Modelling the Mechanics of Timber Cell Walls
Euan Richardson  1, *@  , Pearce Chris  1@  , Lukasz Kaczmarczyk  1@  
1 : School of Engineering, The University of Glasgow  (Glasgow Univ.)  -  Website
Glasgow G12 8QQ Scotland -  United Kingdom
* : Corresponding author

Timber is a highly complex naturally occurring material, with properties adapted to its local environment. These properties, on its many length scales, determine its strength and stiffness and also how it interacts with moisture in the environment, causing dimensional instability both during drying and the lifetime of any building. Of particular importance is how the cell wall polymers interact with moisture in the environment and how this effects the properties, due to their strong dependence on intra-molecular hydrogen bonds. To model the dimensional behaviour of a wood cell under varying moisture conditions, the cell wall polymer matrix is modelled using a formulation of coupled deformation and moisture transport. These governing equation of mass and linear momentum conservation are strongly coupled and nonlinear and solved using the Finite Element Method. The associated constitutive equations are complex. The free energy is described through the deformation of the polymer matrix and the mixing with solvent (in this case, water). It is assumed that the polymer chains and water molecules are incompressible so that a change in volume of the polymer matrix corresponds to a change in the number of solvent molecules. The viscoelastic behaviour is resolved using a Zener spring-dashpot model, capturing both creep and relaxation phenomena, and the moisture transport is resolved using Fick's 2nd Law. The effects of wetting upon the stiffness and relaxation characteristics of the polymer matrix is taken into account through the chemical kinetics of hydrogen bond dissociation. Proper linearisation is achieved with automatic differentiation, using the library ADOL-C integrated with the group's FE code MOFEM.

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