Simulation of Paperboard with the EBT Paperboard Model and Cohesive Zones

Abstract

Previous numerical investigations have simulated the delamination of paperboard using
various mechanical and cohesive models. This has given satisfactory agreement between
the simulation results and experimental data when comparing force-depth curves during
creasing and moment-angle curves during folding. However, the simulation results are
dependent on the user’s definition of the delamination zones.
The EBT paperboard model, used in this work, can predict the location of the delamina-
tion. However, the reaction force during folding is overestimated compared to experimental
results due to a lack of cohesive behaviour. Thus, different options for implementing co-
hesion in the software Abaqus were investigated. The cohesive interaction property was
found to have good agreement with expected experimental behaviour while the compressive
behaviour of cohesive elements was unphysical.
The creasing and folding of paperboard was simulated with a non-cohesive setup as well
as with multiple interfaces and interface locations. The addition of interfaces was shown to
unload the strain in the paperboard and result in a flatter profile due to an overly elastic
behaviour. The location of the interface greatly affected the shape and strain distribution
of the paperboard, as well as the size of the interface opening.
A proof of concept was shown for the stop-start simulation: the paperboard was loaded
in its non-cohesive state, a cohesive layer was applied, and then the paperboard with the
cohesive interface was unloaded. The cohesive unloading proved to have a response that
was closer to the experimental data than the non-cohesive unloading.

Popular Abstract

Milk. Juice. Tomato sauce. All can be packaged in neatly shaped paper-based food car-
tons. But did you know computer simulations can be used to model the origami-like way
in which the carton is put together? The detail with which this process, called forming,
can be simulated, relies on the physics and numerical models used in the simulation soft-
ware. By introducing so-called cohesive zones into the previously developed physics model
for paperboard, we are aiming for more detail than ever before. This adds physics to the
simulation of the creasing and folding of paperboard that was not there before: cohesive be-
haviour, which describes how attached the layers of paperboard are to each other. Indeed,
introducing these cohesive zones has resulted in the simulation having a good agreement
with experimental behaviour.
In addition, simulating changes in the location and amount of the cohesive zones along
the thickness of the paperboard has led to more insight on how to better use these zones
for practical application. More is not necessarily better – having too many zones will make
the paperboard flatter in the simulation than in real life. Having too little zones makes it
too stiff. Somewhere in between is ideal, though the exact number can vary depending on
the dimensions of the paperboard. Changing the location of one zone can give different
shapes and strain distributions of the paperboard. All of this information can be used for
future simulations in order to change the location and number of zones so that the results
can match experiments even better, as well as optimize the use of computational power.
An accurate yet computationally efficient model is vital in capturing detailed phe-
nomena that happen when the paperboard is folded in the machine. This can help predict
potential cracks in the packaging. It can also allow for testing to happen virtually before
testing experimentally, which can greatly reduce cost and time. Not only that, it is more
environmentally friendly as there is less waste.
How was this work done? First, a one-dimensional test was done with the cohesive
zones to see if they behave in a physical manner, as well as to calibrate them. Next, a
simulation was performed to crease and fold the paperboard. From this, the reaction force
and shape of the paperboard were evaluated and compared to experimental findings.
This zoomed-in virtual simulation has helped us look at food and beverage cartons
from a more detailed perspective. We have also seen how improving virtual simulations,
such as with cohesive zones in this case, can help obtain a more accurate simulation. Using
the power of physics and programming, we further use these simulations to gain a deeper
understanding of the processes that shape the cartons we know and use every day.

• author: Anghel, Maria
• supervisor: Mathias Wallin
• organization: Solid Mechanics; Department of Construction Sciences
• course: FHLM01 20191
• year: 2019
• type: H3 - Professional qualifications (4 Years - )
• subject: Technology and Engineering
• keywords: FEM, FEA, computer simulation, solid mechanics, paperboard
• publication/series: TFHF-5000
• report number: TFHF-5254
• other publication id: ISRN LUTFD2/TFHF-19/2019-SE(1-42)
• language: English
• id: 9109747
• date added to LUP: 2023-03-08 09:40:17
• date last changed: 2023-03-08 09:40:17