Numerical modelling of the time-dependent mechanical behaviour of softwood

When using wood as a structural material it is important to consider its time-dependent mechanical behaviour and to predict this behaviour for decades ahead. For this purpose, several rheological mathematical models, spanning from fairly simple to very complex ones, have been developed over the years.

Often these models assume contributions from elastic, viscoelastic and viscous processes acting within the material. However, the physical interpretation of the input parameters is often difficult. This is because these models are mathematical tools which typically are not related to the physical mechanisms causing the observed mechanical behaviour.

In this study, the mechanical behaviour of softwood tracheids is described using numerical modelling. The basic composition and orientation of the tracheid constituents is incorporated by establishing a local coordinate system aligned with the microfibrils of the dominant S2 layer. Composite theory for laminar structures is used to generate the elastic properties in the local coordinate system based on literature values for the properties of the chemical constituents.

Time-dependent behaviour is thought to be a result of sliding between the microfibrils. This assumption is incorporated in the numerical model by only allowing non-elastic behaviour in shear deformation modes in the local coordinate system. The rate of shearing is described by deformation kinetics. The results indicate that time-dependent behaviour such as creep and relaxation originates from simple physical processes.

However, the interaction between the sliding of the microfibrils on the microscale (local coordinate system) and the orientation of the microfibrils in the tracheid becomes complex on the macroscale. An example of the simplicity of the current numerical model is that no viscoelastic property is assigned on the microscale; only elastic and viscous properties.

Nonetheless, the mechanical behaviour on the macroscale is viscoelastic, i.e. the time-dependent macroscopic behaviour is to some extent reversible.