PhD Oral Exam - Amin Saber, Mechanical Engineering

When studying for a doctoral degree (PhD), candidates submit a thesis that provides a critical review of the current state of knowledge of the thesis subject as well as the student’s own contributions to the subject. The distinguishing criterion of doctoral graduate research is a significant and original contribution to knowledge.

Once accepted, the candidate presents the thesis orally. This oral exam is open to the public.

Abstract

Magnetorheological elastomers (MREs) are smart composite materials whose mechanical response can be actively tuned by an external magnetic field. Owing to their field-dependent stiffness, damping capacity, and actuation potential, they have attracted considerable interest for adaptive vibration control, soft robotics, tunable devices, and biomedical systems. Their practical implementation, however, requires constitutive models capable of predicting material behavior under realistic coupled mechanical, magnetic, and thermal loading conditions. Despite recent progress in MRE modeling, key limitations remain in the available literature, particularly regarding the treatment of temperature effects within finite-strain thermo-magneto-mechanical coupling, particle-chain anisotropy, and dynamic viscoelastic behavior within a unified thermodynamically consistent framework. To address these limitations, this thesis develops a set of experimentally validated, physics-based nonlinear continuum-mechanics models for predicting the coupled thermo-magneto-mechanical response of soft isotropic and transversely isotropic MREs under realistic operating conditions. A nonlinear continuum-mechanics formulation is first developed for isotropic MREs subjected to coupled thermo-magneto-hyperelastic loading. The deformation gradient, magnetic induction, and temperature are introduced as independent state variables in the proposed total Helmholtz free-energy function. To relate the total energy function to temperature, the constant heat-capacity assumption is employed. Furthermore, in order to account for the mechanical and magnetic energy contributions, a modified second-order Yeoh hyperelastic energy function is adopted, in which the stiffness-like parameter is defined through a multiplicative decomposition sub-model. Accordingly, the initial structural stiffness of the MRE is expressed in terms of the applied magnetic induction, temperature, and axial compressive stretch. This formulation enables the model to account for the effects of a uniform temperature distribution within the MRE medium, the applied magnetic field, and axial pre-compression. In addition to the uniform temperature effect, the heat-conduction problem associated with the proposed formulation is analytically solved under more realistic thermal boundary conditions. As a result, the model is also capable of accounting for non-uniform temperature distributions within the MRE sample. The modeling framework is then extended to transversely isotropic MREs by incorporating a preferred particle-chain direction within the material. To investigate the time-dependent viscoelastic response of MREs, the proposed framework is further extended by introducing internal time-dependent variables into the formulation. For this purpose, a three-branch Maxwell viscoelastic representation is combined with a Scott–Blair fractional viscous element to capture a broad relaxation spectrum using a limited number of material parameters. Moreover, the shear-strain softening behavior of filled rubber, known as the Payne effect, is incorporated into the constitutive framework. This enables the model to predict stiffness degradation at higher imposed shear strains, followed by full recovery after removal of the load or partial recovery along the unloading path under oscillatory loading. In addition to the analytical model, a comprehensive set of experimental tests was conducted to characterize the quasi-static and viscoelastic responses of both isotropic and transversely isotropic MREs. The resulting experimental data were used for both model verification and parameter calibration. For this purpose, cylindrical MRE specimens were fabricated using an Ecoflex-0010 elastomeric matrix with different volume fractions of carbonyl iron particles (CIPs). Using an advanced TA Discovery rheometer, frequency-sweep and strain-amplitude-sweep tests were performed under different levels of magnetic induction, temperature, and axial pre-stretch. The model predictions were then compared with the corresponding experimental data. For all considered quasi-static and viscoelastic coupled loading conditions, the predicted results indicated a coefficient of determination of (R^2 > 0.90) and a normalized RMSE below 8.15%, demonstrating the robustness and accuracy of the proposed modeling framework.