Elementary units of paper structure [1]. 

Contexts in source publication

Context 1

... the actual contact area of the surface is much smaller than the nominal contact area because of the roughness of the contact surfaces. According to Schaffrath’s model [1], the surface structure is characterized by pyramid units (Fig. 3). The following relation express can be obtained Combined with the force-deformation relation express, the relationship between pressure and contact area is showed in Fig. 10. The equipment used here is ZWICK Z050, which can be utilized for strain, shear and bending tests with different substrates and machine components with high accuracy of the cross head speed (0.0005- 2000 mm/min), position repetition accuracy (± 2 μ m) ...

Context 2

... is a composite made up of fibers, moisture, voids and chemical additives that are in the form of discrete fibers cross-linked in a complex network. The mechanical behavior of paper has a very close relationship with many operations in the printing production, such as printing, paper counting, folding, creasing, calendaring, cutting, etc. A number of studies have been made with the objective of predicting the stress-strain behavior of paper materials under the forces in MD and CD- directions, but the research in ZD-direction is limited. The purpose of this paper is to improve the mathematical model proposed by Schaffrath and extend the model to multiple sheets. Additionally, based on image processing technique, a new approach for measuring the actual contact area and calculating the relationship between force and actual contact area is presented. In the model proposed by Schaffrath [ 1, 2], who divided paper body into three parts, developed the models respectively and derived the force- deformation relationship of paper materials by using the Newton formula. Also, Stenberg [3, 4] published some articles between 2001 and 2003, in which he summarized the literature, developed a new device to measure the stress-strain properties of paperboard in ZD- direction, and built an elastic-plastic model for paper materials. The topography of paper surface could be measured today very precisely with different measurement methods, e. g., a NanoFocus μ SCAN system. For further processing, these physical data have to be transferred in an analysis model. As mentioned above, Stenberg and Schaffrath proposed mathematical models of paper materials in ZD-direction. Compared with the model proposed by Stenberg, the parameters needed in Schaffrath’s model are much easier to obtain. In this model, the paper body was divided into three parts: two surface structures and one internal structure, which can be described by using the following units (Fig. 3). After that Schaffrath built the models for the surface and internal structures. According to Hooke’s Law   E    F  E  A 0  x  ...