An in-plane phase-field ductile fracture model for orthotropic paperboard material

A phase-field ductile fracture formulation for orthotropic paperboard materials is proposed, based on an anisotropic, multi-surface elastoplastic model describing the in-plane behavior of paperboard. A variational statement for the finite-step elastoplastic problem is extended to include the variational description of Griffith-type brittle fracture by a phase-field gradient term. The interaction between plastic and fracture dissipation mechanisms is modeled by introducing a scalar modulation function, assuming plasticity driven damage growth. This function depends on a scalar measure of the plastic strain components in the material orthotropy frame. It modifies the fracture activation criterion in a non-variational fashion, resulting in a direction-dependent material strength against crack propagation. The model performance is assessed by comparing numerical simulations and experimental tests conducted in a climate-controlled laboratory.