Bending efficiency through property gradients in bamboo, palm, and wood-based composites

Nature, to a greater extent than engineering, takes advantage of hierarchical structures. These allow for optimization at each structural level to achieve mechanical efficiency, meaning mechanical performance per unit mass. Palms and bamboos do this exceptionally well; both are fibre-reinforced cellular materials in which the fibres are aligned parallel to the stem or culm, respectively. The distribution of these fibres is, however, not uniform: there is a density and modulus gradient across the section. This property gradient increases the flexural rigidity of the plants per unit mass, mass being a measure of metabolic investment made into an organism’s construction. An analytical model is presented with which a ‘gradient shape factor’ can be calculated that describes by how much a plant’s bending efficiency is increased through gradient structures. Combining the ‘gradient shape factor’ with a ‘microstructural shape factor’ that captures the efficiency gained through the cellular nature of the fibre composite’s matrix, and a ‘macroscopical shape factor’ with which the tubular shape of bamboo can be described, for example, it is possible to explore how much each of these three structural levels of the hierarchy contributes to the overall bending performance of the stem or culm. In analogy, the bending efficiency of the commonly used wood-based composite medium-density fibreboard can be analysed; its property gradient is due to its manufacture by hot pressing. A few other engineered materials exist that emulate property gradients; new manufacturing routes to prepare them are currently being explored. It appears worthwhile to pursue these further.