Department of Mechanics: Seminar: Abstract Peerlings 2015

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Dimensional stability of paper sheets undergoing hygroscopic loading – a multiscale study

Ron Peerlings, Emanuela Bosco, Mary Bastawrous, Marc Geers

Significant dimensional variations may occur in paper materials when subjected to changes in moisture content. Gradients of the moisture content in the plane of the sheet, in particular, may result in instabilities and out-of plane deformation of the sheet, which are problematic in e.g. printing operations.

Moisture induced deformations are governed by the swelling of individual fibres, which is transferred through inter-fibre bonds within the fibrous network. Complex interactions between mechanical and hygro-expansive properties take place in the bonding areas, affecting the overall material response.

We study these mechanisms experimentally, by a combination of Scanning Electron Microscopy, Optical Microscopy and Digital Image Correlation. In particular, we aim to quantitatively characterise them at the scale of individual fibres and bonds, as well as at the sheet level.

At the same time, models are developed to bridge these two scales, i.e. to predict the sheet-level hygro-expansivity as a function of the properties of the fibre network – and in particular of the bonds; in many existing network models, the role of inter-fibre bonds is not explicitly incorporated.

A first version of the model is based on a periodic meso-structural model of the discrete fibrous network, which considers the free fibre segments and inter-fibre bonds. Despite its simplicity, the reference unit cell enables to naturally take into account relevant microstructural features such as network structure, fibre and bond geometry and hygro-mechanical properties. The proposed model is solved analytically, allowing to recover the paper sheet's anisotropic hygro-mechanical response in terms of effective constitutive constants and effective hygro-expansive coefficients, based on the coupling at the microstructural level between hygroscopic and mechanical behaviour. A comparison with experimental results obtained from the literature shows that the presented approach is an accurate tool to predict the overall paper response and to study how it is influenced by the microscale parameters (e.g. fibre orientation, dimensions, mechanical strength).

In ongoing work the model is refined, in particular geometrically, by considering a random network of fibres. Periodic homogenisation is employed to extract the effective sheet-level expansivity and mechanical properties from unit cell computations. We in particular study the influence of anisotropy of the fibre orientation distribution on these effective properties and compare them with predictions of the earlier, highly idealised model.

Brief bio

Ron Peerlings is working as an Associate Professor in the Materials Technology Institute.

After four years as a PhD student in the same group, he obtained his PhD in March 1999. Title of his thesis was `Enhanced damage modelling for fracture and fatigue'. The project was aimed at developing mathematically consistent Continuum Damage models, which do not suffer from pathological localisation and mesh sensitivity.

From November 1999 until May 2000 he worked together with Prof. Norman Fleck at the Engineering Department of the University of Cambridge on enriched effective relations for heterogeneous elastic materials.

Back in Eindhoven, he is teaching and doing research in the field of mechanics of materials. Current research interests include damage mechanics, homogenisation and numerical modelling of in particular metal forming and fatigue, as well as the mechanical reliability of electronic components and devices.