Determination of the shear stress shear strain relationship of wood by torsion tests

In this paper, we modified the Nadai-Hill equation representing the shear stress-shear strain relationship at the surface of an isotropic cylindrical bar under the torsional loading to the one for representing the relationship of a rectangular bar of wood, and examined the applicability of the modified formula by several numerical analyses based on the strain-incremental theory. First, the numerical calculations were made for several models of isotropic rectangular bars, and the equation for the cylindrical bar was modified. Then, the applicability of the modified formula was examined with the mechanical properties of Sitka spruce (Picea sitchensis Carr.) and katsura (Cercidiphyllum japonicum Sieb. and Zucc.) whose stress-strain behaviors are different from each other. The calculation results suggested that the modified formula was in good agreement with the shear stress-shear strain relationship obtained by the strain-incremental theory. Therefore, we concluded that the shear stress-shear strain relationship can be represented appropriately by the modified formula.