Variational Formulation and Numerical Implementation of Diffusion in Hydrogels at Finite Strains

• Published in: Proceedings in applied mathematics and mechanics Vol. 15; no. 1; pp. 411 - 412
• Main Authors: Nateghi, Aref, Mauthe, Steffen, Miehe, Christian
• Format: Journal Article
• Language: English
• Published: Berlin WILEY-VCH Verlag 01.10.2015; WILEY‐VCH Verlag
• ISSN: 1617-7061; 1617-7061
• DOI: 10.1002/pamm.201510196

Hydrogels are polymeric materials with a cross‐linked network which can absorb water. Due to their bio‐compatibility, hydrogels have many applications in biology and medicine. Recently modeling the mechanical behavior of hydrogels has attracted a great deal of attention among researchers, see e.g., [1] and [2]. Following our previous works [3], [4] and [5] we now present a variational framework for swelling phenomenon in hydrogels. The variational formulation of the problem can be done using a saddle‐point principle or a minimization principle. Saddle‐point principle has to fulfill the Ladyzhenskaya‐Babuška‐Brezzi (LBB) condition in order to lead to a stable finite element scheme. The key aspect of our proposed minimization principle is its advantage with regard to an unconstrained fem implementation. In this work we aim to compare the numerical performance of these two variational formulations for swelling of hydrogels. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)