Past exam of the materials science course of the University of Cambridge / 2015 / Paper 1 / 5 / e / ii / Solution

A physical mechanics model of wood must at least acknowledge anisotropy: stiffness and creep depend on loading direction. Direction-dependent elastic elements can represent different small-strain moduli, and delayed elastic branches can approximate time-dependent strain. A linear-solid network can therefore be a local fit under specified direction, moisture and temperature, rather than a universal scalar constitutive law.

An immediate strain followed by delayed material creep is captured locally by a spring plus a Kelvin-Voigt model branch. If residual deformation remains after unloading, a Burgers material adds a free series dashpot ${\eta }_0$. Under a constant load,After a hold time $t_h$, the two elastic contributions recover and the dashpot retainsThus immediate recovery, delayed recovery and a residual set identify different roles for the components; an observed permanent set would rule out a purely recoverable linear-solid fit. A viscous dashpot does not itself model a yield threshold or structural damage. Strength loss, splitting, moisture-dependent response and nonlinear compression cannot be represented by one fixed linear Kelvin-Voigt model. No direction-specific measured trace is supplied, so selecting numerical parameters requires the practical data; the constitutive predictions and their limitations are the model comparison that can be made from the paper.