Session: 12-29-02: Mechanics of Soft Materials

Paper Number: 149630

149630 - Magnetorhelogical Elastomers as Soft Programmable Materials: Some Theoretical Considerations 

Most current magnetorheological elastomers (MREs) are broadly categorized into hard(h-MREs) and soft(s-MREs) [1] depending on the magnetic properties of the underlying particles. The former consist of particles exhibiting strong magnetic dissipation (e.g., NdFeB), while the later are purely energetic (e.g., carbonyl iron). In this work, we present a unified modeling framework for h-MREs [2] including the response of the s–MREs  as a limiting case when the dissipation is set to zero. In addition, the proposed framework is dual in the sense of a partial Legendre-Fenchel transform of the magnetic part, i.e., we propose exactly equivalent models in the F−H and F−B variable spaces. Specifically, the models are capable of modeling the magnetic and the induced mechanical dissipation in the h-MREs, resulting from the ferromagnetic hysteresis of the underlying particles. In the limit of vanishingly small magnetic coercivity, both models yield a purely energetic response relevant for the s−MREs. The proposed dual models mostly involve the matrix and the particle material parameters except the particle volume fraction of the composite and a coupling coefficient, which is obtained via calibration with available full-field numerical homogenization estimates. Efficient finite element, numerical solutions for various boundary value problems (BVPs) involving h- and s-MREs are obtained via incremental variational principles. The calculations for the end-tip deflection of a uniformly pre-magnetized cantilever exhibit excellent agreement with the experimental data. The investigations on the remanent fields and the magnetic actuation performance of hybrid h-/s-MRE rank-1 laminated cantilevers and non-uniformly pre-magnetized, functionally graded beams are also carried out. The analysis shows that the profiling of the h-MRE beams plays a crucial role in their deflection patterns and magnitudes depending on the actuation field direction. Moreover, the analysis reveals that concentrating the hard-magnetic particles near the beam flanks reduces the actuation field considerably without altering substantially the deflection patterns. The above analysis shows that both isotropic s- and h-MREs exhibit a stretch independent response which is a fundamanetal characteristic of such materials. This is in contrast with existing empirical theories for h-MREs that consider that magnetization evolves with the deformation gradient. A critical discussion of this feature will also be made in this presentation in an effort to clarify in which situation such empirical models hold. Direct connection between the different models will be established and the importance of modeling the surrounding air will be highlighted in certain cases of interest. The conclusions will be suppoorted by available experimental results in the literature. 

Presenting Author: Kostas Danas CNRS, Ecole Polytechnique

Presenting Author Biography: Kostas Danas holds a tenured position as a CNRS Director of Research and Professor at the Solid Mechanics Laboratory (LMS), Department of Mechanics at Ecole Polytechnique. He is currently (2023-2024) a visiting professor at the ELyTMaX laboratry of CNRS and Tohoku university in Sendai, Japan. He was born and raised in Kozani, Greece and studied at the Department of Mechanical Engineering at the University of Thessaly, Volos, Greece where he received his Dipl. Ing. in Mechanical Engineering (2003) with highest honors (rank 1st). He received his M.Sc (2004) from the University of Pennsylvania and his Ph.D. (2008) from the Ecole Polytechique, France and the University of Pennsylvania, PA, USA. After the end of his graduate studies, he moved to the University of Cambridge, U.K. as a postdoctoral Research Associate. In 2009, he moved back to LMS, Ecole Polytechnique as a tenured CNRS research scientist (equivalent to assistant/associate professor). He was promoted to Director of Research in 2022 (equivalent to Professor). He has obtained his HDR (Habilitation à diriger des recherches, 2016) from University of Pierre and Marie Curie, Paris. His main research interests are in the field of solid mechanics and composite materials. He is currently working on the experimental, numerical and theoretical analysis of microstructured active elastomers and their instabilities as well as on the modelling and fracture of metallic and 3D printed polymeric porous materials. He has been awarded an ERC starting grant (2014) and ERC Proof-of-Concept (2022) to carry out research on the low energy control of instabilities in magnetorheological elastomers (MREs). He is the recipient of the Bronze Medal from the CNRS in 2017 and the Jean Mandel Prize (2019) awarded bi-annually for excellence in research in mechanics to young scientists (below 40) working in France .

Authors:

Kostas Danas CNRS, Ecole Polytechnique