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Porous ferrogels are a new class of magnetoactive composite materials that consist of a polymeric hydrogel matrix with embedded magnetizable particles. The mutual particle interaction within the soft elastic matrix enables ferrogels to deform and alter their material characteristics upon magnetic stimulation. Due to these unique properties, ferrogels have attracted significant attention for potential uses in a variety of engineering applications, especially in biomedical engineering and microfluidics. Therefore, it is crucial to develop precise mathematical models capturing the complex material behavior of ferrogels, which spans over multiple length scales. The aim of this work is to present suitable modeling approaches for porous ferrogels. Following the hierarchical structure of scales, we present modeling frameworks for two different scenarios: (i) the modeling of ferrogels at the macroscale level and (ii) the modeling of ferrogels at the microscale level. Regarding the constitutive modeling of ferrogels, we limit our attention to locally nondissipative isotropic material response. For both modeling approaches, we provide comprehensive variational principles and briefly discuss relevant ingredients of a stable finite element implementation. In each section, numerical simulations are outlined in order to demonstrate the capabilities and relevant features of each modeling approach. Main emphasis of the numerical studies lies on the investigation of the macroscopic shape effect as well as on the characterization of the magnetomechanical material response of ferrogels with random monodisperse microstructures.

Multiphysics modeling of porous ferrogels at finite strains