A computational micromechanics constitutive model for the unloading behavior of paper

In this study, a computational micromechanics material model for the unloading behavior of paper and other nonwoven materials is presented. The asymptotic fiber and bond (AFB) model for paper elastic–plastic behavior [Sinha, S.K., Perkins, R.W., 1995. Micromechanics constitutive model for use in finite element analysis, In: Proceedings of the 1995, Joint ASME Applied Mechanics and Materials Summer Meeting, Los Angeles, CA, USA, Jun 28–30, 1995] has been extended to model the unloading process through a computational algorithm and implemented using the UMAT subroutine in ABAQUS finite element code. For every unloading increment, the material model assumes elastic unloading with a slope equal to the initial elastic modulus. The Jacobian matrix of the constitutive model is updated at every unloading increment by applying the incremental form of AFB model for a planar element with an elastic fiber and bond condition. A uniaxial tensile and a biaxial Mullen burst loading–unloading experiments were carried out for a paperboard sample and simulated using the model. The stress–strain curve and residual strain for the uniaxial loading were in good agreement with experimental results. The finite element model of the burst test with the AFB unloading material model predicted the general shape of the pressure versus deflection curve. However, the model over predicted the residual deflection by more than 50%. The loading portion of the pressure–deflection curve had a significant offset from experimental curves, and the nonlinearity in the unloading curve towards the end was not predicted. The discrepancies with experimental results are attributed to the burst test itself, model parameter estimation inadequacies, boundary conditions used in the FEA, and neglecting time-dependant effects. Nevertheless, the model can be useful in parametric studies relating microstructure to unloading behavior in structural problems.