Constitutive Relation
Numerical simulation of adhesive failure in paperboard converting utilizes a simplified mathematical relationship to describe the progressive degradation of a bonded interface. The bilinear traction separation model defines this interaction by tracking the tension or shear stress as a function of interfacial displacement. During the initial stage, the cohesive layer behaves elastically until the stress reaches a critical threshold that represents the peak strength of the bond.
Once this threshold is surpassed, damage initiates and the material enters a softening phase where the load-bearing capacity decays linearly to zero. This boundary establishes the limit beyond which the cohesive zone exerts no further resistive force.
Softening Regime
Degradation of the bond proceeds through a controlled softening phase where the material loses cohesive stiffness. Within this stage, microstructural damage accumulates as the adhesive or paper fibers begin to detach. Numerical solvers decrease the local stiffness matrix based on the damage variable.
This softening controls the simulated tear behavior.
Damage Evolution
Calculating the area under the entire stress-displacement path yields the critical energy release rate required for complete failure. This total energy must equal the fracture toughness of the paperboard or adhesive layer. Numerical solvers track this evolution to prevent non-convergence during unstable crack growth.
The process concludes when the separation exceeds the critical displacement limit.
