cases, CSPs minimizing underproduction and CSPs with master rolls of different widths and availability, we have developed new column generation approaches. The methods are numerically tested using real world data instances. An assembly of current solved and unsolved standard and non-standard CSPs at the forefront of research are put in perspective.

In this short communication the solution of a steady state model of a sextuple evaporator system used in a paper industry has been presented. With the help of the residual values of model equations (a set of 12 nonlinear algebraic equations) it has been shown that the presently obtained results are superior to the previously published results. The importance of the number of significant digits in calculation are also briefly discussed.

Migration paths of animals are rarely the same. The paths may change according to seasonal and circadian rhythms. We study the effect of temporal migration on population dynamics of rock-paper-scissors (RPS) games with mutation by using the metapopulation dynamic model with two patches. Via mutation, an individual R changes to S with rate μ. All agents move by random walk between two patches and the RPS game is performed in each patch. The migration path between two patches is switched on or off periodically. The dynamics are represented by the reaction-diffusion equations with time-dependent diffusion coefficients in diffusively coupled reactors. We obtain the solutions of time-dependent reaction-diffusion equations numerically and analytically. The time-varying migration path induces complex behavior for the RPS dynamics, depending on the frequency of the periodical path. We find that the phase transitions occur by varying mutation rate μ. The phase transition depends highly on the frequency.

The cross-directional (CD) basis weight control on paper machines is improved by optimizing the path of the scanning measurement. The optimal path results from an LQG problem and depends on how the uncertainty of the present estimate of the basis weight and the intensity of process noise vary in CD. These factors are assessed by how accurately the CD basis weight estimate predicts the measured optical transmittance with a linear adaptive model on synchronized basis weight and transmittance data. Simulations on optimized scanner path in disturbance scenarios are presented, and the practical implementation of scanner control is discussed.

Much literature exists for rock-paper-scissors (RPS) game. It is well known in a single habitat that spatial models are more stable than well-mixed population. However, the mechanism of spatial stabilization has been unclear. In the present article, we study multilayer model of RPS game in a patchy environment; respective patches are set as lattices. The predation probability of one of three species is assumed to be reduced as a parameter. Simulations on two-layer system reveal the opposite result to those on a single-habitat system. Namely, the well-mixed population becomes stable. In contrast, extinction occurs by random migration in spatially-explicit model, when the reduced predation probability is below a certain critical value. The extinction in spatial model is found to be caused by the collapse of a kind of swarm intelligence (SI). In RPS system, large swarms of each species are automatically protected from its predator. Such a self-organized protection is one of the simplest examples of SI. We also discuss some serious problems for random migration.

The paper is devoted to correcting structure of the representation for Rayleigh waves at non-semisimple degeneracy of the fundamental matrix. The incorrect representation was given in a paper “Implicit and explicit secular equations for Rayleigh waves in two-dimensional anisotropic media” by Cerv and Plesek (2013) .

The conventional office paper recycling process reduces used paper to a pulp prior to cleaning and re-forming. The difficulty of collecting and sorting waste paper, the low process yield and the energy required to re-form the used paper make this process economically unattractive and potentially environmentally less preferable than virgin production. Together these have resulted in a low recycling level for European office papers. An attractive alternative is the possibility of recycling office paper within the office, without destroying the mechanical structure of the paper. This paper reviews 104 patents filed mainly since the mid 1990s that propose technologies to achieve this. The patents are grouped into three categories: de-colouring the toner or ink; obscuring existing print; print removal by adhesion, ablation, abrasion or chemical processes. Some of these processes require new substrates, coatings, inks or toners, and to date only one has been released commercially. The various technology options are compared, and an assessment is offered of their likely future development.

This work is concerned with the adhesion strength between a paper web and a metal roll surface, which is a common situation in paper machines world-wide. It is shown that the classic expression relating the work of adhesion to the peeling angle and web tension is, in general, insufficient. An improved model is suggested to take into account the energy dissipation due to elastic–plastic deformation behavior of wet paper materials. To judge the model, an industrially relevant example of wet newsprint and a mild steel surface is studied. It is found that the agreement between theory and experimental observations is excellent. A key result is that elastic–plastic material behavior must always be included for wet paper materials in peeling processes.

Availability analysis has been an important issue in the design field of any Industrial system as the system structure has become more complicated. Also, the system availability is affected by many factors such as design, manufacturing, installation, etc., and so it may be extremely difficult to model, analyze and predict the failure behavior of the system. The purpose of this paper is to develop a new approach for computing various performance measures, namely reliability, availability, MTBF (mean time between failures), ENOF (expected number of failures), failure rate and repair time, for any industrial system. In the proposed approach, the failure rates and repair times of all constituent components are obtained using genetic algorithms and then various performance measures are computed using fuzzy lambda–tau methodology. Washing system, the major part of paper industry is the subject of study. The interactions among the working components are modeled using Petri nets. Failure and repair rates are represented using triangular fuzzy numbers as they allow expert opinion, linguistic variables, operating conditions, uncertainty and imprecision in reliability information to be incorporated into system model. Based on calculated reliability parameters, a structured framework has been developed that may help the maintenance engineers to analyze and predict the system behavior.

In a recent paper referred to in the title, the author used the concept of quasi self-adjointness to obtain conservation laws for a system of the ( 2 + 1 ) -dimensional Bogoyavlensky–Konopelchenko equation. Apart from the adjoint system of equations, all the results on the quasi self-adjointness and the subsequent conservation laws obtained are inaccurate. In this comment, we clarify these inaccuracies and also generate conservation laws for a potential form of the underlying equation through Noether theorem.

In this corrigendum we correct an error in our paper [T. Caraballo, R. Colucci, J. Lopez-de-la-Cruz and A. Rapaport. A way to model stochastic perturbations in population dynamics models with bounded realizations, Commun Nonlinear Sci Numer Simulat, 77(2019) 239–257]. We present a correct way to model real noisy perturbations by considering a slightly different stochastic process based, as in the original paper, on the Ornstein-Uhlenbeck process. Namely, we correct the formulae that generates the noisy realizations to ensure the boundedness property to be satisfied with probability one (which turns out not to be true in our original paper even though it was observed in all the simulations).

Fine paper mills produce a variety of paper grades to satisfy demand for a large number of sheeted products. Huge reels of different paper grades are produced on a cyclical basis on paper machines. These reels are then cut into rolls of smaller size which are then either sold as such, or sheeted into finished products in converting plants. A huge number of roll sizes would be required to cut all finished products without trim loss and they cannot all be inventoried. An assortment of rolls is inventoried with the implication that the sheeting operations may yield trim loss. The selection of the assortment of roll sizes to stock and the assignment of these roll sizes to finished products have a significant impact on performances. This paper presents a model to decide the parent roll assortment and assignments to finished products based on these products demand processes, desired service levels, trim loss and inventory holding costs. Risk pooling economies made by assigning several finished products to a given roll size is a fundamental aspect of the problem. The overall model is a binary non-linear program. Two solution methods are developed: a branch and price algorithm based on column generation and a fast pricing heuristic, and a marginal cost heuristic. The two methods are tested on real data and also on randomly generated problem instances. The approach proposed was implemented by a large pulp and paper company.

Zinc oxide (ZnO) is a potential pigment material for paper coating to impart brightness and better printing properties. Nano-ZnO, due to its extremely small size, gives paper coating pigment a high covering power apart from anti-fungal and UV-protecting properties. In this work, zinc oxide–soluble starch nanocomposites (nano-ZnO) was prepared by a simple and novel wet chemical method using zinc nitrate and sodium hydroxide as precursors and soluble starch as stabilizing agent. Primary particle size distribution was extracted from small angle X-ray scattering (SAXS) measurements by the hard sphere model and calculated to have an average size of 4.1 nm. This nano-ZnO was coated on the surface of base paper (59 GSM) in a laboratory paper coater and their properties were studied. The brightness, whiteness, paper smoothness, print density, print uniformity, picking velocity and oil absorbency of nano-ZnO coated paper showed significant improvement than that of bulk-ZnO coated paper. In addition, the nano-ZnO coated paper showed excellent anti-fungal and UV-protecting properties that are much essential to enhance the life of a paper.

A hybrid method of ecological habitat survey and mapping is presented, bridging paper-based methods and mobile electronic procedures. The hybrid approach uses a hand-held PDA with real-time dGPS to map habitats and record habitat attributes. It retains paper field maps to facilitate ecological decisions and to overcome the need for field surveyors to operate a fully functional mobile GIS system. The transition from paper records to a full GIS implementation is bridged by secondary digitisation in which a GIS specialist, trained in field survey procedures, interacts routinely with the field surveyors, throughout the field season to assure data quality standards. The methodology is practical and affordable, particularly if there are multiple field surveyors.

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.

Corrugated paper is produced by gluing three types of papers of the same breadth. Given a set of orders, we first assign each order to one of the standard breadths, and then sequence those assigned to each standard breadth so that they are continuously manufactured from the three rolls of the specified standard breadth equipped in the machine called corrugator. Here we are asked to achieve multi-goals of minimizing total length of roll papers, total loss of papers caused by the differences between standard breadths and real breadths of the orders, and the number of machine stops needed during production. We use integer programming to assign orders to standard breadths, and then develop a special purpose algorithm to sequence the orders assigned to each standard breadth. This is a first attempt to handle scheduling problems of the corrugator machine.

An experimental investigation is performed and analyzed in order to examine the onset and evolution of damage processes in thin isotropic paper sheets made of mechanical pulp. A microscopy technique has been used to estimate the relative fraction of bond and fibre breaks. It has been found that the active damage mechanism is bond failure, hence supporting the assumption of an isotropic scalar valued damage variable.All experiments have been performed by simultaneous with the mechanical loading monitoring the acoustic emission activity. Three different experimental setups have been designed offering the possibility to analyze the influence of stress gradients, as well as different levels of the ratios between the in-plane normal stresses, on the onset of damage. It is concluded that stress gradients in the paper specimens have a large influence on the onset of damage. When stress gradients are present a non-local theory has to be used in the analysis. In this way compliance with an isotropic damage criterion is achieved. The characteristic length, determining the gradient sensitivity, has been found to be of the same order of magnitude as some average fibre length.To study the evolution of the damage processes, wide and short specimens have been loaded in tension resulting in stable damage processes. With the assumptions made regarding the mechanical behavior of the paper material after onset of damage, the damage and the cumulative number of acoustic events curve correlates very well. The experimentally obtained data is used to determine material parameters in a proposed damage evolution law. It is found that the assumed damage evolution law can, for isotropic paper materials with bond rupture as the prevalent failure mechanism, be further simplified as only one specific material dependent damage evolution parameter has to be determined in experiments.

In this paper a simplified network model for mechano-sorptive creep is presented, which is a further development of an earlier paper [Strömbro, J., Gudmundson, P., 2008. Mechano-sorptive creep under compressive loading – a micromechanical model. International Journal of Solids and Structures 45 (9), 2420–2450.]. It is assumed that the anisotropic hygroexpansion of the fibres leads to large stresses at the fibre bonds when the moisture content changes. The resulting stress state will accelerate creep if the fibre material obeys a constitutive law that is non-linear. Fibre kinks are included in order to capture experimental observations of larger mechano-sorptive effects in compression than in tension. Moisture dependent material parameters and anisotropy in the fibre distribution have been introduced. Theoretical predictions based on the model are compared to experimental results for an anisotropic paper both under tensile and compressive loading at varying moisture content and it is found that the important features in the experiments are captured by the model. Different kinds of drying conditions have also been examined.

An anisotropic elasto-plastic constitutive model of paper material is presented. It is formulated in a spatial setting in which anisotropic properties are accounted for by use of structural variables. A multiplicative split of the deformation gradient is employed to introduce plasticity. A similar approach is used to model the plastic deformation of the substructure. The yield surface adopted is based on the Tsai–Wu failure criterion, used previously to model failure of paper material. A non-associated plasticity theory is employed to calibrate the model to experimental data. It turns out that a multi-axial loading situation is needed to calibrate the model and here a biaxial tension test is audited. The model was implemented into a finite element environment and the creasing process of a corrugated board panel is investigated.

Polymorphisms are usually associated with defenses and mating strategies, affecting the individual’s fitness. Coexistence of different morphs is, therefore, not expected, since the fittest morph should outcompete the others. Nevertheless, coexistence is observed in many natural systems. For instance, males of the side-blotched lizards ( Uta stansburiana ) present three morphs with throat colors orange, yellow and blue, which are associated with mating strategies and territorial behavior. The three male morphs compete for females in a system that is well described by the rock-paper-scissors dynamics of game theory. Previous studies have modeled the lizards as hermaphroditic populations whose individual’s behavior were determined only by their phenotypes. Here we consider an extension of this dynamical system where diploidy and sexual reproduction are explicitly taken into account. Similarly to the lizards we represent the genetic system by a single locus with three alleles, o, y , and b in a diploid chromosome with dominance of o over y and of y over b . We show that this genotypic description of the dynamics results in the same equilibrium phenotype frequencies as the phenotypic models, but affects the stability of the system, changing the parameter region where coexistence of the three morphs is possible in a rock-paper-scissors game.

We propose a new concept which is a generalization of fuzzy soft subset and fuzzy soft equal. Using such notions, we will be able to consider the distributive law of fuzzy soft sets. Using the distributive law of fuzzy soft sets, we point out that the distributive law of trapezoidal fuzzy soft sets as proposed by Xiao et al. (2012) is not true. The correction will further improve further extensions of the results of Xiao et al. (2012). We will also establish the generalized distributive law of trapezoidal fuzzy soft sets along with illustrative examples.

Strains, computed by the finite element method, are evaluated and compared to an experimentally determined strain field. The analyzed low-density paper has been designed to ensure bond–breakage as the dominating damage mechanism and the paper material is approximately in-plane isotropic. An optical non-contact displacement measuring system has been used in fracture tests to determine the strain field in the crack-tip region of a pre-fabricated crack. Additionally, acoustic emission monitored tensile tests have been conducted to determine onset and evolution of damage processes and thereby enabling calibration of required constitutive parameters. The results suggest that the investigated paper material can tolerate significantly higher strains than what is predicted by a classic elastic–plastic J2-flow theory. Immediately before onset of the final fracture (i.e., localization), the experimental measured normal strain in the near-tip region is around 60% higher than the computed strain when using exclusively an elastic–plastic theory for the corresponding load while the strain computed utilizing a non-local damage theory is of the same order of magnitude as the experimentally measured strain. Hence, it seems essential to include a non-local continuum theory to describe strains in the near-tip region quantitatively correct for paper materials. It is demonstrated that path independence of the well-known J-integral does not prevail for this class of material models. Only for the special situation of a homogenous damage field in the crack-tip region may the stress and strain fields be described by the well-known HRR-solutions.

We estimate the orientation of wood fibers in porous networks like paper, paperboard or fiberboard by computing digital thermal conductivity experiments on micro-computed tomography ( μ CT) images with artificial isotropic thermal conductivity parameters. The accuracy of mechanical and thermal constitutive models for porous wood fiber based materials crucially depends on knowing the wood fiber orientation. Unfortunately, due to the high porosity, the micro-heterogeneity of wood fibers, the high carbon content of organic materials and the unknown additives present in industrial paper, μ CT-scans often exhibit low contrast and strong artifacts. Conventional image processing approaches encounter difficulties, as they rely upon convex fiber cross sections. We propose a solution by circumventing the segmentation of single wood fibers in μ CT images, by performing thermal conductivity simulations on binarized wood fiber structures, where an artificial isotropic thermal conductivity is associated to the fibers and the pore space is considered as isolating. The local and global temperature fluxes are assembled into a fiber orientation tensor. This method overcomes the limitations of the mentioned local image processing approaches, as individual fibers need not be resolved and convergence for increasing resolution is a consequence of abstract mathematical theory. We use our novel method to analyze large three-dimensional μ CT-scans and a synchrotron scan of a paperboard sample, serving as the starting point of an accurate micromechanical modeling of the effective anisotropic mechanical behavior of paper and paperboard. These results are crucial for calculating the mechanical strength of deep-drawn paperboard, which will be accomplished in a subsequent article.

The addition of a large amount of conductive filler to paper in order to increase electrical conductivity adversely affects some physical properties of the paper. Hence, it is desirable that conductive paper can be manufactured by adding only a small amount of conductive filler. Reinforced paper was manufactured by adding (1) electroless Ag-plated carbon fiber or (2) activated carbon fiber to the pulp. We investigated the effects of adding Ag-plated carbon fiber on the microstructure, physical properties, electrical conductivity, etc., of the paper. We found that the addition of a small amount of Ag-plated carbon fiber to the pulp made it possible to manufacture conductive paper with a high level of electrical conductivity and great physical strength.

Continuum damage mechanics (CDM) is used to describe the post-elastic behavior of low-basis-weight paper. The relevance of undertaking studies of the mechanical behavior of low-basis-weight paper is that it enables characterization, optimization and quality control. In accordance with a CDM theory, an internal variable is introduced that represent the degree to which the material has degraded in a continuum sense and details inherent in a damage evolution law contain information about the rupture mechanism. To account for long ranging micro-structural effects, because of the fiber structure in the paper material, a non-local formulation of the constitutive law is considered. Of particular interest is the fracture toughness of the material, i.e. the ability to resist further crack propagation, as it is often a good measure of flaw tolerance and durability in the context of paper. The constitutive model discussed is verified against tensile tests on rectangular paper specimens containing pre-fabricated cracks. Acoustic emission was used to study the damage evolution in paper specimens during tensile loading. An orthotropic material description has been utilized. The model is contrasted with a purely isotropic formulation. It seems that for the type of problem analyzed in this work, an orthotropic material description does not significantly improve the predictive capability as compared to an isotropic formulation. It is concluded that the model can be used to evaluate the influence of arbitrary defect geometries, defect size and loading conditions and can easily be incorporated into a finite element code.

We consider a vertically integrated papermaking operation composed of an integrated pulp and paper mill with its regional supply network. Considering land procurement and harvest rotation as strategic decision variables, we construct a model to establish a long-range timber supply plan that minimizes the total discounted cost of meeting annual virgin wood fiber demand over an infinite horizon. Under appropriate assumptions on costs and storage, the land procurement and harvest rotation decisions are separable with harvest rotation being determined via a forest economics-type equation and land procurement being determined by a newsvendor-type equation.

A mechanistic nonlinear model of the wet end of paper machine 6 (PM6) at Norske Skog Saugbrugs, Norway has been developed, and used in an industrial MPC implementation. The MPC uses an infinite horizon criterion, successive linearization of the model, and estimation of states and parameters by an augmented Kalman filter. Variation in important quality variables and consistencies in the wet end have been reduced substantially, compared to the variation prior to the MPC implementation. The MPC also provides better efficiency through faster grade changes, control during sheet breaks and start ups, and better control during periods of poor measurements. From May 2002 of the MPC has been the preferred controller choice for the process operators at PM6. In this paper we also study if the model can be applied to PM4 at Norske Skog Saugbrugs, and PM3 at Norske Skog Skogn, Norway. No structural changes were necessary in order to fit the model to PM4 and PM3 data. The time spent on fitting the PM6 model to PM4 and PM3 is approximately 1% of the time spent on developing the original model. This should be a strong incentive for focusing on mechanistic modeling in industries were there are many similar production lines or units.

This paper describes the ongoing research on the physical modeling of AssiDoman paper mill in Frovi (Sweden). This project includes the developing of a Modelica base library for thermohydraulic, pulp and paper systems. Up to now, the model includes the wet end part of the paper process, that is the approaching system from the mixing chests to the cyclone systems, the headboxes and the wires.

A controllability analysis of a paper machine forming zone in a newsprint mill was performed to determine the maximum allowable variability of the pulp furnished to the process. The goal was to keep the output variables, basis weight and first-pass retention between certain limits in spite of disturbances and paper grade changes. The results indicate that the process is more disturbed at high frequencies, and that the two output variables may be maintained within the interval ±1% of their nominal values if the maximum variability in the consistency and fines content of the thick-stock is kept lower than ±1 and ±2%, respectively.

In this paper the deep drawing of cups from fiber-based materials, which is explored for some time now, is further developed through the use of micron-small vibrations in an ultrasonic frequency range within the deep-drawing tools. The design of such tools required preliminary investigations concerning the limitations of use and feasibility of this technology. These include tests for necessary clearances between punch and die, occurring pressure in this clearance, necessary punch forces and the heating of the material under the vibrational influence. According to these experiences a flexible test machine was developed enabling the examination of the deep drawing process with vibrating tools as well as its possibilities and limits. The dependence of punch force and cup quality from the ultrasonic parameters was determined and it was found that the required punch force can be reduced by up to 80% and a significant smoothing of the cup surface as well as an improved stiffness of the 3D-shapes is achieved.

Laminated paperboard and paper is widely used in packaging products. It generally exhibits highly anisotropic and nonlinear mechanical behavior. The aim of this study is to describe the in-plane material behavior with an orthotropic elastic-plastic model based on the observed experimental behavior. A structural tensor-based approach was applied to model the elastic deformation, while a multi-surface based yield criterion was adopted to describe the yield behavior. The model incorporated nonlinear kinematic and isotropic hardening to capture the anisotropic hardening effect. In the experiment, the compressive yield stress was found to be insensitive to the previous tensile deformation. The proposed model could capture this compression yield stress preserving effect under reverse loading, which in turn reduced the required material parameters as expected. With the material parameters calibrated from a set of simple uniaxial tests in various directions, the model was shown to predict the stress-strain behavior for other orientations satisfactorily. The model was further validated with experiments under complex loading conditions and found to capture the highly anisotropic, elastic-plastic behavior accurately.

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.