Phase-field ductile fracture in orthotropic fiber-based materials
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Paperboard is a fiber-based material widely employed in the food-package industry with the purpose of providing the mechanical properties to the final package. The annual production of packages amounts to several hundred billions units, motivating intensive research efforts focused on characterizing and improving the packaging material for waste reduction. While experimental test methods can provide useful insight, practical applications necessitate a mathematical modeling based on a profound understanding of the material response. In the elastoplastic regime preceding failure, the mathematical description of paperboard has been extensively explored in the literature. The main objective of the current work is to extend the state-of-the-art modeling of paperboard material to include damage and subsequent crack onset and propagation. Starting from established finite-step variational frameworks for elastoplastic solids, the energetic formulation is enriched with the fracture dissipation terms of the phase-field approach to brittle fracture. Following an effective stress approach, a variationally consistent formulation providing the yield and fracture activation criteria is arrived at. The latter is non-variationally modified to account for the plasticity-driven nature of the crack evolution and for the orthotropic nature of paperboard. The approach has been validated against experimental tests provided by laboratories at Tetra Pak, and the model predictivity has been successfully assessed. Despite the specific application, it is expected that the proposed description of orthotropic fracture can be applied to a wide class of orthotropic standard materials.
