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Asymptotic behavior for textiles with loose contact
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  • Riccardo Falconi,
  • Georges GRISO,
  • Julia Orlik,
  • Stephan Wackerle
Riccardo Falconi
Fraunhofer-Institut fur Techno und Wirtschaftsmathematik ITWM

Corresponding Author:[email protected]

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Georges GRISO
UPMC Paris 6
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Julia Orlik
Fraunhofer ITWM
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Stephan Wackerle
Fraunhofer-Institut fur Techno und Wirtschaftsmathematik ITWM
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The paper is dedicated to the modeling and asymptotic investigation of a linear elasticity problem, in the form of variational inequality, for a textile structure. The textile is made of long and thin fibers crossing each others, forming a periodic squared domain. The domain is clamped only partially and an in plane sliding between the fibers is bounded by a contact function, which is chosen to be loose. We also assume a non-penetration condition for the fibers. Both partial clamp and loose contact arise a domain split, leading to different behaviors in each of the four parts. The homogenization is made via unfolding method, with an additional dimension reduction to further simplify the problem. The four cell problems are inequalities heavily coupled by the outer plane macro-micro constraints, while the macroscopic limit problem results to be an inequality of Leray-Lions type with only macro in plane constraints. On both scales, no uniqueness is expected.
10 May 2022Submitted to Mathematical Methods in the Applied Sciences
12 May 2022Submission Checks Completed
12 May 2022Assigned to Editor
24 May 2022Reviewer(s) Assigned
22 Aug 2022Review(s) Completed, Editorial Evaluation Pending
25 Aug 2022Editorial Decision: Revise Minor
13 Dec 20221st Revision Received
14 Dec 2022Submission Checks Completed
14 Dec 2022Assigned to Editor
14 Dec 2022Review(s) Completed, Editorial Evaluation Pending
16 Dec 2022Reviewer(s) Assigned
02 Jun 2023Editorial Decision: Accept