Modeling the anisotropic elasto‐plastic material behavior of paper and paperboard at finite deformations

Abstract

AbstractAccurately modeling the material behavior of paper and paperboard is proven to be highly demanding. Most difficulties arise from the pronounced anisotropic nature of the material. Additionally, differences in the in‐plane and out‐of‐plane behavior as well as non‐isochoric plasticity, which affects the elastic behavior, further deepen the issue at hand. Therefore, an material model is proposed, capable of capturing the anisotropic elasto‐plastic behavior of paper and paperboard. The constitutive framework was derived in a thermodynamically consistent manner, valid for finite deformations, and accounting for the coupling of in‐plane and out‐of‐plane behavior. The influence of the orthotropic anisotropy on the elasto‐plastic material response was introduced through the concept of structural tensors. A slight generalization of the elastic part of the free energy was made in order to incorporate the densification effect. A well known yield criterion was modified in order to account for some inconsistencies. Non‐isotropic hardening was considered by defining a set of coupled internal variables. The model's capabilities were demonstrated by simulating the process of folding and creasing.