A Numerical Scheme and Validation of the Asymptotic Energy Release Rate Formula for a 2D Gel Thin-Film Debonding Problem

IF 1.9 4区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Applied Mathematics Pub Date : 2024-08-13 DOI:10.1137/23m1579042

Maria Carme Calderer, Duvan Henao, Manuel A. Sánchez, Ronald A. Siegel, Sichen Song

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引用次数: 0

Abstract

SIAM Journal on Applied Mathematics, Volume 84, Issue 4, Page 1766-1791, August 2024.
Abstract. This article presents a numerical scheme for the variational model formulated by Calderer et al. [J. Elast., 141 (2020), pp. 51–73] for the debonding of a hydrogel film from a rigid substrate upon exposure to solvent, in the two-dimensional case of a film placed between two parallel walls. It builds upon the scheme introduced by Song et al. [J. Elast., 153 (2023), pp. 651–679] for completely bonded gels, which fails to be robust in the case of gels that are already debonded. The new scheme is used to compute the energy release rate function, based on which predictions are offered for the threshold thickness below which the gel/substrate system is stable against debonding. This study, in turn, makes it possible to validate a theoretical estimate for the energy release rate obtained in the cited works, which is based on a thin-film asymptotic analysis and which, due to its explicit nature, is potentially valuable in medical device development. An existence theorem and rigorous justifications of some approximations made in our numerical scheme are also provided.

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二维凝胶薄膜脱粘问题的数值方案和渐近能量释放率公式验证

SIAM 应用数学杂志》，第 84 卷第 4 期，第 1766-1791 页，2024 年 8 月。摘要本文介绍了 Calderer 等人[《弹性学报》，141 (2020)，第 51-73 页]所建立的变分模型的数值方案，该方案用于二维情况（薄膜置于两平行壁之间）下水凝胶膜暴露于溶剂时与刚性基底的脱粘。它建立在 Song 等人[《弹性学报》，153 (2023)，第 651-679 页]针对完全粘合的凝胶提出的方案基础上，该方案在凝胶已经脱粘的情况下不稳定。新方案用于计算能量释放率函数，并在此基础上预测凝胶/基底系统稳定抗脱落的阈值厚度。这项研究反过来又验证了引用著作中获得的能量释放率理论估计值，该估计值基于薄膜渐近分析，由于其明确性，在医疗设备开发中具有潜在价值。此外，我们还提供了一个存在定理，并对我们数值方案中的一些近似值进行了严格论证。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

SIAM Journal on Applied Mathematics 数学-应用数学

CiteScore

3.60

自引率

0.00%

发文量

审稿时长

12 months

期刊介绍： SIAM Journal on Applied Mathematics (SIAP) is an interdisciplinary journal containing research articles that treat scientific problems using methods that are of mathematical interest. Appropriate subject areas include the physical, engineering, financial, and life sciences. Examples are problems in fluid mechanics, including reaction-diffusion problems, sedimentation, combustion, and transport theory; solid mechanics; elasticity; electromagnetic theory and optics; materials science; mathematical biology, including population dynamics, biomechanics, and physiology; linear and nonlinear wave propagation, including scattering theory and wave propagation in random media; inverse problems; nonlinear dynamics; and stochastic processes, including queueing theory. Mathematical techniques of interest include asymptotic methods, bifurcation theory, dynamical systems theory, complex network theory, computational methods, and probabilistic and statistical methods.