Complas 2023

COMPLAS 2023

Modeling the influence of temperature and moisture on the elasto-plastic behavior of paper and paperboard

Kopic-Osmanovic, Nadir (University of Wuppertal)
Schubert, Holger (Steinbeis Hochschule)
Rief, Stefan (Fraunhofer ITWM)
Orlik, Julia (Fraunhofer ITWM)
Andrä, Heiko (Fraunhofer ITWM)
Hauptmann, Marek (Steinbeis Hochschule)
Simon, Jaan-Willem (University of Wuppertal)

In session: THa-200a - - CT200a - Advanced Material Models and Computational Material Design

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Building a more sustainable future requires the utilization of environmentally friendly materials. Paper and paperboard are excellent candidates, yet a complicated material behavior is hindering a wider engineering application. One key unknown is the interplay between temperature, moisture and mechanical behavior. Therefore, this work focused on the theoretical derivation, algorithmic implementation, and numerical evaluation of a thermo-hygro-mechanically coupled model. The standard thermo-mechanical continuum framework was extended by an additional balance equations, which governs the transport of moisture. The Helmholtz free energy function was additively decomposed into an in-plane and out-of-plane part in order to capture the material's anisotropic mechanical behavior. Similarly, anisotropic heat conduction and moisture diffusion were addressed by defining an anisotropic heat and moisture flux. Temperature and moisture dependent mechanical material parameters alongside thermal expansion, drying of the material, and heat generation due to inelastic deformation couple the global balance equations and their respective solution fields (displacements, temperature and moisture content). The model was implemented into a finite element solver, where automatic differentiation techniques were used for calculating the stiffness matrix, assuring quadratic convergence of the global Newton-Rapshon scheme near the solution. The models capabilities were demonstrated on several numerical examples. The models potential to assess the material response of paper and paperboard subjected to complex thermo-hygro-mechanical loading could possibly improve the simulation of advanced 3D forming processes as well as give answers on how to optimize the machine adjustment and the storing of the material.