Multiscale modeling of magnetosensitive materials using experimental microstructural data

本项目的总体目标是磁活性材料的建模和仿真，以研究它们的结构-性质关系。本文特别关注了磁流变弹性体（MREs）在多尺度上的建模。从聚合物基体和磁性颗粒的本构性质出发，考虑磁性颗粒的微观结构排列，预测了材料的有效宏观行为。对于微观和宏观尺度，都使用了基于连续体的建模方法。这种多尺度策略允许与优先项目的其他小组合作，并有助于深入了解杂化磁性材料的结构-性质关系。最终，获得的见解将有助于提高这些材料在执行器和传感器领域的适用性。对于磁-力均质问题的数值求解，本项目发展了基于有限元法的仿真技术。这允许在微观尺度上任意形状和可磁化粒子的分布。此外，还可以考虑单个成分的复杂非线性行为。在模拟中，明确地解析了局部磁场和力学场，因此在建模方法中考虑了颗粒的一般不均匀磁化和聚合物基体的非仿射变形。MREs的相关宏观行为遵循一个能量一致的尺度转变过程。在前两个资助期，主要的重点是研究由磁性软颗粒和纯弹性矩阵组成的磁流变体。因此，这种材料的有效行为没有任何迟滞，即完全可逆。第三个资助期的主要目标是研究具有磁滞效应和机械滞回效应的磁滞回效应，这种磁滞回效应是由颗粒的磁硬行为和基体的粘弹性特性引起的。为此，计划与优先计划的实验工作组合作，详细表征颗粒和聚合物基质的磁性和机械行为。基于构件的本构特性和微观结构的详细信息，对MREs的有效性能进行了预测。利用预测的有效曲线，确定了描述磁力耦合性能的宏观本构模型参数。最后，可以模拟实际样品和部件的宏观行为，并将结果与实验数据进行比较。

The overarching goal of the present project is the modeling and simulation of magnetoactive materials, to investigate their structure-property relationships. Special attention is paid to the modeling of magnetorheological elastomers (MREs) on multiple scales. Starting from the constitutive properties of the polymer matrix as well as the magnetic particles and accounting for the microstructural arrangement of the latter, the effective macroscopic material behavior is predicted. For both, the micro- as well as the macroscale, a continuum-based modeling approach is used. This multiscale strategy allows for a cooperation with other groups of the priority program and helps to provide an in-depth understanding of the structure-property relationships of hybrid magnetic materials. Eventually, the gained insights will help to improve the applicability of these materials in the fields of actuators and sensors.For the numerical solution of magneto-mechanical homogenization problems, simulation techniques based on the finite element method (FEM) are developed within this project. This allows for arbitrary shapes and distributions of the magnetizable particles on the microscale. Furthermore, it is possible to consider a complex nonlinear behavior of the individual constituents. Within the simulation, the local magnetic and mechanical fields are resolved explicitly, so that the generally inhomogeneous magnetization of the particles and the non-affine deformation of the polymer matrix is taken into account in the modelling approach. The related macroscopic behavior of the MREs follows from an energetically consistent scale transition process. In the first two funding periods, the principal focus was on the investigation of MREs consisting of magnetically soft particles and a purely elastic matrix. Hence, the effective behavior of such materials was free of any hystereses, i. e. completely reversible. The main objective of the third funding period is the investigation of MRE with magnetic and mechanical hysteresis effects which results from the magnetically hard behavior of the particles and the viscoelastic properties of the matrix. To this end, a detailed characterization of the magnetic and mechanical behavior of the particles and the polymer matrix is planned in cooperation with experimental working groups of the priority program. Based on the constitutive properties of the components and detailed information of the microstructure, the effective behavior of the MREs is predicted. The parameters of a macroscopic constitutive model, which describes the coupled magneto-mechanical properties of MRE, are identified by means of the predicted effective curves. Finally, it is possible to simulate the macroscopic behavior of realistic samples and components and to compare the results with experimental data.