This work has been motivated by configurations designed in our laboratory for which wood samples undergo large displacements that result in more accurate measurements.
From a theoretical point of view, such configurations require a formulation able to take into account the geometrical non-linearities in the case of a highly anisotropic material. This paper proposes a solution to this specific problem in the case of large displacements, where the rotations may be large but the pure strain field is assumed to remain small. We propose to show how it is possible to extend existing rate-form small displacement constitutive laws in order to use them in a large displacement formulation. The strategy adopted in order to account for the anisotropy of the material and, at the same time, to respect the principle of tensorial objectivity, is to express the constitutive law in a co-ordinate system, which rotates during the deformation. Therefore we use tensors whose eigenvectors have a Lagrangian orientation while the eigenvalues have a sense in the Eulerian configuration.
In order to exhibit the possibilities of the resulting formulation, two different configurations are tested:
• The curvature due to shrinkage of a board section submitted to a linear moisture content profile,
• The deflection of a cantilever beam.
Both examples are compared to an analytical calculation obtained using the material resistance results.
The numerical calculation uses a viscoelastic orthotropic constitutive law, which is integrated using an implicit time scheme and eight node isoparametric finite elements.