Elasticity Definition
Mathematical representation of the relationship between stress and strain in an anisotropic material. The compliance tensor defines how paper or board deforms under specific loads by mapping three dimensional stress components to their resulting strains. It contains thirty six individual constants for a general material, though the number reduces noticeably for orthotropic substances like machine made paper.
Mathematical Matrix
Symmetry within the mechanical response ensures that the reciprocal relationship between stress and strain remains consistent across the material axes. Within the compliance tensor, the diagonal elements represent the primary compliance while off diagonal elements account for the coupling between different directions of force. This arrangement allows engineers to predict how a paper web stretches or thins during high speed printing operations.
The specific values are typically derived from ultrasonic testing or tensile trials conducted in the machine and cross directions. Precise mapping of these coefficients prevents registration errors caused by unintended web widening.
Conversion Application
Values within this matrix determine the susceptibility of a substrate to permanent deformation during embossing or creasing. If the compliance tensor is not accurately calculated for a specific grade, the resulting strain may exceed the elastic limit of the fibers. This data informs the setup of nip pressures on a coating line.
