{"title":"Viscoelasticity and accretive phase-change at finite strains.","authors":"Andrea Chiesa, Ulisse Stefanelli","doi":"10.1007/s00033-025-02434-9","DOIUrl":null,"url":null,"abstract":"<p><p>We investigate the evolution of a two-phase viscoelastic material at finite strains. The phase evolution is assumed to be irreversible: One phase accretes in time in its normal direction, at the expense of the other. Mechanical response depends on the phase. At the same time, growth is influenced by the mechanical state at the boundary of the accreting phase, making the model fully coupled. This setting is inspired by the early stage development of solid tumors, as well as by the swelling of polymer gels. We formulate the evolution problem by coupling the balance of momenta in weak form and the growth dynamics in the viscosity sense. Both a diffused- and a sharp-interface variant of the model are proved to admit solutions and the sharp-interface limit is investigated.</p>","PeriodicalId":54401,"journal":{"name":"Zeitschrift fur Angewandte Mathematik und Physik","volume":"76 2","pages":"53"},"PeriodicalIF":1.7000,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11782464/pdf/","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Zeitschrift fur Angewandte Mathematik und Physik","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00033-025-02434-9","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2025/1/30 0:00:00","PubModel":"Epub","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
We investigate the evolution of a two-phase viscoelastic material at finite strains. The phase evolution is assumed to be irreversible: One phase accretes in time in its normal direction, at the expense of the other. Mechanical response depends on the phase. At the same time, growth is influenced by the mechanical state at the boundary of the accreting phase, making the model fully coupled. This setting is inspired by the early stage development of solid tumors, as well as by the swelling of polymer gels. We formulate the evolution problem by coupling the balance of momenta in weak form and the growth dynamics in the viscosity sense. Both a diffused- and a sharp-interface variant of the model are proved to admit solutions and the sharp-interface limit is investigated.
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The Journal of Applied Mathematics and Physics (ZAMP) publishes papers of high scientific quality in Fluid Mechanics, Mechanics of Solids and Differential Equations/Applied Mathematics. A paper will be considered for publication if at least one of the following conditions is fulfilled:
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