Historically, buckling and large deformations are often viewed as the onset of failure, and much investigation has gone into improving materials' performance to avoid them. As interest in metamaterials has grown, so has interest in leveraging controlled buckling/deformation to achieve more exotic and controllable material properties such as stiffness, shape change, or acoustic properties. Understanding microstructural behaviour under loading is necessary for designing metamaterials for specific target applications or interpreting results from inverse design schemes. This work seeks to develop a proper understanding of the relationship between microstructural morphology, buckling-like patterning modes and resulting macroscopic stiffness. We aim to provide design principles for creating microstructures that enable passive and active control of buckling behaviour, achieved through microstructure design and magnetic actuation. A numerical study of microstructural morphology variations shows that small changes strongly influence the competition between local and global buckling modes. Furthermore, the derivation of an idealised analytical model representing the microstructure shows good qualitative agreement with numerical simulations. Using the insights gained from the idealised model, basic design principles are developed for actuated materials with switchable properties. Using these design principles, we successfully design and numerically validate magnetic patterns that demonstrate different buckling modes, depending on the choice of pattern and application of external magnetic fields. Having understood the effect of microstructure on deformation and buckling, new material microstructures are proposed to promote different buckling modes. Hence, the proposed analytical model serves as a versatile design guide to achieve target deformations and active control of metamaterials.

The slip system activity in microtensile tests of ferrite single crystals is compared with predictions made by the discrete slip plane model proposed by Wijnen et al. (2021) [24]. This is an extension of conventional crystal plasticity in which the stochastics and physics of dislocation sources are taken into account in a discrete slip band. It results in discrete slip traces and non-deterministic mechanical behavior, similar to what is observed in experiments. A detailed analysis of which slip systems are presumed to be active in experiments is performed. Non-Schmid effects are incorporated by extending a non-Schmid framework commonly used to model {110} slip to {112} planes. The slip activity in the simulations is compared to that in the tests. Conventional crystal plasticity fails to predict the diversity in active slip systems that is observed experimentally. The slip activity obtained with the discrete slip plane model is in much better agreement with the experiments. Including non-Schmid effects only entails minor differences. This suggests that stochastic effects dominate the behavior of ferrite crystals with dimensions in the order of a few micrometers and that non-Schmid effects may not play a large role.

The role of heterogeneity in the plastic flow of thin ferrite specimens is investigated in this study. This is done through a recently introduced quasi-2D experimental-numerical framework that allows for a quantitative comparison of the deformation fields of metal microstructures between experiments and simulations at a high level of detail and complexity. The method exploits samples that are locally ultra-thin ("2D") and hence have a practically uniform microstructure through their thickness. This allows testing more complex loading conditions compared to uniaxial micromechanical experiments while avoiding the complexity of an unknown subsurface microstructure, which limits comparisons between experiments and simulations in traditional integrated approaches at the level of the polycrystalline microstructure. The present approach enables to study the effect of microstructural features such as grain boundaries. To study the role of stochastic fluctuations, a constitutive model is employed which introduces random heterogeneity into a crystal plasticity model. A detailed analysis of the simulations is performed at the level of individual slip systems. Since both experimental and numerical results are susceptible to stochastic fluctuations, the outcomes of many simulations are compared to the experimentally obtained result. This comparison allows us to determine how a single experiment relates to an ensemble of simulations. Additionally, results obtained with a conventional crystal plasticity model are considered. The analysis reveals that the heterogeneity in the plasticity model is essential for accurately capturing the deformation mechanisms.

The transient dimensional changes during hygro-expansion and hydro-expansion of freely and restrained dried, softwood and hardwood sheets and fibers is monitored, to unravel the governing micro-mechanisms occurring during gradual water saturation. The response of individual fibers is measured using a full-field global digital height correlation method, which has been extended to monitor the transient hydro-expansion of fibers from dry to fully saturated. The hygro- and hydro-expansion is larger for freely versus restrained dried and softwood versus hardwood handsheets. The transient sheet-scale hydro-expansion reveals a sudden strain and moisture content step. It is postulated that the driving mechanism is the moisture-induced softening of the so-called ”dislocated regions” in the fiber’s cellulose micro-fibrils, unlocking further fiber swelling. The strain step is negligible for restrained dried handsheets, which is attributed to the ”dislocated cellulose regions” being locked in their stretched configuration during restrained drying, which is supported by the single fiber hydro-expansion measurements. Finally, an inter-fiber bond model is exploited and adapted to predict the sheet-scale hygro-expansion from the fiber level characteristics. The model correctly predicts the qualitative differences between freely versus restrained dried and softwood versus hardwood handsheets, yet, its simplified geometry does not allow for more quantitative predictions of the sheet-scale hydro-expansion.

The onset of plasticity in quenched martensitic microstructures is characterized by a low initial yield stress, extreme initial hardening, and sudden saturation. The existing literature attributes these phenomena to residual stresses or microstructural heterogeneities. We introduce a novel perspective, suggesting that orientationdependent yielding of lath martensite, induced by inter -lath sliding, significantly contributes to the observed behavior. To support this, we employ a numerical microstructural model, considering the yielding anisotropy of martensite packets due to sliding along their habit plane orientation. The combined response of early yielding in martensite packets with a favorable habit plane, along with those initially remaining elastic due to an unfavorable orientation, results in a macro -scale behavior with a low initial yield stress, followed by substantial initial hardening until the saturation stress level is approached. The simulations also qualitatively capture other observations reported for quenched martensitic steels, e.g. the effect of carbon content.

Integrated experimental-numerical testing on bulk metal alloys with fine, complex microstructures is known to be highly challenging, since measurements are restricted to the sample surface, thereby failing to capture the effects of the 3D subsurface microstructure. Consequently, a quantitative comparison of deformation fields between experiments and simulations is hardly possible. To overcome this, we propose a novel 'quasi -2D' integrated experimental-numerical testing methodology that hinges on the fabrication of mu m-thin specimens with practically through -thickness microstructures over large regions of >100 mu m. The specimens are fully characterized from both surfaces and tested in -situ to retrieve microstructure -resolved deformation fields. Simultaneously, the full microstructure is discretized in 3D and simulated. This allows for a detailed, oneto-one quantitative comparison of deformation fields between experiments and simulations, with negligible uncertainty in the subsurface microstructure. Consequently, a degree of agreement between experiments and simulations is attained which we believe to be unprecedented at this scale. We demonstrate the capabilities of the framework on polycrystalline ferritic steel and dual -phase ferritic-martensitic steel specimens. At the mesoscale, the methodology enables quantitative comparisons of the interaction between multiple grains, while, at the microscale, it enables advancement of numerical models by direct confrontation with detailed experimental observations. Specifically, it is revealed that the individual slip system activity maps, identified with SSLIP, near a grain boundary can only be reasonably predicted by enhancing the adopted crystal plasticity simulations with a discrete slip plane model. Additionally, the experimentally observed strong anisotropic plasticity of martensite can only be captured with a substructure -enriched crystal plasticity model.

The plastic behavior of microscale lath martensite samples is highly anisotropic. Depending on the orientation, the deformation of such samples may be heterogeneous, with only a few localized slip traces while the remainder of the sample remains largely elastic. Although several continuum plasticity models that account for the anisotropy exist, they cannot reproduce the heterogeneous response observed in experiments. In this study, a model for lath martensite at the microscale is proposed which captures the orientation-dependent heterogeneous behavior observed in experiments. Before formulating the model we first study in detail two idealized cases, in which two different deformation mechanisms are activated. In both cases, the lath martensite is modeled using a discrete slip plane model. In the model, the activation stress of the individual slip systems varies randomly in space according to a distribution based on the underlying dislocation motion. The two configurations differ only in the orientation of the applied tensile load relative to that of the laths – either perpendicular or at 45°. In the latter case, slip along the so-called habit plane results in localized plastic deformation, while the former results in a more diffuse activation of plasticity. Insights obtained based on the idealized cases are used to formulate a three-dimensional constitutive model, which captures both deformation mechanisms. The model is applied to microtensile tests of single-packet lath martensite samples. It is shown that the orientation-dependent heterogeneity is accurately captured by the two deformation mechanisms accounted for by the model.

In particular types of layer- or lamellar-like microstructures such as pearlite and lath martensite, plastic slip occurs favorably in directions parallel to inter-lamellar boundaries. This may be due to the interplay between morphology and crystallographic orientation or, more generally, due to constraints imposed on the plastic slip due to the lamellar microstructural geometry. This paper proposes a micromechanics based, computationally efficient, scale independent model for particular type of lamellar microstructures containing softer lamellae, which are sufficiently thin to be considered as discrete slip planes embedded in a matrix representing the harder lamellae. Accordingly, the model is constructed as an isotropic visco-plastic model which is enriched with an additional orientation-dependent planar plastic deformation mechanism. This additional mode is activated when the applied load, projected on the direction of the soft films, induces a significant amount of shear stress. Otherwise, the plastic deformation is governed solely by the isotropic part of the model. The response of the proposed model is assessed via a comparison to direct numerical simulations (DNS) of an infinite periodic two-phase laminate. It is shown that the yielding behavior of the model follows the same behavior as the reference model. It is observed that the proposed model is highly anisotropic, and the degree of anisotropy depends on the contrast between the slip resistance (or yield stress) of the planar mode versus that of the isotropic part. The formulation is then applied to model the substructure of lath martensite with inter-layer thin austenite films. It is exploited in a mesoscale simulation of a dual-phase (DP) steel microstructure.The results are compared with those of a standard isotropic model and a full crystal plasticity model.

Paper, a porous-fibrous network, is made up of hydrophilic fibres, which are notably susceptible to deformations due to variations in moisture content. The response of paper sheets to full or partial wetting, based on the water-induced fibre swelling, has mostly been predicted in the past using highly idealised two-dimensional network geometries. The purpose of the present paper is to establish how precisely the two-stage process of determining effective hygro-expansivity under uniform wetting by a two-dimensional model followed by bending analysis using a continuum model predicts the curl of a fully three-dimensional network. In the present multi-scale modelling work, the moisture-induced homogenised sheet scale curl, derived from hygro-elastic deformations using non-uniform moisture profiles, is analysed based on an idealised non-woven three-dimensional fibrous network finite element model. First, the effective paper sheet swelling properties, derived computationally for the uniform wetting condition, are compared with analytically homogenised hygro-elastic properties. Whereas the analytically predicted elastic modulus has an inaccuracy of only ∼5%, the hygro-expansivity coefficient is over-predicted by roughly a third for a network with straight fibres. The difference is smaller if waviness of the fibres and wrap-around in the fibre bonds are taken into account. Fibre alignment turns out to have little influence. Subsequently, paper sheet curl predictions made by the analytical model are compared with that computed from the three-dimensional network model. The inaccuracy of the fully analytical model, based on the two-dimensional network description, relative to the fully detailed three-dimensional computational model with straight fibres is on the order of 40%–50%. The fidelity of the simple model is primarily constrained by the inaccuracy of the effective hygro-expansion coefficient. If the expansivity extracted from the three-dimensional simulations under uniform wetting is inserted, the inaccuracy drops to less than 10%. The continuum bending description hence performs adequately, provided it is based on a reliable estimation of the uniform expansion behaviour of the material.

The state-of-the-art in paper micro-mechanics calls for novel experimental data covering the full-field hygro-expansion of inter-fiber bonds, i.e., the 3D morphological changes and inter-fiber interactions. Therefore, a recently developed full-field single fiber hygro-expansion measurement methodology based on global digital height correlation is extended to orthogonal inter-fiber bonds, to investigate their full-field quasi-3D hygroscopic behavior. A sample holder has been developed which enables the quasi-3D characterization of the initial geometry of individual inter-fiber bonds, including the fiber thickness and width along the length of the fibers as well as the degree of wrap around and contact area of the bond, which are vital for understanding the inter-fiber bond hygro-mechanics. Full-field hygroscopic testing reveals the inter-fiber interactions: (i) the transverse hygro-expansion of each fiber strongly reduces when approaching the bonded area, due to the significantly lower longitudinal hygro-expansion of the other bonded fiber. (ii) The relatively large transverse strain of one fiber stretches the other crossing fiber in its longitudinal direction, thereby significantly contributing to the sheet scale hygro-expansion. (iii) Out-of-plane bending is observed in the bonded region which is driven by the significant difference in transverse and longitudinal hygro-expansion of, respectively, the top and bottom fiber constituting the bond. A bi-layer laminate model is employed to rationalize the bending deformation and an adequate match is found with the experimental data. Under the assumption of zero bending, which represents constrained inter-fiber bonds inside a paper sheet, the model can predict the contribution of the transverse strain in the bonded regions to the sheet-scale hygro-expansion.

Elastomeric mechanical metamaterials exhibit unconventional behaviour, emerging from their microstructures often deforming in a highly nonlinear and unstable manner. Such microstructural pattern transformations lead to non-local behaviour and induce abrupt changes in the effective properties, beneficial for engineering applications. To avoid expensive simulations fully resolving the underlying microstructure, homogenization methods are employed. In this contribution, a systematic comparative study is performed, assessing the predictive capability of several computational homogenization schemes in the realm of two-dimensional elastomeric metamaterials with a square stacking of circular holes. In particular, classical first-order and two enriched schemes of second-order and micromorphic computational homogenization type are compared with ensemble-averaged full direct numerical simulations on three examples: uniform compression and bending of an infinite specimen, and compression of a finite specimen. It is shown that although the second-order scheme provides good qualitative predictions, it fails in accurately capturing bifurcation strains and slightly over-predicts the homogenized response. The micromorphic method provides the most accurate prediction for tested examples, although soft boundary layers induce large errors at small scale ratios. The first-order scheme yields good predictions for high separations of scales, but suffers from convergence issues, especially when localization occurs.

The ductility of sheet metal is typically limited by either localized necking or by damage and fracture. A recent ductility classification refers to these failure modes respectively as “global” and “local” formability. The forming limit curve (FLC) and the uniaxial tensile test assess global formability, whereas the fracture forming limit (FFL), the true thickness fracture strain, hole expansion ratios (HER), etc. are indicators of local formability. Experimental hole expansion data in the literature for different dual-phase (DP) steel grades of similar strength and composition presents a paradox: grades which are found to be ductile in a tensile test and/or FLC show a low ductility in hole expansion, whereas other grades with a low ductility in conventional tests perform surprisingly well at cut edges. In this work, an in-depth systematic statistical analysis of idealized artificial two-phase microstructures is carried out to unravel the underlying mechanisms of the observed paradoxical trends. This is done by scaling the hardness of martensite and its volume fraction to generate virtual DP steels of the same strength but different strain hardening and mechanical phase contrast (hardness difference). The proposed micromechanical model adequately reproduces the experimentally observed trends. The results show that in DP steels, a higher global (necking-driven) ductility is obtained upon delaying martensite plasticity by increasing the mechanical contrast of the two phases. Consequently, the stress–strain distributions becomes more heterogeneous, resulting in a lower fracture limit of one of the phases or interfaces in shear loading, thereby, reducing the local ductility. Global ductility is improved by higher mechanical phase contrast and lower martensite volume fraction, whereas local ductility is improved by low phase contrast and higher martensite volume fraction. The hardening behavior of martensite is the key to avoiding the above trade-off between local and global ductility. It is shown that if the strain hardening capacity of martensite in the later stages of deformation (in high strains) can be increased, this would result in removing the observed paradoxical trends of local and global ductility in DP steels.

A micromorphic computational homogenization framework has recently been developed to deal with materials showing long-range correlated interactions, i.e. displaying patterning modes. Typical examples of such materials are elastomeric mechanical metamaterials, in which patterning emerges from local buckling of the underlying microstructure. Because pattern transformations significantly influence the resulting effective behaviour, it is vital to distinguish them from the overall deformation. To this end, the following kinematic decomposition into three parts was introduced in the micromorphic scheme: (i) a smooth mean displacement field, corresponding to the slowly varying deformation at the macro-scale, (ii) a long-range correlated fluctuation field, related to the buckling pattern at the meso-scale, and (iii) the remaining uncorrelated local microfluctuation field at the micro-scale. The micromorphic framework has proven to be capable of predicting relevant mechanical behaviour, including size effects and spatial as well as temporal mixing of patterns in elastomeric metamaterials, making it a powerful tool to design metamaterials for engineering applications. The long-range correlated fluctuation fields need to be, however, provided a priori as input parameters. The main goal of this study is experimental identification of the decomposed kinematics in cellular metamaterials based on the three-part ansatz. To this end, a full-field micromorphic Integrated Digital Image Correlation (IDIC) technique has been developed. The methodology is formulated for finite-size cellular elastomeric metamaterial specimens deformed in (i) virtually generated images and (ii) experimental images attained during in-situ compression of specimens with millimetre sized microstructure using optical microscopy. The proposed IDIC method identifies the different kinematic fields, both before and after the microstructural buckling, and without any prior knowledge determines correctly the relevant patterning modes required by the homogenization scheme. It is further argued that patterning modes are independent of the unit cell size, the hole diameter to cell size ratio, as well as local material properties, allowing for modelling and design of (finite- and infinite-size) metamaterials and specimens with graded microstructures in terms of geometry and/or material properties. It is shown that the proposed methodology is also applicable to cellular metamaterials and structures with different microstructural designs.

Crystallographic slip system identification methods are widely employed to characterize the fine scale deformation of metals. While powerful, they usually rely on the occurrence of discrete slip bands with clear slip traces and can struggle when complex mechanisms such as cross-slip, curved slip, diffuse slip and/or intersecting slip occur. This paper proposes a novel slip system identification framework, termed SSLIP (for Slip Systems based Local Identification of Plasticity), in which the measured displacement gradient fields (from Digital Image Correlation) are locally matched to the kinematics of one or multiple combined theoretical slip systems, based on the measured crystal orientations. To identify the amount of slip that conforms to the measured kinematics, an optimization problem is solved for every datapoint individually, resulting in a slip activity field for every considered slip system. The identification framework is demonstrated and validated on an HCP virtual experiment, for discrete and diffuse slip, incorporating 24 slip systems. Experimental case studies on FCC and BCC metals show how full-field identification of discrete slip, diffuse slip and cross-slip becomes feasible, even when considering 48 slip systems for BCC. Moreover, the methodology is extended into a dedicated cross-slip identification method, which directly yields the orientation of the local slip plane trace orientation, purely based on the measured kinematics and on one or two chosen slip directions. For even more challenging cases revealing a persistent uncertainty in the slip identification, a two-step identification approach can be employed, as is demonstrated on a highly challenging HCP virtual experiment.

Earlier work on the hygro-expansion of paper states that the larger hygro-expansivity of freely compared to restrained dried handsheets is due to structural differences between the fibers inside the handsheet. To study this hypothesis, first, the hygro-expansion of freely and restrained dried, hardwood and softwood handsheets has been characterized. Subsequently, the transient full-field hygro-expansion (longitudinal, transverse, and shear strain) of fibers extracted from these handsheets was measured using global digital height correlation, from which the micro-fibril angle was deduced. The hygro-expansivity of each individual fiber was tested before and after a wetting period, during which the fiber’s moisture content is maximized, to analyze if a restrained dried fiber can “transform” into a freely dried fiber. It was found that the longitudinal hygro-expansion of the freely dried fibers is significantly larger than the restrained dried fibers, consistent with the sheet-scale differences. The difference in micro-fibril angle between the freely and restrained dried fibers is a possible explanation for this difference, but merely for the hardwood fibers, which are able to “transform” to freely dried fibers after being soaked in water. In contrast, this “transformation” does not happen in softwood fibers, even after full immersion in water for a day. Various mechanisms have been studied to explain the observations on freely and restrained dried hardwood and softwood, fiber and handsheets including analysis of the fibers’ lumen and cross-sectional shape. The presented results and discussion deepens the understanding of the differences between freely and restrained dried handsheets.

As a result of their heterogeneous two-phase microstructure, dual-phase (DP) steels reveal various damage mechanisms leading to the nucleation of voids, microcracks, and other defects at all stages of deformation. Defects may also preexist in the microstructure due to thermomechanical processing of the material. The literature has ample evidence that DP steels, while offering a good compromise between ductility and strength, are sensitive to these types of preexisting defects. However, the quantitative dependency of mechanical properties of DP steels on such preexisting defects is still to be explored. In this paper, a systematic statistical analysis of this sensitivity is carried out using an idealized microstructural model of randomly generated two-phase volume elements with embedded preexisting defects. The proposed model also enables a methodological study probing the influence of mechanical phase contrast (i.e., the hardness difference between the constituent phases) and volume fractions. It is observed that high phase contrast microstructures are less sensitive to initial defects since the inherent extreme heterogeneity of the microstructure leads to the nucleation of new damage incidents irrespective of the presence of preexisting defects. At constant contrast, the volume fraction of the hard phase has less influence. These conclusions are insensitive to the precise type of defect considered.

Micromechanical constitutive parameters are important for many engineering materials, typically in microelec-tronic applications and material design. Their accurate identification poses a three-fold experimental challenge: (i) deformation of the microstructure is observable only at small scales, requiring SEM or other microscopy techniques; (ii) external loadings are applied at a (larger) engineering or device scale; and (iii) material parameters typically depend on the applied manufacturing process, necessitating measurements on material produced with the same process. In this paper, micromechanical parameter identification in heterogeneous solids is addressed through multiscale experiments combined with Integrated Digital Image Correlation (IDIC) in conjunction with various possible computational homogenization schemes. To this end, some basic concepts underlying multiscale approaches available in the literature are first reviewed, discussing their respective advantages and disadvantages from the computational as well as experimental point of view. A link is made with recently introduced uncoupled methods, which allow for identification of material parameter ratios at the microscale, still lacking a proper normalization. Two multiscale methods are analysed, allowing to bridge the gap between microstructural kinematics and macroscopically measured forces, providing the required normalization. It is shown that an integrated experimental-computational scheme provides relaxed requirements on scale separation. The accuracy and performance of the discussed techniques are analysed by means of virtual experimentation under plane strain and large strain assumptions for unidirectional fibre-reinforced composites. The robustness against image noise is also assessed. The obtained results demonstrate that the expected accuracy is typically within 10% RMS error for all multiscale methods, but decreasing to 1% RMS error for the optimal method.

In dual-phase steels, microstructural characteristics such as phase volume fraction and phase contrast tend to have opposite effects on the ductility measured in hole expansion capacity (HEC) testing as compared to the forming limit curve (FLC). This has lead to a number of paradoxical observations in the literature, in which microstructures which were optimized for ductility in terms of the FLC turned out to perform poorly on HEC and vice versa. This study systematically analyzes the issue by means of microstructural simulations. Artificial, highly idealized two-phase microstructures are constructed with have the same nominal strength, but which achieve this strength by different combinations of martensite volume fraction and hardness. They are subjected to pure shear deformation and based on the computed response their hardening curve and damage resistance are predicted; furthermore, the point of necking in plane-strain tension is predicted based on a Considère-like criterion. If the latter is taken as representative of the FLC and the strain to (local) failure due to damage of the HEC, the paradoxical trend discussed above is reproduced. It may furthermore be traced to the distinct hardening behavior of martensite, with a rapid hardening at low strain levels followed by early saturation.

The state-of-the-art in paper mechanics calls for novel experimental data covering the full-field hygro-expansion of inter-fiber bonds in paper, i.e., the 3D morphological changes and inter-fiber interactions. Therefore, a recently developed full-field single fiber hygro-expansion measurement methodology based on global digital height correlation is extended to orthogonally bonded inter-fiber bonds, to investigate their full-field quasi-3D hygroscopic behavior. A sample holder has been developed which enables the quasi-3D characterization of the initial geometry of individual inter-fiber bonds, including the fiber thickness and width along the length of the fibers as well as the degree of wrap around and contact area of the bond, which are vital for understanding the inter-fiber bond hygro-mechanics. Full-field hygroscopic testing revealed novel insights on the inter-fiber interactions: (i) the transverse hygro-expansion of each fiber strongly reduces when approaching the bonded area, due to the significantly lower longitudinal hygro-expansion of the other bonded fiber. (ii) The relatively large transverse strain of one fiber stretches the other crossing fiber in its longitudinal direction, thereby significantly contributing to the sheet scale hygro-expansion. (iii) Out-of-plane bending is observed in the bonded region which is driven by the significant difference in transverse and longitudinal hygro-expansion of, respectively, the top and bottom fiber constituting the bond. A bi-layer laminate model is derived to rationalize the bending deformation and an adequate match is found with the experimental data. Under the assumption of zero bending, which represents constrained inter-fiber bonds inside a paper sheet, the model is able to predict the contribution of the transverse strain in the bonded regions to the sheet-scale hygro-expansion.

This chapter presents a multiscale approach to investigate the dependence of the effective hygro-mechanical behaviour of paper sheets on the properties of the underlying fibrous network. Despite the vast amount of literature on the hygro-expansion of paper, the relation between the effective material properties and the underlying micro-structural features is not fully understood. The point of departure of this work is a highly idealised micro-structural model of paper that is based on two main assumptions: (i) the underlying fibrous structure is described as a lattice, consisting of two orthogonal fibre families and (ii) paper is simplified to a two-dimensional (2D) material. Despite its simplicity, this model reproduces representative features, such as the network-level hygro-elastic properties, the areal coverage, etc. The model can be solved analytically, providing closed-form expressions that explicitly reveal the influence of the individual micro-scale parameters on the effective hygro-mechanical response. Taking this idealised model as a reference, the effect of the two main underlying modelling assumptions on the predicted effective hygro-elastic response is explored, by relaxing them one at a time. First, instead of a lattice description, a planar fibrous network is considered. The network model is generated by random deposition of the fibres within a planar region according to a uniform probability density function. Asymptotic homogenisation is used to determine its effective properties numerically. Second, instead of a 2D representation, a three-dimensional (3D) model is considered, which extends the reference lattice description in the out-of-plane direction. In the 3D representation, the fibres may bend and be wrapped around each other, which may affect the effective hygro-elastic response. The effective properties of the 3D model are computed by numerical homogenisation. The properties predicted by the reference 2D lattice model are compared with those obtained from the network model and the 3D lattice model. Assuming a 2D lattice description has in general a strong influence on the predicted mechanical behaviour of the material. For realistic values of the average thickness of the network, the elastic properties calculated with the 2D lattice model overestimate the response of the planar random network model by about 30%. Moreover, the elastic properties of the 3D lattice are overestimated by less than 5%, up to a factor of approximatively 2 for high degrees of fibre waviness. As for the hygroscopic behaviour, the 2D lattice idealisation appears to have a smaller influence on the predicted response. The hygroscopic properties obtained from the 2D lattice model match those of the random network well, to within a range of 10% for realistic coverages, while the difference with those of the 3D unit cells is within approximately 30% for realistic average network thicknesses.