Rivka Gilat

The Lyapunov exponents as a quantitative criterion for the dynamic buckling of composite plates

The dynamic stability of infinitely wide composite plates subjected to suddenly applied thermal or mechanical loading is investigated. The stability analysis is performed by evaluating the largest Lyapunov exponent, the sign of which characterizes the nature of the response. It is shown that this approach forms an efficient tool which provides a quantitative and unequivocal answer to the question of dynamic buckling of composite plates subjected to various types of loading.

Thermal buckling of activated shape memory reinforced laminated plates

The analysis of thermal buckling of rectangular active laminated composite plates is presented. The plates consist of layers of a unidirectional composite with shape memory alloy fibers embedded in polymeric or metallic matrices. The fibers are activated by a mechanical loading–unloading cycle which is applied to the laminated plate, prior to the application of the thermal loading. Micromechanically established constitutive equations for the unidirectional composite in conjunction with the laminated plate analysis enable the accurate modeling of the layered structure behavior through the activation and the thermally induced loss of stability. The conditions for the occurrence of the latter are discussed.

Experimental dynamic trapping of electrostatically actuated bistable micro-beams

We demonstrate dynamic snap-through from a primary to a secondary statically inaccessible stable configuration in single crystal silicon, curved, doubly clamped micromechanical beam structures. Nanoscale motion of the fabricated bistable micromechanical devices was transduced using a high speed camera. Our experimental and theoretical results collectively show, that the transition between the two stable states was solely achieved by a tailored time dependent electrostatic actuation. Fast imaging of micromechanical motion allowed for direct visualization of dynamic trapping at the statically inaccessible state. These results further suggest that our direct dynamic actuation transcends prevalent limitations in controlling geometrically non-linear microstructures, and may have applications extending to multi-stable, topologically optimized micromechanical logic and non-volatile memory architectures.

Symmetry Breaking Criteria in Electrostatically Loaded Bistable Curved/Prebuckled Micro Beams

The symmetric and asymmetric buckling of micro beams subjected to distributed electrostatic force is studied. The analysis is carried out for two separate cases: a case of a stress-free beam, which is initially curved by fabrication and a case of a pre-stressed beam buckled due to an axial force. The analysis is based on a reduced order (RO) model resulting from the Galerkin decomposition with vibrational or buckling modes of a straight beam used as the base functions. The criteria of symmetric, limit point, buckling and of non-symmetric bifurcation are derived in terms of the geometric parameters of the beams. While the necessary symmetry breaking criterion establishes the conditions for the appearance of bifurcation points on the unstable branch of the symmetric limit point buckling curve, the sufficient criterion assures a realistic asymmetric buckling bifurcating from the stable branches of the symmetric equilibrium path. It is shown that while the symmetry breaking conditions are affected by the nonlinearity of the electrostatic force, its influence is less pronounced than in the case of the symmetric snap-through. A comparison between the results provided by the reduced order model, and those obtained by other numerical analyses confirms the accuracy of the symmetry breaking criteria and their applicability for the analysis and design of micro beams.

Investigation of shape memory alloy honeycombs by means of a micromechanical analysis

Shape memory alloy (SMA) honeycombs are promising new smart materials which may be used for light-weight structures, biomedical implants, actuators and active structures. In this study, the behavior of several SMA honeycomb structures is investigated by means of a continuum-based thermomechanically coupled micromechanical analysis. To this end, macroscopic inelastic stress?strain responses of several topologies are investigated, both for pseudoelasticity and for shape memory effect. It was found that the triangular topology exhibits the best performance. In addition, the initial transformation surfaces are presented for all possible combinations of applied in-plane stresses. A special two-phase microstructure that is capable of producing an overall negative coefficient of thermal expansion is suggested and studied. In this configuration, in which one of the phases is a SMA, residual strains are being generated upon recovery. Here, the negative coefficient of thermal expansion appears to be associated with a larger amount of residual strain upon recovery. Furthermore, a two-dimensional SMA re-entrant topology that generates a negative in-plane Poissons ratio is analyzed, and the effect of the full thermomechanical coupling is examined. Finally, the response of a particular three-dimensional microstructure is studied.

Thermomechanically micromechanical modeling of prestressed concrete reinforced with shape memory alloy fibers

Concrete is a very popular material in civil engineering, although it exhibits some limitations. The most crucial limitation is its low tensile strength, compared to its compressive strength, which results from the propagation of micro-cracks. This may be prevented by using prestrained shape memory alloy wires that are embedded in the concrete matrix. Upon activation, these wires regain their original shape, and consequently initial compressive stresses are transmitted to the concrete matrix. In this study, a thermomechanically micromechanical model of prestressed concrete reinforced by shape memory alloy fibers is presented and examined for different reinforcement aspects. It was found that there is a strong relation between the activation temperature deviation and the behavior of the prestressed concrete. The relation between the fibers volume fraction and the composite response and the effect of the shape of the reinforcing fibers and residual strain orientations is examined in detail.

Dynamic trapping experiment in an elctrostaticlly actuated initially curved beam

We report on a first experimental demonstration of dynamic trapping of electrostatically actuated double clamped curved micro beam. The beam is configured in an isolated singular post-buckled configuration, showing enhanced gap usage which cannot be reached by either static or by a suddenly applied single step load. The trapping is achieved using a dynamic snap-through induced by a tailored two step time dependent electrostatic loading.

Dynamic Trapping in Bi-Stable Electrostatically Actuated Curved Micro Beams

Micro and nano devices incorporating bi-stable structural elements such as micro beams are designed to exploit the fact that the latter possess two stable configurations at the same actuation force. Generally, the transition of a micro beam from one table state to another, namely the snap-through which is essentially dynamic phenomenon, can be initiated by either static or dynamic activations. In this work, results of theoretical and numerical investigations of the transient dynamics of a pre-stressed initially curved double clamped micro beams actuated by a time dependent electrostatic load are presented. We show by means of a reduced order model of a shallow beam, derived using the Galerkin procedure, that the beam may exhibit various types of responses. For certain beam characteristics, the second stable state is inaccessible under a static loading but is attainable only by means of a specially tailored dynamic actuation. This gives way to the possibility of trapping the dynamically bi-stable beam at a stable configuration which is close to the electrode by applying special loading sequences.Copyright

Limit Points Behavior in Electrostatically Actuated Initially Curved Micro Plate

The axisymmetric snap-through of an initially curved circular micro plate, subjected to a transversal distributed electrostatic force is studied. The analysis is based on a reduced order (RO) model resulting from the Galerkin decomposition, with buckling modes of a flat plate used as the base functions. In order to check the validity of the RO model, the corresponding problem for a displacement-independent (“mechanical”) load is solved, and a comparison between the RO model and those obtained using finite elements (FE) analysis is carried out. It is shown, that the two are in good agreement, indicating that the RO model can be used for a plate undergoing electrostatic loading. However, the study shows that at least three degrees of freedom (DOF) are required for an accurate prediction of the equilibrium path and bistability. The coupled electromechanical analysis shows that due to the nonlinearity of the electrostatic load, the snap-through occurs at a lower displacement than in the case of the “mechanical” load. Moreover, the study concludes that actuation of plates of realistic dimensions can be achieved by reasonably low voltages.Copyright

Latching Criteria in Bistable Prestressed Curved Micro Beams

Curved beams subjected to transverse force may exhibit a latching phenomena, namely remain in their buckled configuration under zero force such that an opposite force is required for their release. In this study, we investigate the latching in bistable electrostatically actuated prestressed curved beams. The analysis is based on a reduced order (RO) model resulting from the Galerkin decomposition with buckling modes of a straight beam as base functions. Criteria for the existence of latching are derived in terms of the beam geometric parameters and the axial load. Two conditions are formulated: A necessary criterion establishes the appearance of latching on the symmetric response curve and a sufficient condition which assures the existence of latching in the presence of bifurcations. A comparison between the model results and those obtained by numerical analysis shows good agreement up to a certain elevation. It is noted that as the latching is not affected by the nonlinear electrostatic load, the obtained criteria stand for all types of loading.Copyright