The poroelastic role of water in cell walls of the hierarchical composite "softwood"

Wood is an anisotropic, hierarchically organized material, and the question how the hierarchical organization governs the anisotropy of its mechanical properties (such as stiffness and strength) has kept researchers busy for decades. While the honeycomb structure of softwood or the chemical composition of the cell wall has been fairly well established, the mechanical role of the cell wall water is less understood. The question arises how its capability to carry compressive loads (but not tensile loads) and its pressurization state affect mechanical deformations of the hierarchical composite "wood". By extending the framework of poro-micromechanics to more than two material phases, we here provide corresponding answers from a novel hierarchical set of matrix-inclusion problems with eigenstresses: (i) Biot tensors, expressing how much of the cell wall water-induced pore pressure is transferred to the boundary of an overall deformation-free representative volume element (RVE), and (ii) Biot moduli, expressing the porosity changes invoked by a pore pressure within such an RVE, are reported as functions of the material's composition, in particular of its water content and its lumen space. At the level of softwood, where we transform a periodic homogenization scheme into an equivalent matrix-inclusion problem, all Biot tensor components are found to increase with decreasing lumen volume fraction. A further research finding concerns the strong anisotropy of the Biot tensor with respect to the water content: Transverse components increase with increasing water content, while the relationship "longitudinal Biot tensor component versus volume fraction of water within the wood cell wall" exhibits a maximum, representing a trade-off between pore pressure increase (increasing the longitudinal Biot tensor component, dominantly at low water content) and softening of the cell wall (reducing this component, dominantly at high water contents). Soft cell wall matrices reinforced with very stiff cellulose fibers may even result in negative longitudinal Biot tensor components. The aforementioned maximum effect is also noted for the Biot modulus.