Multi-scale finite element model for a new material inspired by the mechanics and structure of wood cell-walls

Abstract This paper proposes a fully coupled multi-scale finite element model for the constitutive description of an alumina/magnesium alloy/epoxy composite inspired in the mechanics and structure of the wall of wood cells. The mechanical response of the composite (the large scale continuum) is described by means of a representative volume element (RVE, corresponding to the intermediate scale) in which the fibre is represented as a periodic alternation of alumina and magnesium alloy fractions. Furthermore, at a lower scale the overall constitutive behavior of the alumina/magnesium alloy fibre is modelled as a single material defined by a large number of RVEs (the smallest material scale) at the Gauss point (intermediate) level. Numerical material tests show that this new composite maximises its toughness when the hierarchical design of wood cellulose fibres is replicated. The above results provide for the first time new clues into the understanding of how trees and plants optimise their microstructures at the cellulose level in order to absorb a large amount of strain energy before failure. These findings are likely to shed more light into natural materials and bio-inspired design strategies, which are still not well-understood at present.