Jörg Brummund

Modeling and simulation of the bending behavior of electrically-stimulated cantilevered hydrogels

A systematic development of a chemo–electro–mechanical continuum model—for the application of electrically-stimulated cantilevered hydrogels—and its numerical implementation are presented in this work. The governing equations are derived within the framework of the continuum mechanics of mixtures. The finite element method is then utilized for the numerical treatment of the model. For the numerical simulation a cantilevered strip of an anionic hydrogel immersed in a NaCl solution bath is considered. An electric field is applied to electrically stimulate the aforementioned hydrogel. The application of the electric field alters the initial concentrations of the ionic species due to the chemo–electrical coupling. The gradual increase in the applied electric field leads to the bending movement of the hydrogel. Concluding, the presented multi-field continuum model is capable of simulating hydrogel bending actuators and also more complex systems e.g. gel finger grippers.

Modeling and Simulation of Hydrogels for the Application as Bending Actuators

Polyelectrolyte gels show a quite large swelling or bending behavior under external physical, chemical, thermal or electrical stimulation. In this paper the bending actuation of polyelectrolyte gels under applied electric fields is studied and the mechanisms occurring in polyelectrolyte gels due to the applied stimulus are investigated.In the present research, a complete formulation for describing actuation of polyelectrolyte gels in a solution bath is presented. First, the kinematics, the balance laws of continuum chemo-electro-mechanics and the constitutive equations of the involved fields are given.Then, in the numerical simulation part, the changes of the mobile concentrations, of the electric potential and the displacements in the gel domain are shown. It is demonstrated by a comparison between a chemo-electrical and a chemo-electro-mechanical test case, that the full coupling also leads to a change of the concentration of bound groups resulting in alterations of the local concentrations of the mobile ions, of the electric potential and again of the local gel displacement. It will be shown, that the presented coupled multi-field model is predestined for investigating electrical stimulation of hydrogels, and for simulating hydrogel bending actuation.

Computation of Effective Stiffness Properties for Textile-Reinforced Composites Using X-FEM

The macroscopic material behaviour of novel textile-reinforced composites is defined by its constituents (micro-level) and the design of the textile reinforcement (meso-level). Consequently, a multi-scale approach to the prediction of the material behaviour is necessary because only in this vein the adaptability of the textile reinforcement can be used to develop materials whose features can be adjusted precisely to certain applications.

Development of a continuum model for ferrogels

A systematic development of a continuum model is presented, which is capable of describing the magneto-mechanical behavior of magnetic polymer gels commonly referred to as “ferrogels”. In the present research, ferrogels are treated as multicomponent, multiphase materials. They consist of a polymer network (P), fixed magnetic particles (f), mobile magnetic particles (m), and liquid (L). By considering ferrogels as multicomponent materials, interaction among constituents of ferrogels can be captured. This helps in understanding the process occurring inside ferrogels under the influence of external stimuli, such as magnetic fields. In our modeling approach, the field equations of ferrogels are derived within the framework of the theory of mixtures. The basic equations include Maxwell’s equations, balance of mass, linear momentum, angular momentum, energy, and entropy. In the framework of the theory of mixtures, balance relations are first presented at the constituent level also referred to as partial balance relations. By summing partial balance relations over all constituents and imposing the restrictions of theory of mixtures, balance relations of mixture (for the ferrogel) are obtained. In the current work the specific magnetization (magnetization per density) is considered as an evolving variable. It is demonstrated that balance of angular momentum is satisfied using the evolution equation of specific magnetization and constitutive laws. In the process of modeling, a suitable free energy function is introduced and thermodynamically consistent constitutive laws are formulated. Introducing certain assumptions, a reduced model of the ferrogel, a coupled magneto-mechanical formulation, is subsequently presented. The reduced model consists only of a polymer network (P) and fixed magnetic particles (f). It is concluded that the reduced model compares well to the existing ones in the literature. The magneto-mechanical problem based on the reduced model is solved in 2D using the finite element method. The only unknowns for the finite element method implementation are mechanical displacement and magnetic potential. Deformation of a ferrogel in a magnetic field is subsequently investigated. Elongation and contraction of a ferrogel are observed when a magnetic field is applied in the x- and y-directions, respectively. The numerical results were compared with existing experimental work in the literature. A good qualitative agreement was found between numerical and experimental results.