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were the variables to be optimized and, for this case, the best configuration was achieved with a blank distance of 0.1 mm and a 0.56 ◦ inclination in terms of the perforation line, achieving an increase of 29.3% in perforation efficiency. Both the best and mean values converged for almost the same value for this case. For the case where the only variable to be optimized was the inclination of the cuts, with the blank distance fixed at 1.0 mm, the genetic algorithm found the best inclination angle to be 0.67 ◦ , achieving an increase of 7.6% in perforation efficiency, but the average values of the population did not converge. This was due to the complex failure mode of the paper and its kinematics as the damage evolved. Despite the complex failure behavior, the optimum configuration was achieved for both cases (with and without a blank distance fixed at 1.0 mm), and only a small inclination in the perforation line will reduce the tear force, regardless of the rupture progression along the perforation line. Digital twining is an emergent simulation tool that will be commonly used in the near future because it will permit optimization in a digital environment and the subsequent transition to and application in the industrial environment, as proved with this work. The main limitation of this work was that it considered the material to be homogeneous and orthotropic. In fact, the material used experimentally contained heterogeneously distributed fibers, preferentially oriented in the MD. But this macroscale model is accurate enough to simulate different geometries in terms of both the perforation line and the cut itself, such as waves, triangles, etc. Author Contributions: J.C.V.: data acquisition and curation, investigation, writing—original draft, writing—review and editing. A.C.V.: FEM analysis, writing—original draft, simulation supervision, writing—review and editing. M.L.R.: FEM analysis, writing—original draft, simulation supervision, writing—review and editing. P.T.F.: supervision, writing—review and editing. A.P.C.: project supervisor, writing—review and editing. All authors have read and agreed to the published version of the manuscript. Funding: The authors gratefully acknowledge the funding of this work that was granted under the Project InPaCTus—Innovative Products and Technologies from Eucalyptus, Project No. 21874 funded by Portugal 2020 through the European Regional Development Fund (ERDF) in the framework of COMPETE 2020 no. 246/AXIS II/2017. The authors are also very grateful for the support given by the research unit Fiber Materials and Environmental Technologies (FibEnTech-UBI), under the project reference UIDB/00195/2020, and by the Center for Mechanical and Aerospace Science and Technologies (C-MAST-UBI), under the project reference UIDB/00151/2020, both funded by the Fundaç ã oparaaCi ê ncia e a Tecnologia, IP/MCTES through national funds (PIDDAC). Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable. Data Availability Statement: Not applicable.
Acknowledgments: The authors acknowledge the materials, access to equipment and installations, and all the general support given by The Navigator Company, RAIZ, the Optical Center, Depart- ment of Physics, Department of Textile Science and Technology, Department of Chemistry of the Universidade da Beira Interior. Conflicts of Interest: The authors declare no conflict of interest.
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