Implementation of moisturedependent constitutive model for paperboard

Abstract: There has been a considerable increase in the usage of paper products due to its sustainability in the product cycle. Many environmental and process variables can affect the mechanical behavior of paper from its making to finished products. Of these variables, moisture is of particular importance and strongly influences both papermaking, converting, and end-use of the paper products. Experimental investigations at different humidity levels reveals that normalized in-plane constitutive parameters, such as elastic parameters and the linear hardening modulus, in both MD and CD1) follow a linear relationship with normalized moisture ratio. This relation is found to be acceptable for a wide range of commercial paperboards. To capture this observation, a novel material model with orthotropic elasticity and anisotropic hardening2 is proposed. An associative flow rule for the evolution of plastic strain is proposed. The proposed flow rule is such that all stresses contribute to plastic flow rather than an effective stress. A simple version using anisotropic linear hardening is implemented. The mechanical properties, such as elastic parameters and hardening moduli are considered functions of the moisture ratio. An implicit variant of the material model is implemented in LS-DYNA®. The simulations with the proposed material model at different humidity levels follow the experimental results well for uniaxial loading, but discrepancies are obtained for simulation of biaxial loading tests. The moisture is assumed constant in the proposed model since the experiments are done in a moisture-controlled environment.