Continuum Models for the Mechanical Response of Paper and Paper Composites: Past, Present, and Future

Abstract

ABSTRACTPaper and paper composites are utilized in applications where they are subjected to multiaxial stress states and changing environmental conditions. Such materials exhibit nonlinear anisotropic material behavior which is time dependent and affected adversely by slight changes in moisture content and temperature. At present, lack of adequate theoretical models often hampers the design and development of structurally optimized paper products. Therefore, it has been common practice in the pulp and paper industry to use trial and error, and empirical approaches. Accurate continuum models for the mechanical behavior of paper and paper composites are needed to guide the paper product design process.In this work, a limited review of the existing methods for modeling the mechanical response of paper and paper composites is given. At first, a brief overview of the goals of current modeling techniques based on hydrogen bond, fiber network, and continuum approaches is presented. The governing equations and capabilities of current continuum models are then discussed in greater detail. Theories which include linear elastic (generalized Hooke's Law), nonlinear elastic (hyperelastic), linear viscoelastic, nonlinear viscoelastic, and inelastic constitutive relations are addressed. Finally, applications of existing continuum theories to the analysis of paper materials in structural configurations are presented. After these discussions, the limitations of the available continuum models are assessed and future research needs are suggested.