Variational Settings and Domain Decomposition Based Solution Schemes for a Coupled Deformation‐Diffusion Problem

• Published in: Proceedings in applied mathematics and mechanics 2021-12, Vol.21 (1), p.n/a
• Main Authors: Kiefer, Björn, Prüger, Stefan, Rheinbach, Oliver, Röver, Friederike, Roth, Stephan
• Format: Article
• Language: English
• ISSN: 1617-7061; 1617-7061
• DOI: 10.1002/pamm.202100163

Our general goal is to study chemo‐mechanical problems at various length scales by means of a fully‐integrated approach in terms of a co‐design of variational formulations and tailored parallel solvers. Based on prior experience in electro‐magneto‐mechanics [1], we know that the advantages and disadvantages of different variational settings for such coupled problems is always multifaceted. Theoretical characteristics, physical interpretability and numerical aspects may even play competing roles in this regard. In this work, we particularly consider the swelling of hydrogels as a first model problem featuring finite deformation coupled to the diffusive solute transport. The 3D finite‐element simulation of a free‐swelling cube under solute flux control is studied as a representative numerical example. As a first step towards seamless integration, we discuss the implementation of the hyperelastic subproblem into the open source finite element library deal.II which directly interfaces with the Fast and Robust Overlapping Schwarz (FROSch) preconditioner. Using this environment, an additional numerical study is performed with respect to the scaling behavior of the finite deformation Neo‐Hookean model in parallel computations.