An empirical model for describing the mechanical behavior of paper stacks in the perpendicular to the in-plane direction DOI 10.14622/JPMTR-1910

Abstract

The mechanical behavior of paper materials under compression in the out-of-plane direction is highly nonlinear. If the influence of the surface topography is not taken into account, the stress–strain curve of paper materials in the loading process is a typical example of materials with J-shaped compressive curves. When compression is released, the stress–strain curve in the unloading process is also nonlinear. The main purpose of this paper is to establish a suitable mathematical model and actualize the description of the compression curve for paper and paper stacks. The loading and unloading nonlinearities of paper stress–strain relations can be approximated by using different equations. In this paper, the loading curve of paper is calculated by using the sextic polynomial equation and the unloading curve is described by using the modified exponential function. All the used coefficients for determining the functions are expressed as the functions of the stress at the start point of unloading. The compressive behavior of paper under some given forces are also calculated by using the identified equation and verified by means of the experimental data. For multiple sheets, it is assumed that when the force is the same, the deformation of the paper stack is directly proportional to the number of sheets. Based on this assumption, the force–deformation relation of the paper stack is derived. The comparative analysis of the experimental results demonstrates the effectiveness of the description model.