Homogenization-Based Constitutive Models for Magnetorheological Elastomers at Finite Strain

卡斯塔涅达桥0708271 磁流变弹性体（MRE）是一种多相、多功能的材料体系，它是由磁性“硬”或“软”颗粒嵌入弹性体基体相而形成的。 由于颗粒之间的磁相互作用，这些材料是磁致伸缩的，并且它们的机械响应可以实时地平滑和可逆地修改。 相反，这些材料中应变的存在可以通过整体磁化强度的感应变化来检测。虽然“宏观”（连续介质力学）的方法MRE已经存在，自20世纪50年代以来，更“微观”的理论与真正的预测能力是最近，到目前为止，已被限制在线性（无限小应变）政权。 研究者开发了非线性均匀化技术，并将其应用于有限应变状态下有效的磁流变弹性体的本构模型。 这是建立在早期的工作由调查员增强弹性体和使用扩展的变“线性比较”均匀化技术thathave以前已经开发。 在理论水平上，这些模型解释了：（i）组分的强非线性响应，包括颗粒的非线性铁电行为，以及弹性体基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）耦合磁弹性本构行为，以及（iv）有限变形。 在应用层面，该方法用于优化选择组成属性（例如，磁硬颗粒对软颗粒，磁各向同性颗粒对各向异性颗粒）和微观结构变量（例如，颗粒形状和浓度、取向的对齐分布与随机取向等）to enhance增强the magnetostrictive磁致伸缩and sensing传感capabilities能力of these materials材料. 磁流变弹性体（MRE）是一种具有“机敏”或“智能”特性的复合材料。 由于这些特殊的性能，磁流变弹性体在许多工业应用中，包括汽车、电子和机器人行业，都有很大的应用前景。 此外，它们重量轻，价格便宜，易于加工成各种形状。 然而，为了实现其全部潜力，更好的数学理解是必要的复杂-高度耦合和非线性-宏观行为，特别是在大变形制度。 为了帮助在这个过程中，研究人员开发了一种基于均匀化的方法来准确地模拟MRE的宏观行为，将依赖于粒子的磁性，它们的初始分布和取向（微观结构），以及大变形下这种微观结构的演变。 最后，由于它们的致动特性，MRE提供了人类肌肉的人工模拟物，该项目对其他类型的智能材料具有影响，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.