Continuum Mech. Thermodyn. https://doi.org/10.1007/s00161-020-00897-x ORIGINAL ARTICLE Alireza Beheshti · Ramin Sedaghati · Subhash Rakheja Finite deformation analysis of isotropic magnetoactive elastomers Received: 25 January 2020 / Accepted: 23 May 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020 Abstract In this study, the large deformation analysis of the magnetoactive elastomers based on continuum mechanics approach has been conducted. First, the governing differential equations for the spatial configuration are presented. Stored energy density function defined with respect to the invariants of the right or left Cauchy– Green deformation tensor and the magnetic field induction vector is adopted to develop a material model for finite deformation of isotropic magnetoactive elastomers (MAEs). An isotropic magnetoactive sample with 15% iron particle volume fraction is then fabricated, and a test setup has been designed to measure its magnetic permeability. Using an advanced magnetorheometer, quasi-static tests are then carried out on MAE circular cylindrical samples to find their torque-twist response under various magnetic fields. The experimental results are then effectively utilized to identify the unknown parameters in the proposed material model. The accuracy of the proposed constitutive model in predicting the response behavior of the MAE is then demonstrated through comparison of theoretical results with those obtained experimentally. Keywords Finite deformation · Magnetoactive elastomers · Torsion · Constitutive equation 1 Introduction Magnetoactive elastomers (MAEs) are smart materials which consist of elastomeric medium impregnated with micron-sized ferromagnetic particles. The dynamic characteristics and viscoelastic properties of MAEs can be instantly and reversibly varied under the applied magnetic field. Due to their unique adaptive properties, MAEs can be effectively utilized for design of smart systems and devices for control of noise and vibration under a wide range of frequencies and varying environmental conditions [1]. Furthermore, the coupled magneto-mechanical properties of MAEs render them suitable for design of smart sensors and actuators [2]. In MAEs, the size and distribution of the iron particles distributed in the matrix play a key role in their performance and typically the size of iron particles and the volume fraction ranges from 0.1 μm to 10 μm and 10% to 50%, respectively [3, 4]. Using finer particles (lower than 0.1 μm) with a low volume fraction generally leads to a poor MAE response. Soft particles made of materials such as iron, cobalt and its oxides Communicated by Andreas Öchsner. A. Beheshti · R. Sedaghati (B ) · S. Rakheja Department of Mechanical, Industrial and Aerospace Engineering, Concordia University, Montreal, QC H3G 1M8, Canada E-mail: ramin.sedaghati@concordia.ca A. Beheshti E-mail: a_behesh@encs.concordia.ca S. Rakheja E-mail: subhash.rakheja@concordia.ca