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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]

In this paper, a three-dimensional anisotropic multi-surface model for the in-plane elastoplastic deformation of paper and paperboard is developed. The model is based on the concept of structural tensors. It employs three different yield functions and parameterised consistency conditions for three different loading scenarios. The evolution of the yield surface with plastic strain is described by multiple hardening variables. Furthermore, the evolution equations are integrated using the unconditionally stable backward Euler method. Also, the internal variables are updated using a particular form of the elastic predictor/plastic corrector algorithm. The constitutive model is calibrated from a set of simple uniaxial tension tests performed in various directions of the material and is validated against loading in other directions. Additionally, the predictive capability as well as the numerical performance of the constitutive model is accessed against an existing non-quadratic plasticity model. Finally, the applicability of the constitutive model is demonstrated by performing a tensile test on a paperboard with a hole. [ABSTRACT FROM AUTHOR]

The fracture process in two fiber network materials, a low- and a high-density paper, is analyzed experimentally and numerically. The high-density paper is able to localize continued fracture to very small defects while a rather large defect is required in the low-density paper. Whereas the high-density paper has a homogeneous and limited variation in local mass density, the low-density paper is substantially more heterogeneous and has a higher local mass density variation. It is hypothesized that these fairly large regions of lower mass density govern the fracture process in paper and similar fiber network materials. A nonlocal fracture model is applied to describe and capture this length scale phenomenon and intents to simulate forces bridged over distant regions in the material via connected fibers. The suggested fracture hypothesis is consistent with experiments and hence offers an explanation to why network materials with different mass density variation may fracture differently. [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]

Laminated paperboard and paper is widely used in packaging products. Its out-of-plane properties play a crucial role in converting paperboard to a carton through the creasing and folding process. The aim of this study is to describe the out-of-plane mechanical response with an elastic-plastic model based on the observed experimental behavior. The model was derived from a thermodynamic framework and was based on the multiplicative split of the deformation gradient in the context of hyperelasticity. A structural tensor-based approach was applied to model the elastic deformation, while a multi-surface based yield criterion was adopted to describe the plastic behavior. The model considers both material densification and internal friction effects, which were observed experimentally. According to the experimental behavior, a quadratic yield locus under pure shear loading was assumed in the model. Finally, the model was validated with a cylinder compression test and found to capture the highly anisotropic, elastic-plastic behavior accurately. [ABSTRACT FROM AUTHOR]

The paper presents an effective plate formulation based on isogeometric analysis (IGA) and a novel simple quasi-3D hyperbolic shear deformation theory (S-Q3HSDT) to study static bending, free vibration, and buckling behaviors of functionally graded plates. In S-Q3HSDT fashion, five unknowns per node are included; both shear deformation and thickness-stretching effects across the thickness are taken into account; and the awkward shear locking phenomenon is avoided. The requirement for C 1 -continuity in terms of the S-Q3DHSDT is straightforwardly possessed with the aid of inherent high-order continuity of non-uniform rational B-spline (NURBS), which serve as basis functions in our IGA formulation. The superior performance and accuracy of the proposed method is demonstrated through numerous numerical examples. The calculated results are then compared with reference solutions, investigating the effects of boundary conditions, gradient index, and other aspect ratios on mechanical responses of functionally graded plates. [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]

Dimensional stability issues may occur in paper sheets when subjected to moisture content variations. Paper is in fact mainly composed of hydrophilic wood fibres that experience significant dimensional changes upon humidity variations. The hygro-expansive deformations at the single fibre level and their effects on the meso-structural fibrous network govern the hygro-mechanical response of paper at the macroscopic, sheet scale. The present contribution aims at offering a relation between theoretical predictions and experimental measurements of the hygro-expansive behaviour of paper. Experimental observations of the hygroscopic and mechanical response at the sheet level have been performed, providing the anisotropic hygro-elastic properties of the material in the in-plane principal directions. To understand the multi-scale nature of the phenomenon, a periodic two dimensional meso-structural model of the fibrous network has been developed. The effective material response is extracted via homogenization. The influence of several meso-scale parameters (hygro-mechanical properties and geometry of fibres, inter-fibre bonds and of the network) on the overall behaviour of the material can be studied; in particular, the in-plane fibre orientation distribution along a preferential direction affects strongly the anisotropy of the macro-scale response. The proposed model has been adopted to represent the effective material response, focusing on the hygro-elastic response only and thus neglecting possible irreversible effects occurring at the different scales. A comparison of the experimental data with the results obtained from the model as a function of the fibre orientation distribution reveals a good accuracy of the prediction, thereby showing its applicability to estimate paper’s hygro-expansive response. [ABSTRACT FROM PUBLISHER]

Significant dimensional variations may occur in paper-based materials when subjected to changes in moisture content. Moisture induced deformations are governed by the swelling of individual fibres, which is transferred through inter-fibre bonds to the entire fibrous network. Complex interactions between mechanical and hygro-expansive properties take place in the bonding areas, affecting the overall material response. In most network models, the role of these inter-fibre bonds is not explicitly incorporated. This work presents a periodic meso-structural model for the discrete fibrous network, which considers the free-standing fibre segments and inter-fibre bonds. Despite its simplicity, the reference unit-cell enables the incorporation of relevant micro- and meso-structural features such as network structure, fibres and bond geometry and hygro-elastic properties. The proposed model is solved analytically through a proper homogenization strategy, allowing to recover the paper’s anisotropic hygro-mechanical response in terms of effective elastic constants and effective hygro-expansive coefficients, exploiting the coupling at the meso-structural level between hygroscopic and mechanical behavior. A comparison with experimental results obtained from the literature shows that the presented approach is quite accurate in predicting the overall paper response, thereby revealing the influence of several meso-scale parameters (e.g. fibre orientation, dimensions, mechanical strength). [ABSTRACT FROM AUTHOR]

Abstract: Graphene oxide (GO) paper is a promising candidate for novel applications in energy storage systems such as electrical batteries, supercapacitors and multi-layered composites where the material undergoes deformation mechanisms. In particular, the strength of graphene oxide paper is critical in such applications and is defined by the interaction between the GO sheet constituents of the paper. The deformation behavior and tensile strength of focused ion beam (FIB) fabricated GO micro-beams was measured using in situ atomic force microscopy (AFM). GO sample deformation and failure was dependent on both the size of the micro-beams and the environmental testing conditions. Specifically, the failure stress of GO paper micro-beams tensile tested in air was found to increase when compared to testing in vacuum. This environmental dependent tensile strength of GO paper is attributed to water promoting stress transfer between GO sheets within the paper for higher strength during air testing while vacuum conditions remove water, leading to poor stress transfer between GO sheets for lower tensile strength results. A two-parameter Weibull distribution is introduced to quantify the micro-beam size dependent strength, which is attributed to interfacial defects determining GO paper failure strength. [Copyright &y& Elsevier]

We present a technique for simulating plastic deformation in sheets of thin materials, such as crumpled paper, dented metal, and wrinkled cloth. Our simulation uses a framework of adaptive mesh refinement to dynamically align mesh edges with folds and creases. This framework allows efficient modeling of sharp features and avoids bend locking that would be otherwise caused by stiff in-plane behavior. By using an explicit plastic embedding space we prevent remeshing from causing shape diffusion. We include several examples demonstrating that the resulting method realistically simulates the behavior of thin sheets as they fold and crumple. [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  In this study, a simplified Acoustic Emission (AE) equipment, in essence an AE signal conditioner and a USB (Universal Serial Bus) data acquisition system, is used to study what happens in paper structures during mechanical loading. By the use of such equipment, some parameters that can be extracted are e.g. the stress and strain at onset of AE, the stress and strain at the onset of rapid AE defined as some numerical factor (larger then one) times the initial emission rate, the emission rate at the first stage of loading and the stress and strain at final failure i.e. when the specimen loses its load carrying ability.In this study however, the interest is focused on one particular parameter i.e. the elastic strain energy density W c at onset of AE. This is a parameter with a clear physical meaning and in this study, the correlation between this parameter and a fracture toughness measure, is investigated.The conclusion is that when nine different paper materials (with a large span regarding properties) are considered, there is a correlation (however not linear) between these two parameters. [ABSTRACT FROM AUTHOR]

The article discusses that the mathematical expressions of plate instability could be applied to thin webs such as paper that have small but finite plate bending stiffness. It recalls the subject of plate instability and expand the theory to broaden the orthotropic properties of many webs. It examines the effects of web shear stiffness, web tension, and the traction between webs and rollers on troughs and wrinkles. It determines what levels of misalignment are acceptable in each span of a process machine for a given web material.

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]

Microindentation as a method for determining important material properties of paper coating materials is studied experimentally and numerically. The bulk of the investigation is concentrated upon the short-lived elastic part of a spherical indentation test, but determination of the failure stress of the coating is also discussed. The results indicate that microindentation can be a powerful tool for material characterization of these materials, but only if careful efforts are made to account for the influence from plasticity as well as from boundary effects. [ABSTRACT FROM AUTHOR]

This paper reports on a new method for the measurement of sheet fracture toughness. In this method, samples cut in DENT geometry are cyclically loaded. The maximum load for each cycle is incremented after each cycle until the sample fractures. The work in the final cycle is then the work required to fracture the sample. The fracture toughness determined using the new cyclic technique is compared with that determined using the Essential Work of Fracture (EWF) technique, for samples with a wide range of fracture toughness, and it is shown that cyclic technique gives a fracture toughness around 8% lower than the EWF technique. For 3 samples, cyclic fracture toughness values were measured for ligament lengths from 3.3 to 14.0 mm and compared with the EWF fracture toughness in each case. The cyclic fracture toughness was found to be independent of the ligament length, except for very weak samples, and to be 5–10% lower than the EWF fracture toughness. The differences between the EWF and cyclic fracture toughnesses were probably due to the development of damage zones around the crack tips before the fracture. The advantages of the new cyclic technique over the EWF technique are that it requires less sample area as only one ligament length is required, is quicker and can be readily automated. [ABSTRACT FROM AUTHOR]

The use of Raman spectroscopy in probing the deformation mechanisms of cellulose fibres (regenerated and natural), and two natural cellulose composite systems (wood and paper) is described. It is shown that during tensile deformation the 1095 cm−1 Raman band, corresponding to the stretching of the cellulose ring structure, shifts towards a lower wavenumber due to molecular deformation. By analysing a number of fibres with different microstructures this shift is shown to be invaluable in understanding the micromechanisms of deformation in these materials. Moreover, the rate of Raman band shift is shown to be invariant with stress for all fibre types, consistent with a fibre microstructure based on a modified series aggregate model. In the composite systems, such as wood and paper, it is shown that the stress-induced Raman band shift in the cellulose gives an important insight into their local deformation micromechanics. [ABSTRACT FROM AUTHOR]

Presents a quantitative description of the shape, response and stability of conical dislocation in crumpling of paper. Results of deformation; Scaling laws for the size of the core; Characteristics of the geometry of the dislocation away from the core; Interaction between conical dislocations in a simple geometry.

Flexible actuators have important applications in artificial muscles, robotics, optical devices, and so on. However, most of the conventional actuators have only actuation function, lacking in real‐time sensing signal feedbacks. Here, to break the limitation and add functionality in conventional actuators, a graphene‐based actuator with integrated‐sensing function is reported, which avoids the dependence on image post‐processing for actuation detection and realizes real‐time measurement of the shape‐deformation amplitudes of the actuator. The actuator is able to show a large bending actuation (curvature of 1.1 cm−1) based on a dual‐mode actuation mechanism when it is driven by near infrared light. Meanwhile, the relative resistance change of the actuator is −17.5%. The sensing function is attributed to piezoresistivity and thermoresistivity of the reduced graphene oxide and paper composite. This actuator can be used as a strain sensor to monitor human motions. A smart gripper based on the actuators demonstrates perfect integration of the actuating and sensing functions, which can not only grasp and release an object, but also sense every actuation state of the actuator. The developed integrated‐sensing actuator is hopeful to open new application fields in soft robotics, artificial muscles, flexible wearable devices, and other integrated‐multifunctional devices. A graphene‐based actuator with integrated‐sensing function is developed. It realizes real‐time measurements of the shape deformation of the actuator. A smart gripper based on the actuator demonstrates perfect integration of actuating and sensing functions. It can not only grasp and release an object, but also sense every actuation state of the actuator. [ABSTRACT FROM AUTHOR]