A multiphysics finite element model of the wood cell wall

[摘要] 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 its lifetime as a construction material. 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 equations 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 on the stiffness and relaxation characteristics of the polymer matrix is taken into account through the chemical kinetics of hydrogen bond dissociation. The implementation using the finite element method is discussed in detail and comprehensively verified using a series of numerical tests. Finally, the model is applied to wood cells and the behaviour of the polymers is compared to experimental findings.The resulting model is capable of predicting the interaction between viscoelastic material effects and diffusion and has the ability to predict viscoelastically limited diffusion within wood cell polymers. The model can also predict sorption hysteresis in wood cell wall polymers and therefore could be a valuable tool in future research into wood-water interactions.

[发布机构] University:University of Glasgow;Department:School of Engineering

[关键词] Finite element, multiphysics, numerical modelling, polymers, timber, vicsoelastic, soprtion, wood cell, hysteresis.