Homogenization-Based Constitutive Models for Magnetorheological Elastomers at Finite Strain

磁流变弹性体（MREs）是一种多相、多功能的材料体系，由嵌入弹性基体相中的磁性“硬”或“软”颗粒组成。由于粒子之间的磁相互作用，这些材料具有磁致伸缩性，并且它们的机械响应可以被平滑地、可逆地实时修改。相反，这些材料中应变的存在可以通过诱导总体磁化强度的变化来检测。尽管“宏观”（连续介质力学）方法自20世纪50年代以来就已经存在，但具有真正预测能力的更多“微观”理论是最近才出现的，到目前为止还局限于线性（无穷小应变）体系。研究者开发了非线性均匀化技术，并将其应用于生成磁流变弹性体的本构模型，该模型在有限应变下有效。这建立在研究者早期对增强弹性体的工作基础上，并使用了先前开发的变分“线性比较”均质技术的扩展。在理论层面上，这些模型解释了：(i)成分的强烈非线性响应，包括颗粒的非线性铁电行为，以及弹性体矩阵的非线性力学响应，（ii）微观结构信息，如颗粒形状和方向，以及它们的空间和方向分布，（iii）耦合磁弹性本构行为，（iv）有限变形。在应用层面，该方法用于优化选择组成特性（例如，磁硬与软颗粒，磁各向同性与各向异性颗粒）和微观结构变量（例如，颗粒形状和浓度，取向与随机取向的排列分布等），以增强这些材料的磁致伸缩和传感能力。磁流变弹性体（MREs）是具有“智能”或“智能”性能的复合材料。由于这些特殊性能，MREs在许多工业应用（包括汽车、电子和机器人工业）中使用传感器和执行器具有很大的前景。此外，它们重量轻、价格便宜，而且很容易加工成各种形状。然而，为了充分发挥它们的潜力，对它们复杂的——高度耦合和非线性的——宏观行为，特别是在大变形状态下，有必要有更好的数学理解。为了在这一过程中提供帮助，研究人员开发了一种基于均质化的方法来准确地模拟MREs的宏观行为，包括对颗粒磁性的依赖，它们的初始分布和取向（微观结构），以及这种微观结构在大变形下的演变。最后，由于它们的驱动特性，MREs提供了人类肌肉的人工模拟，该项目对其他类型的智能材料有影响，包括电活性聚合物（EAPs），它可以在生物技术和联邦战略兴趣的其他领域找到应用。

Ponte Castaneda0708271 Magnetorheological elastomers (MREs) are multi-phase,multi-functional material systems consisting of magnetically"hard" or "soft" particles embedded in an elastomeric matrixphase. Because of the magnetic interactions between theparticles, these materials are magnetostrictive and theirmechanical response can be modified smoothly and reversibly inreal time. Conversely, the presence of strain in these materialscan be detected by induced changes in the overall magnetization. Although "macroscopic" (continuum mechanics) approaches for MREshave been in existence since the 1950s, more "microscopic"theories with truly predictive capabilities are much more recentand so far have been restricted to the linear (infinitesimalstrain) regime. The investigator develops nonlinearhomogenization techniques and applies them to generateconstitutive models for magnetorheological elastomers that arevalid in the finite-strain regime. This builds on earlier work bythe investigator for reinforced elastomers and uses extensions ofvariational "linear comparison" homogenization techniques thathave been developed previously. At the theoretical level, themodels account for: (i) the strongly nonlinear response of theconstituents, including nonlinear ferrolectric behavior for theparticles, as well as nonlinear mechanical response for theelastomeric matrix, (ii) microstructural information, such asparticle shape and orientation, as well as their spatial andorientational distribution, (iii) coupled magnetoelasticconstitutive behavior, and (iv) finite deformations. At theapplications level, the methodology is used to optimally selectthe constituent properties (e.g., magnetically hard vs. softparticles, magnetically isotropic vs. anisotropic particles) andthe microstructural variables (e.g., particle shape andconcentration, aligned distribution of orientations vs. randomorientations, etc.) to enhance the magnetostrictive and sensingcapabilities of these materials. Magnetorheological elastomers (MREs) are composite materialswith "smart" or "intelligent" properties. As a consequence ofthese special properties, MREs hold great promise for use assensors and actuators in many industrial applications, includingthe automotive, electronics, and robotic industries. In addition,they are lightweight, inexpensive and easily processed into amyriad of shapes. However, in order to achieve their fullpotential, a better mathematical understanding is necessary oftheir complex -- highly coupled and nonlinear -- macroscopicbehavior, especially in the large-deformation regime. To aid inthis process, the investigator develops a homogenization-basedapproach to accurately model the macroscopic behavior of MREs,incorporating the dependence on the magnetic properties of theparticles, their initial distribution and orientation(microstructure), as well as the evolution of this microstructureunder large deformation. Finally, because of their actuationproperties MREs provide an artificial analogue of human muscle,and the project has implications for other types of smartmaterials, including electroactive polymers (EAPs), which couldfind applications in biotechnology and other areas of Federalstrategic interest.