Multiphysics modeling and simulation of fluid‐saturated porous ferrogels at finite strains

Over the last years there has been a growing interest in the study of the behavior of field‐responsive or so called smart materials. Porous ferrogels are a class of these materials consisting of a porous polymeric matrix with dispersed micro‐ or nano‐sized ferromagnetic particles [1–3]. Due to their ability to exhibit large deformations and alter their effective material characteristics upon external magnetic stimulation, these materials are interesting for a wide range of applications in biomedical engineering, microfluidics and other innovative fields of research. The magneto‐poro‐mechanical response of porous ferrogels is a complex phenomenon that spans over multiple length‐scales and essentially depends on (i) the constitutive behavior of the individual components, (ii) their morphology and microstructural arrangement and (iii) the macroscopic shape of the specimen. In this contribution a theoretical and computational framework for the modeling of isotropic porous ferrogels at the macroscale is presented. Within this modeling approach the porous ferrogel is treated as a homogeneous continuum, whereat its complex microstructure is not resolved explicitly. A prototypical isotropic constitutive model is formulated in a conventional enthalpy‐based setting. Numerical examples show the the crucial impact of the macroscopic specimen shape on the macroscopic deformation response in an uniform external magnetic field.