E Emanuela Bosco

A multi-scale approach to bridge microscale damage and macroscale failure : a nested computational homogenization-localization framework

This paper presents a multi-scale modelling approach for bridging the microscale damage and macroscale failure. The proposed scheme evolves from a classical computational homogenization scheme (FE2) towards a discontinuity enriched framework. The classical homogenization approaches typically rely on the separation of scales principle, which is violated as soon as a strain localization band develops within a microstructural volume element (MVE). The newly developed scheme resolves this limitation by considering the bifurcation of the microscale deformation into a continuum ‘bulk’ part and a localization related part. The most distinct feature of the proposed framework is that both, the local macroscale traction-opening response of the cohesive crack and the stress-strain response of the surrounding ‘bulk’, are obtained from a single MVE analysis. The discontinuity enriched macroscale description is formulated to accommodate for the micro-macro coupling. The macroscale boundary value problem and the corresponding implementation are detailed for the use within the embedded discontinuities approach. The presented multi-scale method is demonstrated on a numerical example of a cohesive crack propagation in a macroscopic double notch specimen, with underlying voided microstructure.

Bridging network properties to the effective hygro-expansivity of paper: experiments and modelling

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.

Hygro-mechanical properties of paper fibrous networks through asymptotic homogenization and comparison with idealized models

This paper presents a multi-scale approach to predict the effective hygro-mechanical behaviour of paper sheets based on the properties of the underlying fibrous network. Despite the vast amount of literature on paper hygro-expansion, the functional dependence of the effective material properties on the micro-structural features remains yet unclear. In this work, a micro-structural model of the paper fibrous network is first developed by random deposition of the fibres within a planar region according to an orientation probability density function. Asymptotic homogenization is used to determine its effective properties numerically. Alternatively, two much more idealized micro-structural models are considered, one based on a periodic lattice structure with a regular network of perpendicular fibres and one based on the Voigt average. Despite their simplicity, they reproduce representative micro-structural features, such as the orientation anisotropy and network level hygro-elastic properties. These alternative models 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. The trend predicted by the random network model is captured reasonably well by the two idealized models. The resulting hygro-mechanical properties are finally compared with experimental data reported in the literature, revealing an adequate quantitative agreement.

Asymptotic homogenization of hygro-thermo-mechanical properties of fibrous networks

The hygro-thermo-expansive response of fibrous networks involves deformation phenomena at multiple length scales. The moisture or temperature induced expansion of individual fibres is transmitted in the network through the inter-fibre bonds; particularly in the case of anisotropic fibres, this substantially influences the resulting overall deformation. This paper presents a methodology to predict the effective properties of bonded fibrous networks. The distinctive features of the work are i) the focus on the hygro-thermo-mechanical response, whereas in the literature generally only the mechanical properties are addressed; ii) the adoption of asymptotic homogenization to model fibrous networks. Asymptotic homogenization is an efficient and versatile multi-scale technique that allows to obtain within a rigorous setting the effective material response, even for complex micro-structural geometries. The fibrous networks considered in this investigation are generated by random deposition of the fibres within a planar region according to an orientation probability density function. Most of the available network descriptions model the fibres essentially as uni-axial elements, thereby not explicitly considering the role of the bonds. In this paper, the fibres are treated as two dimensional ribbon-like elements; this allows to naturally include the contribution of the bonding regions to the effective expansion. The efficacy of the proposed study is illustrated by investigating the effective response for several network realizations, incorporating the influence of different micro-scale parameters, such as fibre hygro-thermo-elastic properties, orientation, geometry, areal coverage.

A model for moisture-induced dimensional instability in printing paper

The dimensional stability of printing paper is strongly related to changes in moisture content. This represents a major issue in the field of digital ink-jet printing, where moisture induced reversible and irreversible deformations may compromise printing quality and runnability. This paper proposes a two-dimensional hygro-mechanical model for paper, that focuses on the prediction of moisture induced out-of-plane deformations, due to inhomogeneous moisture variations in the plane. The model is based on a discrete network of beams. The adopted constitutive model, whose input parameters are calibrated to available experimental data for homogeneous moisture cycling, allows to describe typical irreversible phenomena related to the history of the production of paper, such as the release of dried-in strains. The deformation of paper in the wet and in the dry state predicted by the model is compared with experiments, in which the paper is subjected to a moisture cycle under different types of mechanical constraint. The results of the model capture well the experimental response of paper in terms of buckling patterns and of out-of-plane displacement wavelengths and amplitudes.

Local network effects on hygroscopic expansion in digital ink-jet printing

Dimensional stability of paper is a key problem in the field of digital ink-jet printing. In the literature, this phenomenon is mostly approached through continuum models representing the overall response of paper. However, if the length scale of the applied wetting is comparable to the characteristic length scale of the microstructure a continuum description may be not sufficient to correctly capture the response of the material. The present work explores this question by proposing a two dimensional fibrous network model, which investigates the hygro-expansion phenomena due to the printing process and their effects on the local response of the paper’s microstructure. The proposed description incorporates several microscale features, such as the fibre hygro-elastic properties, orientation, areal coverage. Different moisture patterns are applied to the fibrous networks, allowing to study their behaviour as a function of the coverage, the anisotropic orientation and the size of the wet regions relative to the fibre length. A comparison with a homogenized continuum model is finally performed. This reveals that, for low coverages, a microstructural approach is substantially more accurate, whereas for denser networks the continuum model is a valid alternative, even when the size of the wetting pattern becomes comparable to the fibre length.