Computational Stability Analysis of Diffusion‐Deformation Processes at Finite Strains. Issue 1 (25th January 2021)

• Record Type: Journal Article
• Authors: Sriram, Siddharth; Polukhov, Elten; Keip, Marc-André
• Other Names: Kuhl D. guestEditor.; Meister A. guestEditor.; Ricoeur A. guestEditor.; Wünsch O. guestEditor.
• Is Part Of: Proceedings in applied mathematics and mechanics. Volume 20:Issue 1(2021)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2021-01-25
• Subjects: Applied mathematics -- Periodicals; Engineering mathematics -- Periodicals; Mathematical physics -- Periodicals; 519
• DOI: 10.1002/pamm.202000333
• Languages: English
• ISSNs: 1617-7061

Abstract

Abstract: In the present work, we investigate the onset of structural instabilities occuring in soft hydrophilic elastomers undergoing geometrically constrained swelling, which is characterized by large elastic deformations coupled with transient fluid diffusion. We model this phenomenon using a minimization‐based variational formulation having the deformation map and the fluid flux as the independent variables [1, 3]. The space‐time‐discrete form of the variational problem is implemented using a conforming Raviart–Thomas‐type finite element formulation, which yields a symmetric and positive definite global tangent matrix for a stable deformation state. The onset of instability is captured as the point where the tangent matrix loses its positive definiteness [4, 5]. To validate the proposed theoretical framework, we consider the surface wrinkling phenomenon observed in constrained hydrogel bilayers subjected to fluid diffusion. Variations in the critical buckling load and the corresponding mode number with respect to the geometry and material parameters of the bilayer are studied. These studies could, for instance, serve as potential design guidelines for applications of such materials in microsensors or in the fabrication of soft microgears for actuators, where the buckling modes are exploited to produce a desired mechanical output [8].