Modeling and finite element simulation of the chemo-magneto-mechanical behavior of magnetic polymer gels

多功能材料-由于其刺激响应特性-注定用于致动器和传感器应用，例如微流体或医学工程。这类材料的重要代表是聚合物，它们对外部施加的电场和磁场敏感，因此能够控制变形。在本提案中，将详细研究铁凝胶（即含有磁性颗粒的聚合物凝胶）在外部磁场下的行为。的（化学）磁机械行为的建模和仿真将通过使用有限元进行研究。由聚合物网络、液相和固定或移动的磁性颗粒组成的铁凝胶将基于不同相的多孔介质理论进行描述。通过耦合力学和磁场方程，实现了完整系统的制定。材料模型的参数将从项目合作伙伴的微观实验和理论/数值研究中获得。在该项目的框架内，将研究外部磁场对颗粒的影响以及颗粒与聚合物网络的相互作用以及由于施加磁场而产生的形状变化。对于各向同性和各向异性凝胶-具有固定和/或移动的磁性颗粒-将计算磁场中的行为，然后将其与SPP内实验伙伴的结果进行比较。为此，将分析铁凝胶的磁-机械滞回行为，然后将其整合到开发的模型中。在下文中，还将考虑移动的带电粒子。因此，聚合物凝胶在电场和磁场下的变形行为可以通过数值模拟来确定。通过与SPP内的实验伙伴合作，所导出的化学-电-磁-机械配方的质量将不断提高。因此，一个物理上一致的模型作为数值工具将是可用的，这使得建模和模拟的铁凝胶致动器配置，这是重要的应用在医学和微流体。

Multi-functional materials are - due to their stimuli-responsive properties - predestined for actuator and sensor applications e.g. in microfluidics or in medical engineering. Important representatives of this group of materials are polymers, which are sensitive towards externally applied electric and magnetic fields and thus enable a controlled deformation.In the present proposal, the behavior of ferrogels, i.e. polymer gels with magnetic particles, under an external magnetic field will be studied in detail. The modeling and simulation of the (chemo-)magneto-mechanical behavior will be investigated by using finite elements. The ferrogel consisting of a polymer network, a liquid phase, and fixed or mobile magnetic particles will be described on basis of a theory of porous media for the different phases. The formulation of the complete system is realized by coupling the mechanical and the magnetic field equations. The parameters for the material model will be obtained from experimental and theoretical/numerical investigations on the microscale from project partners. In the framework of the project, the influence of the external magnetic field on the particles and the interactions of the particles with the polymer network as well as the resulting shape change due to an applied magnetic field will be investigated. For isotropic and anisotropic gels – with fixed and/or mobile magnetic particles – the behavior in a magnetic field will be computed and then compared to results from experimental partners within the SPP. For this, the magneto-mechanical hysteretic behavior of ferrogels will be analyzed and then afterwards integrated in the developed model. In the following, also mobile charged particles will be considered. As a result, the deformation behavior of polymer gels under electric and magnetic fields can be determined by numerical simulations.By cooperating with the experimental partners within the SPP, the quality of the derived chemo-electro-magneto-mechanical formulation will be improved consistently. Thus, a thermodynamically consistent model as numerical tool will be made available, which enables the modeling and simulation of ferrogel actuator configurations which are important for applications in medicine and in microfluidics.