A free boundary approach to the quasistatic evolution of debonding models

Fuente: arXiv
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Autori principali: Maggiorelli, Eleonora, Riva, Filippo, Tolotti, Edoardo Giovanni
Natura: Preprint
Pubblicazione: 2025
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author Maggiorelli, Eleonora
Riva, Filippo
Tolotti, Edoardo Giovanni
author_facet Maggiorelli, Eleonora
Riva, Filippo
Tolotti, Edoardo Giovanni
contents The mechanical process of progressively debonding an adhesive membrane from a substrate is described as a quasistatic variational evolution of sets and herein investigated. Existence of energetic solutions, based on global minimisers of a suitable functional together with an energy balance, is obtained within the natural class of open sets, improving and simplifying previous results known in literature. The proposed approach relies on an equivalent reformulation of the model in terms of the celebrated one-phase Bernoulli free boundary problem. This point of view allows performing the Minimizing Movements scheme in spaces of functions instead of the more complicated framework of sets. Nevertheless, in order to encompass irreversibility of the phenomenon, it remains crucial to keep track of the debonded region at each discrete time-step, thus actually resulting in a coupled algorithm.
format Preprint
id arxiv_https___arxiv_org_abs_2503_17023
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle A free boundary approach to the quasistatic evolution of debonding models
Maggiorelli, Eleonora
Riva, Filippo
Tolotti, Edoardo Giovanni
Analysis of PDEs
35R35, 35R37, 74K15, 76D27
The mechanical process of progressively debonding an adhesive membrane from a substrate is described as a quasistatic variational evolution of sets and herein investigated. Existence of energetic solutions, based on global minimisers of a suitable functional together with an energy balance, is obtained within the natural class of open sets, improving and simplifying previous results known in literature. The proposed approach relies on an equivalent reformulation of the model in terms of the celebrated one-phase Bernoulli free boundary problem. This point of view allows performing the Minimizing Movements scheme in spaces of functions instead of the more complicated framework of sets. Nevertheless, in order to encompass irreversibility of the phenomenon, it remains crucial to keep track of the debonded region at each discrete time-step, thus actually resulting in a coupled algorithm.
title A free boundary approach to the quasistatic evolution of debonding models
topic Analysis of PDEs
35R35, 35R37, 74K15, 76D27
url https://arxiv.org/abs/2503.17023