Figure 1: Showing branches laden with oranges.
Whilst looking at the fruit laden orange trees in our garden, I wondered in awe about the branches and how they are structured so that they can not only carry the weight of the fruit but also be flexible and able to bend under the weight of the fruit. After carrying out searches on the internet, I learnt that this phenomenon is known as "viscoelasticity of tree branches". I was heartened to learn that I am not the only person who wonders about such things when I found a link which included a scientific study of the viscoelesaticity of tree branches and also explained about branch shape, growth stresses and growth direction. Here is a brief albeit scientifically worded extract:
BIOMECHANICS. - Equilibrium shape of a tree branch. Bernard Schaeffer
"When the load is permanent, viscous or plastic deformation may occur, but the
coupling between the simultaneous increase of the load and the thickening of the
branch is more important. A branch bends continuously with time, even if it
thickens. Even with a constant load there would be no decrease of the deflection
when the branch thickens. On the contrary, a decrease of the thickness of the
branch, would also increase the deflection. The process of growth being time-
dependent, the shape of a branch is a function of time. Dividing time into
infinitely small intervals, it is possible to divide each time step in a few more
steps: growth, loading and bending. Growth produces an increase in length and
thickness of the branch and therefore a small change in geometry."