Proceedings e report - Firenze University Press

HYGRO-LOCK INTEGRATION IN A KELVIN VOIGT MODEL
Jean Marie Husson, Frédéric Dubois*, Nicolas Sauvat, Octavian Pop
Heterogeneous Materials Research Group, Civil Engineering and Durability team (GEMH-GC&D), University
of Limoges, Centre Universitaire d’Egletons, Boulevard Jacques Derche, 19300 Egletons, France
Abstract
This work deals with the modelling of the viscoelastic behaviour of wood components by taking into account
environmental interactions. The model is based on the integration of elastic behaviour characterized by a hygrolocking
effect in a generalized Kelvin Voigt model. This model requires the memorization of the complete past
history of loading and moisture content variations through a double hereditary integral. This approach, treated
with an incremental algorithm, can be used to develop models for different scale structural elements and to study
the behaviour of joints under moisture content variations.
1. Introduction
The creep deformation of timber structures results in a complex coupling between varying humidity
and temperature in the surrounding environment, the moisture content changes induced by boundary
exchanges characterized by sorption isotherms, mass and heat transfer in wooden material and the
viscoelastic process induced by the external load. The coupling between varying moisture content and
the creep deformation is referred as the mechano-sorptive behaviour. In this context, if we consider
ageing elements like lumbers or joints, see Fig. 1, the coupling between moisture content and loading
histories induces apparent increases of deflexion or compliance and a global resistance decrease.
In the European Code for timber design, Kdef and Kmod coefficients are introduced to take into
account these phenomena. However, the long term behaviour prediction requires the knowledge of the
complete past history of moisture content and loading. One solution consists in the development of
numerical tools which can model the following effects, assuming linear behaviour restriction in
regards to the viscoelastic response under moisture content variations:
- a moisture content dependence on elastic properties expressed by a hygro-lock effect as evidenced
during drying phases by Gril [7],
- a moisture content dependence on viscoelastic properties which is characterized by an amplification
and an acceleration of creep strains for high level of moisture content,
- swelling and shrinkage effects amplified by the strain level as shown by Ranta Maunus,
- a creep limit observed in the linear domain as demonstrated by Hunt
The first section concerns the development of the hygro-lock concept for elastic response. The
adaptation for viscoelastic behaviour is proposed in the second part. Finally, an application example is
proposed in order to highlight hygro-lock effect during a creep-recovery test under climatic variations.
2. Elastic behaviour and mechano-sorptive stress
In order to isolate each process, this paper deals with a numerical approach about the hygro-lock effect
introduced in a viscoelastic model. A first formulation has been developed by Husson who proposed a
specific elastic behaviour under moisture content variations w. For a uniaxial configuration, k(t)
designates the time evolution of elastic rigidity induced by moisture content variations. Considering a
time function for w, k(t) can be expressed by:
⎧⎪ w≥0⇒k≤0 kt () = kwt ( ()) where ⎨
⎪⎩ w≤0⇒k (1)
≥0
In order to model the effect of hygro-lock highlighted by Gril, Husson has shown that the constitutive
equations, for elastic response, can be written as follows:
* E-mail: frederic.dubois@unilim.fr
Joseph Gril (edited by), Wood Science for Conservation of Cultural Heritage –Braga 2008: Proceedings of the International
Conference held by COST Action IE0601 (Braga - Portugal, 5-7 November 2008, ISBN 978-88-6453-157-1 (print)
ISBN 978-88-6453-165-6 (online) © 2010 Firenze University Press