MRE Film/Substrate Instabilities
From an unconventional point of view, a remarkable property of magnetorheological elastomers (MREs) is that while they can become unstable by combined magneto-mechanical loading, their response is well controlled in the post-instability regime. This, in turn, allows us to try to operate these materials in this critically stable region. These instabilities can lead to extreme responses such as wrinkles (for haptic applications), actively controlled stiffness (for cell-growth) and acoustic properties with only marginal changes in the externally applied magnetic fields. Unlike the current modeling of hierarchical composites, MREs require the development of advanced coupled nonlinear magneto-mechanical models in order to tailor the desired macroscopic instability response at finite strains. Due to their coupled magnetoelastic response, MREs are finding an increasing number of engineering applications. One such application is in haptics, where the goal is to actively control surface roughness and curvature. One way to achieve this is by exploiting the unstable regime of MRE substrate/layer assemblies subjected to transverse magnetic fields.
Man-made meta- materials and structures have received much attention over the past decades thanks to their aptitude for tailoring selected properties. Superior acoustic, photonic and mechanical properties can be deliberately achieved at the macroscale by ratioaally designing the structure’s unit-cell geometry and level of hierarchy. Hierarchical nanocomposites mimicking biological materials such as nacre, teeth and bone as well as cellular materials with periodic architecture are both examples of metamaterial systems. In this subject, we combine numerical simulations with compressive testing of 3D printed polymer structures to investigate the buckling response of a slender column, whose architecture employs unit-cell lattices which in turn consist of a sequence of columns uniformly spaced. This way we create a hierarchical structure that can contrallbly become unstable at different scales. The lower-scale columns are both of comparable size with the macro-geometry and a priori susceptible to buckling. Within the accuracy of data, the experimental trends are consistent with the numerical simulations and show that both the buckling and the post-buckling response at the macroscopic (i.e. continuum) level are dependent on the lower-scale microstructure.
3D Printed Materials
The proposed subject aims at developing a dialogue between a real microscopic image of a composite material (such as an MRE) obtained by optical and electron microscopy as well as 3D tomographic techniques and mathematically constructed virtual microstructures. These virtual microstructures can be analyzed via numerical tools such as finite elements and/or fast-Fourrier Transforms (FFT) methods at different scales. Subsequently these virtual microstructures can be directly printed in a 3D printer. The printed material can then be tested experimentally in order to probe the response of the original material and validate the several methods used to reach this point.
This subject provides a rigorous analysis of the effective response, i.e., average magnetization and magnetostriction, of magnetoelastic composites that are subjected to overall magnetic and mechanical loads. It attempts to clarify the differences between a coupled magnetomechanical analysis in which one applies a Eulerian (current) magnetic field and an electroactive one where the Lagrangian (reference) electric field is usually applied. For this, an augmented vector potential variational formulation is developed to carry out numerical periodic homogenization studies of magnetoelastic solids at finite strains and magnetic fields. We show that the developed variational principle can be used for bottom-up design of microstructures with desired magnetomechanical coupling by properly cancelling out the macro-geometry and specimen shape effects. As an example, we show above random isotropic microstructures based on random adsorption algorithms as well as novel three-phase auxetic microstructures. The first takes advantage of particle shape and geometrical chirality to produce negative and positive swelling, while the second uses a periodic distribution of voids and particle chains in a polymer matrix.
Of interest here is the fully three-dimensional analysis of the Freedericksz transition for the twisted nematic device (TND), which is widely used in liquid-crystal display monitors. Using a coupled electromechanical variational formulation, the problem is treated as a bifurcation instability triggered by an externally applied electric field. More specifically, we study a finite thickness liquid-crystal layer, anchored between two infinite parallel plates relatively rotated with respect to each other by a given twist angle and subjected to a uniform electric field perpendicular to these bounding plates. The novelty of the proposed analysis lies in the fully three-dimensional formulation of the TND problem that considers all possible bounded perturbations about the principal solution. By scanning a wide range of the liquid crystal’s material parameter space, we establish whether the Freedericksz transition is global, i.e., has an eigenmode depending solely on the layer thickness coordinate, or local (also termed the periodic Freedericksz transition), i.e., has an eigenmode with finite wavelengths in one or both directions parallel to the plate. It is found that global modes are typical for low values, while local modes appear at large values of the twist angle. Moreover, for certain TND’s, the increase in twist angle can lower the critical electric field, findings that could be useful in guiding liquid-crystal selection for applications.