Elasto-plasticity of paper

We develop a constitutive model of paper’s in-plane biaxial tensile response accounting for the elastic–plastic hardening behavior, and its orthotropic character. The latter aspect is motivated by machine-made papers, which, in contrast to isotropic laboratory handsheets, are strongly oriented. We focus on modeling paper’s response under monotonic loading, this restriction allowing us to treat the elastic-plastic response as a physically nonlinear elastic one. A strain energy function of a hyperbolic tangent form is developed so as to fit the entire range of biaxial and uniaxial experiments on a commercial grade paper. This function may then be introduced as the free energy function into a model based on thermomechanics with internal variables. # 2003 Published by Elsevier Ltd.

[1]  Martin Ostoja-Starzewski,et al.  Microstructural Randomness Versus Representative Volume Element in Thermomechanics , 2002 .

[2]  J. Aboudi,et al.  Higher-order theory for periodic multiphase materials with inelastic phases , 2003 .

[3]  Alexander M. Puzrin,et al.  A thermomechanical framework for constitutive models for rate-independent dissipative materials , 2000 .

[4]  Mary C. Boyce,et al.  A constitutive model for the anisotropic elastic–plastic deformation of paper and paperboard , 2002 .

[5]  Christoph Wehrli,et al.  The Derivation of Constitutive Relations from the Free Energy and the Dissipation Function , 1987 .

[6]  P. Dłużewski,et al.  Anisotropic Hyperelasticity Based Upon General Strain Measures , 2000 .

[7]  M. Ostoja-Starzewski,et al.  Random formation, inelastic response and scale effects in paper , 2003, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[8]  K. Murakami,et al.  BIAXIAL TENSILE BEHAVIOR OF PAPER , 1979 .

[9]  T. Urbanik,et al.  A Nonlinear Theory for Elastic Plates With Application to Characterizing Paper Properties , 1984 .

[10]  Gérard A. Maugin,et al.  The thermomechanics of nonlinear irreversible behaviors : an introduction , 1999 .

[11]  Guy T. Houlsby,et al.  Application of thermomechanical principles to the modelling of geotechnical materials , 1997, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[12]  P. M. Naghdi,et al.  On continuum thermodynamics , 1972 .

[13]  K. Schulgasser,et al.  On the in-plane elastic constants of paper , 1981 .

[14]  D. E. Carlson,et al.  An introduction to thermomechanics , 1983 .

[15]  G. Maugin.  The Thermomechanics of Plasticity and Fracture , 1992 .

[16]  M. Ostoja-Starzewski,et al.  Random Fiber Networks and Special Elastic Orthotropy of Paper , 2000 .

[17]  C. Habeger,et al.  Measurement of the orthotropic elastic constants of paper , 1982 .

[18]  R. E. Mark,et al.  Handbook of physical testing of paper , 2002 .

[19]  Continuum Models for the Mechanical Response of Paper and Paper Composites: Past, Present, and Future , 1990 .