Multi-scale modelling of elastic properties of balsa

The hierarchical structure of the hardwood balsa (Ochroma pyramidale) is modelled sequentially at various length scales to describe the contribution of each to its elastic moduli. The model takes into account the main features of the microstructure at each length scale, including the orthotropic properties of cellulose microfibrils, the microfibrillar angle, the thickness of cell wall layers, as well as the geometry and arrangement of the cells: the rays, fibres and vessels. Similar to some multi-scale models proposed for softwoods, at each length scale, a representative unit cell of the material is identified and the effective stiffness matrix is determined using finite element analysis with appropriate periodic boundary conditions. A comprehensive search in the literature was conducted to obtain input values for the model. The results of the model, over a wide range of densities, gives a good description of experimentally measured values. The model highlights the significance of cellulose crystallinity, microfibrillar angle and the ray and fibre cell geometries (including the density) in determining the overall elastic constants of balsa. In the future, the model can be used as a tool to design lightweight cellular composites with optimized cell wall composition and cell geometry.