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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]

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]

Abstract 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. [ABSTRACT FROM AUTHOR]

A general, dynamic model describing the drying mechanisms of paper has been developed. The model includes shrinkage and predicts temperature, moisture, and pressure profiles. It has been evaluated against steady-state as well as dynamic measurements on a multicylinder paper dryer. The results revealed critical sections where low web strength and maximum gas pressure occur. Measurements of the outer cylinder temperature provide reliable information on the accuracy of the predicted moisture profile since they show the position where the paper surface is dry. [ABSTRACT FROM AUTHOR]

This article examines dynamic behavior of impingement drying. Dynamic relations between the drying variables and the paper moisture are determined and interactivity between the process variables is defined. According to the results, impingement drying is interactive and therefore an advanced control strategy is developed which is based on multivariable model predictive control. The performance of the proposed control strategy is studied by simulation and the simulation results are compared with the simulation results of the present control scheme. [ABSTRACT FROM AUTHOR]