ABSTRACT
IV. Relations Between Loading and Deformation: Constitutive Relations 12 A. Infinitesimal Linear Elasticity 12 B. Other Kinds of Elasticity 17 C. Plasticity 26
V. Relationships Between Fiber Properties, Sheet Structure, and Paper Mechanical Properties 27 A. Methods for Predicting Paper Elastic Behavior in Terms of
Network Structure 27 B. One-Dimensional Mesomechanics Models for Low Density Paper
and Network Structure 28 C. Fiber Structure and Elastic Behavior 43 D. Mechanical Properties of the Fiber-Fiber Bond 47 E. Linear Elastic Response of Medium-High Density Paper 50 F. Computer Simulation of Mesomechanics Models 55 G. Computer Simulation of Fiber Networks Containing Many Fibers 60 H. Plane Stress 2-D Nonlinear Constitutive Model for Paper 65
Appendix. Elastic Coefficients for Moderate to High Density Paper 68
References 71
I. INTRODUCTION
The objective of this chapter is to present a general treatment of material related to the problem of describing the stress-strain behavior of paper. Sections II and III are devoted to a general treatment of the problem of describing the deformation and stressing of materials. Certain of the concepts developed in these sections are necessary to enable a proper description of the constitutive relations that are presented in subsequent sections. Section IV treats the classical elastic and inelastic constitutive equations and their application to paper material. Section V provides a discussion of the prediction of both the elastic and inelastic reponse of paper in terms of the mechanical behavior of the fibers and the fiber network structure of paper.
