Homogenization-Based Constitutive Models for Magnetorheological Elastomers at Finite Strain

University Of Pennsylvania, Philadelphia PA

Investigators

Abstract

Ponte Castaneda 0708271 Magnetorheological elastomers (MREs) are multi-phase, multi-functional material systems consisting of magnetically "hard" or "soft" particles embedded in an elastomeric matrix phase. Because of the magnetic interactions between the particles, these materials are magnetostrictive and their mechanical response can be modified smoothly and reversibly in real time. Conversely, the presence of strain in these materials can be detected by induced changes in the overall magnetization. Although "macroscopic" (continuum mechanics) approaches for MREs have been in existence since the 1950s, more "microscopic" theories with truly predictive capabilities are much more recent and so far have been restricted to the linear (infinitesimal strain) regime. The investigator develops nonlinear homogenization techniques and applies them to generate constitutive models for magnetorheological elastomers that are valid in the finite-strain regime. This builds on earlier work by the investigator for reinforced elastomers and uses extensions of variational "linear comparison" homogenization techniques that have been developed previously. At the theoretical level, the models account for: (i) the strongly nonlinear response of the constituents, including nonlinear ferrolectric behavior for the particles, as well as nonlinear mechanical response for the elastomeric matrix, (ii) microstructural information, such as particle shape and orientation, as well as their spatial and orientational distribution, (iii) coupled magnetoelastic constitutive behavior, and (iv) finite deformations. At the applications level, the methodology is used to optimally select the constituent properties (e.g., magnetically hard vs. soft particles, magnetically isotropic vs. anisotropic particles) and the microstructural variables (e.g., particle shape and concentration, aligned distribution of orientations vs. random orientations, etc.) to enhance the magnetostrictive and sensing capabilities of these materials. Magnetorheological elastomers (MREs) are composite materials with "smart" or "intelligent" properties. As a consequence of these special properties, MREs hold great promise for use as sensors and actuators in many industrial applications, including the automotive, electronics, and robotic industries. In addition, they are lightweight, inexpensive and easily processed into a myriad of shapes. However, in order to achieve their full potential, a better mathematical understanding is necessary of their complex -- highly coupled and nonlinear -- macroscopic behavior, especially in the large-deformation regime. To aid in this process, the investigator develops a homogenization-based approach to accurately model the macroscopic behavior of MREs, incorporating the dependence on the magnetic properties of the particles, their initial distribution and orientation (microstructure), as well as the evolution of this microstructure under large deformation. Finally, because of their actuation properties MREs provide an artificial analogue of human muscle, and the project has implications for other types of smart materials, including electroactive polymers (EAPs), which could find applications in biotechnology and other areas of Federal strategic interest.