Mechanical fatigue in trees mitigated by annual growth: A theoretical model

Abstract

Mechanical forces applied over a period of time tend to cause fatigue failure in natural organisms and in engineering structures. Here, the theoretical approach known as Continuum Damage Mechanics is applied to study fatigue damage development in trees. It is found that growth in the form of an annual ring of new material is a very effective strategy to limit fatigue damage, due to the fact that, over time, each ring moves inside the trunk, reducing stress. If (as is generally assumed) the tree grows so as to keep the bending stress on its trunk constant, then fatigue failure will be effectively impossible until the tree is very old. One interpretation of this finding is that high cycle fatigue simply never occurs in trees: they don’t accumulate fatigue damage but rather fail by instantaneous overload or low cycle fatigue during a single storm. Another interpretation is that the bending stress is maybe not kept constant but changes as the tree grows, which would be a more efficient strategy making the best use of material. These findings are considered using data from the literature and their implications for the creation of biomimetic products are discussed. Possible experiments to test these theoretical predictions are suggested.