Experiments on laboratory paper sheets have indicated that under certain conditions the elastic modulus is inversely proportional to both the drying shrinkage and dimensional stability. Thus it appears that the elastic response of paper to mechanically and hygroscopically induced stresses is determined by the drying strain or shrinkage of the sheet. It is not clear, however, what effect the geometry of paper network and the properties of papermaking fibers have on the relationship between paper elasticity and drying restraints.
We have developed a model for the study of the elastic properties of paper as a function of the drying shrinkage. The model is based on the assumption that there exists a unique relationship between the elastic properties and dried-in compression of fiber. As a consequence, the elastic properties of a fiber depend on its orientation relative to the principal axes of the paper sheet.
The qualitative features obtained from the model calculations are consistent with experimental observations and independent of details of the elastic properties of fiber. It is clearly shown that no unique relationship exists between the drying strain and elastic modulus of the paper sheet. However, to a reasonable accuracy certain simple relatioships do exist that appear to be of general validity.