Measurement of the Orthotropic Elastic Constants of Paper

A wave theory describing paper as a three-dimensional homogeneous orthotropic plate is discussed, and the theory compared with experiment. The results indicate that as long as the wavelength is large compared to typical fibre dimensions, paper may be considered to behave as a homogeneous orthotropic plate. This allows determination of all nine orthotropic elastic constants. Measurement of the three Young’s moduli, the in-plane shear modulus, and the in-plane Poisson’s ratios were made as functions of fibre orientation, wet straining, and density. Qualitatively, the results show that a variable producing a change in properties in one direction, alters the properties in the other two directions in a predictable way. The in-plane shear modulus and the Poisson’s ratios, expressed as (vₓᵧvᵧₓ)¹/² were found to be relatively insensitive to fibre orientation and wet straining, except at the highest levels of each.