Variational modeling of paperboard delamination under bending
We develop and analyze a variational model for laminated paperboard. The model consists of a number of elastic sheets of a given thickness, which – at the expense of an energy per unit area – may delaminate. By providing an explicit construction for possible admissible deformations subject to bounda...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-06-01
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| Series: | Mathematics in Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mine.202303910.3934/mbe.2022310 |
| _version_ | 1797824645858066432 |
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| author | Sergio Conti Patrick Dondl Julia Orlik |
| author_facet | Sergio Conti Patrick Dondl Julia Orlik |
| author_sort | Sergio Conti |
| collection | DOAJ |
| description | We develop and analyze a variational model for laminated paperboard. The model consists of a number of elastic sheets of a given thickness, which – at the expense of an energy per unit area – may delaminate. By providing an explicit construction for possible admissible deformations subject to boundary conditions that introduce a single bend, we discover a rich variety of energetic regimes. The regimes correspond to the experimentally observed: initial purely elastic response for small bending angle and the formation of a localized inelastic, delaminated hinge once the angle reaches a critical value. Our scaling upper bound then suggests the occurrence of several additional regimes as the angle increases. The upper bounds for the energy are partially matched by scaling lower bounds. |
| first_indexed | 2024-03-13T10:42:09Z |
| format | Article |
| id | doaj.art-73b6f9b36ffa4e23ad6a6d4296808a2b |
| institution | Directory Open Access Journal |
| issn | 2640-3501 |
| language | English |
| last_indexed | 2024-03-13T10:42:09Z |
| publishDate | 2023-06-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematics in Engineering |
| spelling | doaj.art-73b6f9b36ffa4e23ad6a6d4296808a2b2023-05-18T01:24:11ZengAIMS PressMathematics in Engineering2640-35012023-06-015212810.3934/mine.2023039Variational modeling of paperboard delamination under bendingSergio Conti0Patrick Dondl 1Julia Orlik21. Institut für Angewandte Mathematik, Universität Bonn, 53115 Bonn, Germany2. Abteilung für Angewandte Mathematik, Albert-Ludwigs-Universität Freiburg, 79104 Freiburg i. Br., Germany3. Fraunhofer-Institut für Techno- und Wirtschaftsmathematik ITWM, 67663 Kaiserslautern, GermanyWe develop and analyze a variational model for laminated paperboard. The model consists of a number of elastic sheets of a given thickness, which – at the expense of an energy per unit area – may delaminate. By providing an explicit construction for possible admissible deformations subject to boundary conditions that introduce a single bend, we discover a rich variety of energetic regimes. The regimes correspond to the experimentally observed: initial purely elastic response for small bending angle and the formation of a localized inelastic, delaminated hinge once the angle reaches a critical value. Our scaling upper bound then suggests the occurrence of several additional regimes as the angle increases. The upper bounds for the energy are partially matched by scaling lower bounds.https://www.aimspress.com/article/doi/10.3934/mine.202303910.3934/mbe.2022310calculus of variationsenergy scalingnonlinear elasticitydelaminationpaperboard |
| spellingShingle | Sergio Conti Patrick Dondl Julia Orlik Variational modeling of paperboard delamination under bending Mathematics in Engineering calculus of variations energy scaling nonlinear elasticity delamination paperboard |
| title | Variational modeling of paperboard delamination under bending |
| title_full | Variational modeling of paperboard delamination under bending |
| title_fullStr | Variational modeling of paperboard delamination under bending |
| title_full_unstemmed | Variational modeling of paperboard delamination under bending |
| title_short | Variational modeling of paperboard delamination under bending |
| title_sort | variational modeling of paperboard delamination under bending |
| topic | calculus of variations energy scaling nonlinear elasticity delamination paperboard |
| url | https://www.aimspress.com/article/doi/10.3934/mine.202303910.3934/mbe.2022310 |
| work_keys_str_mv | AT sergioconti variationalmodelingofpaperboarddelaminationunderbending AT patrickdondl variationalmodelingofpaperboarddelaminationunderbending AT juliaorlik variationalmodelingofpaperboarddelaminationunderbending |