Homogenization-Based Constitutive Models for Magnetorheological Elastomers at Finite Strain

Ponte Castaneda0708271磁流变弹性体(MRE)是由磁性“硬”或“软”粒子嵌入弹性体基质相组成的多相多功能材料体系。由于颗粒之间的磁相互作用，这些材料是磁致伸缩的，它们的机械响应可以实时地进行平滑和可逆的修改。相反，这些材料中应变的存在可以通过总磁化强度的感应变化来检测。虽然磁共振成像的“宏观”(连续介质力学)方法自20世纪50年代就已经存在，但更多具有真正预测能力的“微观”理论要晚得多，到目前为止还局限于线性(无限小应变)区域。研究人员开发了非线性均匀化技术，并将其应用于在有限应变区有效的磁流变弹性体的本构模型。这是建立在加强型弹性体研究人员早期工作的基础上，并使用了先前开发的变分“线性比较”均化技术的扩展。在理论水平上，该模型考虑了：(I)各组分的强非线性响应，包括颗粒的非线性铁电行为，以及弹性体的非线性力学响应；(Ii)微观结构信息，如颗粒的形状和取向，以及它们的空间和取向分布；(Iii)耦合的磁弹性本构行为；以及(Iv)有限变形。在应用程序级别，该方法用于优化选择组成属性(例如，磁性硬颗粒与软颗粒、磁性各向同性颗粒与各向异性颗粒)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(MRE)是一种具有“智能”或“智能”特性的复合材料。由于这些特殊的特性，磁流变液在包括汽车、电子和机器人行业在内的许多工业应用中都有很大的应用前景。此外，它们重量轻，价格便宜，很容易加工成各种各样的形状。然而，为了充分发挥它们的潜力，需要对它们复杂的、高度耦合和非线性的宏观行为有更好的数学理解，特别是在大变形区域。为了帮助这一过程，研究人员开发了一种基于均匀化的方法来精确地模拟磁流变液的宏观行为，包括对粒子的磁性、它们的初始分布和取向(微观结构)的依赖，以及这种微结构在大变形下的演变。最后，由于它们的驱动特性，MRE提供了一种人工模拟人类肌肉的方法，该项目对其他类型的智能材料也有影响，包括电活性聚合物(EAP)，它可以在生物技术和其他联邦战略利益领域找到应用。

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.