Speaker
Description
Anisotropic elasto-plasticity, sensibility to temperature and moisture, wrinkling and damage occurrence are some of the phenomena needed to analyse for a better insight on the performance of a material. Due to this complex material behavior, the usage of certain materials, like paper and paperboard, has been hindered. These materials are highly sustainable and are mostly used in the packaging industry, being a reasonable alternative to other less environmentally friendly materials.
Paper and paperboard undergo large deformations on the elastic and plastic regime, primarily on the forming process. In a continuum-mechanical framework, they can be considered a homogeneous anisotropic material. The anisotropy being present on the machine direction, the cross direction and the out-of-plane direction. Keeping in mind that it was already showed that the Poisson’s ratio in the out-of-plane direction is very close to zero, which allows the decoupling in-plane and the out-of-plane behavior. The larger deformations occur on the out-of-plane direction. A unified model is required for being able to address the complex deformations.
The conventional yield criteria by Hill does not account adequately for the advanced complex material response, since the elastic properties are altered and hardening with anisotropic plasticity is present; due to the evolution of plasticity.
Starting from a non-unique intermediate configuration on the finite elasto-plasticity framework, where the deformation gradient is multiplicatively split into an elastic and a plastic part, the derivation of constitutive laws for anisotropic materials that are frame indifferent and nonlinear, requires the introduction of structural tensors, as well as other additional independent variables. The strain energy function is defined with representations of the right Cauchy-Green deformation tensor and the structural tensor for this intermediate configuration. The decomposition of the elastic strain energy into in-plane and out-of-plane parts, account for their differences. Is possible to obtain a more general treatment of elasto-plastic interactions that allows to capture the densification effect, that increases elastic stiffness because of plastic deformation during out-of-plane compression loading.
Additional changes were made for accounting the inconsistencies of the initial yield stresses and the plastic strain ratios. The anisotropic plastic hardening is considered by the definition of a set of coupled internal variables. This leads to a thermodynamically consistent manner of ensuring the validity of the model for finite deformations. Encompassing several important characteristics of the elasto-plastic behavior of paper and paperboard, promising numerical simulations’ results confirm the model’s validity and the forming process could be optimized.
