Cellulose fibers exhibit a wide range of shapes and sizes. This variation influences the mechanical performance of paper and paperboard by affecting the stress distribution inside the network and the degree of fiber-to-fiber bonding which is possible at a given density. However, the methods used to characterize the distribution of fiber sizes in the pulp neglect that the characteristic features of a fiber are generally not independent.
Here, we resolve this shortcoming by fitting the fiber population to a multivariate distribution without enforcing normality or independence between the properties. The high-dimensional multivariate function is recast as a set of univariate distribution functions and a series of bivariate distributions connected by a canonical vine.
Using a micro-mechanical model of a paper sheet the influence of this improved characterization is investigated. Reasonable margins and a description of the dependency is shown to be superior to assuming independence even for perfectly preserved marginal distributions. This result demonstrates that micro-mechanical models of paper and paperboard cannot by assumption neglect the influence of the interdependence between the characteristic features of fibers.