Composite laminates constructed in an asymmetric layup orientation of [0 i , 90 i ], i > 0, exhibit two stable equilibrium positions and may be actuated to snap from a primary cure shape to an inversely related secondary stable shape. This study aims to aid in developing a comprehensive description of thick bistable laminates, whose increased thickness risks the loss of bistability, through previously established analytical approaches and verification via experimentation. The principle of minimum potential energy is applied to two materials and analyzed using the Rayleigh-Ritz minimization technique to determine the cure shapes of carbon fiber reinforced polymer laminates composed of AS4/8552 and TR50S-12k carbon fibers. These materials were modeled to act as square thick bistable laminated composites with sidelengths up to 0.914m. Visualizations of the out-of-plane displacements are shown with a description of the Rayleigh-Ritz analysis. Additionally, a finite element model (FEM) created in Abaqus CAE 6.14 and experiments using DA409/G35 and TR50S-12K/NP301 prepreg were used to further describe and develop the fundamental description for thick bistable laminates in terms of loss of bistability, actuation load, and principle shape. The analytical model is an extension of Hyer’s (2002) and Mattioni’s (2009) work applied to thick bistable laminates where the primary assumption was the x-axis curvature equaled the negative y-axis curvature for the primary and secondary stable positions, respectively. This assumption leads to the already cemented conclusion that bistable laminates, once cured, take on one of two inversely related paraboloid shapes. FEA simulations contradicted this by showing an average 11% difference in curvature magnitude for the aforementioned shapes. Furthermore, fourth order polynomials were used to describe the curvature along the axes, differing from the previously used Menger curvatures, (three-point approximation). Bifurcation plots using peak deflections and average curvature generated from FEA simulations clearly showed bistability existed to approximately 50 plies; however, the energy landscape plots indicated a significant degradation of bistability starting at 36 plies. Experimentation was performed on a test stand mimicking the same boundary conditions used in FEA while applying a central out-of-plane load. Experimental observations showed decreased peak displacements of stable cure shapes. Observations also indicated that the x-axis curvature had a significant difference in magnitude compared to the negative y-axis curvature. However, the existence of bistability agreed with FEA energy landscape plots, with clear “snaps” ending at thicknesses of 28–36 plies. Moreover, actuation force was found to correlate well with FEA simulations. Differences in the critical point can be attributed to the combination of material property differences for DA409 and TR50S-12K, failure to capture polymer relaxation, limitations of the experimental setup, and hand layup fabrication errors. Lastly, this paper adds viability of thicker laminates for use in macroscale applications where shape morphing or shape-retention attributes are a necessary constraint, although only where low loads are expected.

Recent research has revealed that Nickel Titanium (NiTi) shape memory alloys can produce residual stresses after undergoing constrained recovery and returning to their low temperature, martensitic state while still constrained. The nature and underlying mechanisms that cause this post constrained recovery residual stress (PCRRS) are not well understood. This paper presents experimental research and results seeking to further understand the PCRRS. Experiments were performed on multiple formulations of NiTi subjected to: 1) Cyclic loading and training before producing PCRRS, 2) Repeated thermomechanical loading with large strains followed by a thermal cycle to create and re-generated the PCRRS, and 3) Creation of the PCRRS followed by repeated cycles of small, 0.5% strains. Experiments found that the training in 1) did not significantly alter the ability to produce PCRRS or its magnitude. Straining samples from the PCRRS state could reduce the residual stress state to zero stress, but the PCRRS could be recreated by repeating thermal actuation with the only significant variation being a reduction in magnitude for the first to second cycle. Multiple small strain cycles applied from the PCRRS state caused an incremental reduction in residual stress. The full PCRRS could be re-created by repeating the initial thermomechanical cycle. The values of the residual stress varied across the first 3 sets of cycles, but from the third set onward the response stabilized. These results indicate that the primary mechanisms for generating a PCRRS are stable and recoverable with only minor and diminishing variations due to training or repeated regeneration of the PCRRS. Grain boundary stabilization and similar mechanisms may be responsible for the minor variation between the first few regenerations of the PCRRS. The incremental reduction in the residual stress after exposure to small 0.5% strains must be due to a recoverable process like partial and accumulating detwinning of the NiTi with each load cycle. Further work is underway to perform microstructural analysis of samples in the various states to further the theorized material states. The ability to generate and control PCRRS has the potential to find new application and advance capabilities in fields like self-healing and fatigue resistant materials by generating stresses without the continuous application of heat energy. New forms of actuation could also be developed based on the potential energy stored in a structure through PCRRS.

Glass Fiber Reinforced Polymer (GFRP) beams have shown over a 20% decrease in weight compared to more traditional materials without affecting system performance or fatigue life. These beams are being studied for use in automobile leaf-spring suspension systems to reduce the overall weight of the car therefore increasing fuel efficiency. These systems are subject to large amplitude mechanical vibrations at relatively constant frequencies, making them an ideal location for potential energy scavenging applications. This study analyses the effect on performance of GFRP beams by substituting various composite layers with piezoelectric fiber layers and the results on deflection and stiffness. Maximum deflection and stress in the beam is calculated for varying the piezoelectric fiber layer within the beam. Initial simulations of a simply supported multimorph beam were run in ABAQUS/CAE. The beam was designed with symmetric piezoelectric layers sandwiching a layer of S2-glass fiber reinforced polymer and modeled after traditional mono leaf-spring suspension designs with total dimensions 1480 × 72 × 37 mm 3 , with 27 mm camber. Both piezoelectric and GFRP layers had the same dimensions and initially were assumed to have non-directional bulk behavior. The loading of the beam was chosen to resemble loading of a leaf spring, corresponding to the stresses required to cycle the leaf at a stress ratio between R = 0.2 and 0.4, common values in heavy-duty suspension fatigue analysis. The maximum stresses accounted for are based on the monotonic load required to set the bottom leaf surface under tension. These results were then used in a fiber orientation optimization algorithm in Matlab. Analysis was conducted on a general stacking sequence [0°/45°] s , and stress distributions for cross ply [0°/90°] s , and angle ply [+45°/−45°] s were examined. Fiber orientation was optimized for both the glass fiber reinforced polymer layer to maximize stiffness, and the piezoelectric fiber layers to simultaneously minimize the effect on stiffness while minimizing deflection. Likewise, these fibers could be activated through the application of electric field to increase or decrease the stiffness of the beam. The optimal fiber orientation was then imported back into the ABAQUS/CAE model for a refined simulation taking into account the effects of fiber orientation on each layer.

In this study, a dual-beam piezoelectric energy harvester is proposed. This harvester consists of a main beam and an auxiliary beam with a pair of magnets attached to couple their motions. The potential energy of the system is modeled to understand the influence of the potential wells on the dynamics of the harvester. It is noted that the alignment of the magnets significantly influences the potential wells. A theoretical model of the harvester is developed based on the Euler-Bernoulli beam theory. Frequency sweeps are conducted experimentally and numerically to study the dynamics of the harvester. It is shown that the dual-beam harvester can exhibit hardening effect with different configurations of magnet alignments in frequency sweeps. The performance of the harvester can be improved with proper placement of the magnets.

Magneto-Active elastomers (MAEs) and magneto-rheological elastomers (MREs) are smart materials that consist of hard and soft magnetic particles, respectively, embedded in a flexible matrix. Their actuation capabilities are dependent on the arrangement of particles achieved during the fabrication process. Previous works have shown varying degrees of particle alignment and / or agglomeration as a function of fabrication process variable, most notably volume fraction of the particulates, their magnetic material type (hard vs soft), and the strength of the external field applied during curing. In this work, we simulated the dynamics of magnetic particles suspended in a fluid matrix to predict the evolution of microstructures resulting from these varying process conditions. The simulations accounted for the magnetic interaction of all particles using standard dipole-dipole interaction potentials along with dipole-field potentials developed from the Zeeman Energy. Additionally, the field local to each particle, on which magnetization depends, was determined by the sum of the external fields generated by each member of the ensemble and their demagnetizing fields. Fluid drag forces and short range particle-particle repulsion (non-overlapping) were also considered. These interactions determined the body forces and torques acting on each particle that drove the system of equations of motions for the ensemble of particles. The simulation was carried out over a nearest neighbor periodic unit cell using an adaptive time stepping numerical integration scheme until an equilibrium structure was reached. Structural parameters, related to the magnetic energy, spatial distribution, spatial alignment, and orientation alignments of the particle distributions were defined to characterize the simulated structures. The effect of volume fraction and intensity of the external magnetic field on the achieved particle distributions were studied. At low external field strengths, the particles formed long entangled chains that had very low alignment with the applied field. The remnant magnetic potential energy of these configurations was also significantly low. As the field is increased the length of the chains reduced and the alignment increased. The corresponding change in magnetic potential energy of the system with an increase in the applied field was found to follow a power law fit that spanned a wide range of magnetic field strengths. At low volume fractions the particles aligned rapidly with the field and formed short chains. As the volume fraction of the samples increased the chains grew longer and closer to each other, and magnetic potential of the structure became lower. Results of the simulations suggest that it is possible to tailor the microstructure and thus affect remanent magnetization and magnetization anisotropy, by judicious control of process parameters. This ability could have implications for newly emerging additive manufacturing techniques utilizing suspensions of magnetic particulates.

There is a growing interest to convert ambient mechanical energy to electrical energy by vibration energy harvesters. Realistic vibrations are random and spread over a large frequency range. Most energy harvesters are linear with narrow frequency bandwidth and show low performance, which led to creation of nonlinear harvesters that have larger bandwidth. This article presents a simulation study of a nonlinear energy harvester that contains two cantilever beams coupled by magnetic force. One of the cantilever beam is covered partially by piezoelectric material, while the other beam is normal to the first one and is used to create a variable potential energy function. The variable double-well potential function enables optimum conversion of the kinetic energy and thus larger output. The system is modeled by coupled Duffing oscillator equations. To represent the ambient vibrations, the response to Gaussian random input signal (generated by Shinozuka formula) is studied using power spectral density. The effects of different parameters on the system are also investigated. The results show that the double cantilever harvester has a threshold distance, where the harvester can perform optimally regardless of the excitation level. This observation is opposite to that of the conventional fixed magnet cantilever system where the optimal distance varies with the excitation level. Results of this study can be used to enhance energy efficiency of vibration energy harvesters.

Shape memory alloy (SMA) knitted actuators are a type of functional fabric that uses shape memory alloy wire as an active fiber within a knitted textile. Through intentional design of the SMA knitted actuator geometry, various two- and three-dimensional actuation motions, such as scrolling and contraction [1], can be accomplished. Contractile SMA knitted actuators leverage the unique thermo-mechanical properties of SMA wires by integrating them within the hierarchical knitted structure to achieve large distributed uniaxial contractions and variable stiffness behavior upon thermal actuation. During the knit manufacturing process, the SMA wire is bent into a network of interlacing adjacent loops, storing potential energy within the contractile SMA knitted actuator. Thermal actuation above the wire-specific austenite finish temperature leads to a partial recovery of the bending deformations, resulting in large distributed uniaxial contraction (15–40% actuation contraction observed) of the SMA knitted actuator. The achievable load capacity and %-actuation contraction are dependent on the geometric loop parameters of the contractile SMA knitted actuator. While exact descriptions of the geometric loop parameters exist, a reduction of the geometric complexity is advantageous for high-level contractile SMA knitted actuator design procedures. This paper defines a simple geometric measure, the non-dimensional knit density, and experimentally correlates the contractile SMA knitted actuator performance to this measure. The experimentally demonstrated dependency of relevant actuator metrics on the knit density and the wire diameter, suggests the usability of the simplified geometry definition for a high-level contractile SMA knitted actuator design.

Broadband piezoelectric energy harvesting solutions from ambient loading have been extensively studied with the purpose of increasing the efficiency of vibration-based harvesters. Most of the previously developed methods focus on the transducer’s properties and configurations, and require vibration input excitations. In contrast, we have previously experimentally shown a mechanical energy concentrator system that exploits the quasi-static input deformations (strains) generated within the structure and induces an amplified amplitude and frequency up-converted response. The tested energy converting devices transform low-amplitude and low-rate service strains into an amplified vibration input to the piezoelectric transducer. The snap-through behavior of bilaterally constrained columns was used as the mechanism for energy concentration. This paper presents a theoretical model, based on energy method, for the post-buckling behavior of a bilaterally constrained slender column under quasi-static axial loadings. The total potential energy of the buckled elastic element is the sum of the potential energies due to bending, compression and external applied force. The transverse deflection is limited by the lateral constraints. Therefore a constrained minimization problem of the total potential energy is solved to determine the equilibrium configurations. Equilibrium transitions are correlated to the changes in the magnitude of the weight coefficients that define the contribution of buckling modes to the deflected shape. Transition states are defined in terms of the axial displacements, axial forces, column shape, and energies stored in the system.

A novel class of two-stage electrical energy generators is presented for rotary machinery and rocking platforms in which the input speed is low and varies significantly, even reversing. Applications include wind mills, turbo-machinery for harvesting tidal flows, floating platforms and the like. Current technology using rotary generators requires gearing or similar mechanisms to increase the input speed to make the generation cycle efficient. Variable speed-control mechanisms are also usually needed to achieve high mechanical to electrical energy conversion efficiency. In this paper, electrical energy generators are presented that can efficiently operate at very low and highly variable and even intermittent and reversing speeds without requiring gearing or other speed control mechanisms. The generators are very simple in design and can significantly reduce complexity and cost, especially those pertaining to maintenance and servicing. In addition, these new generators can expand the application of energy harvesting to much slower input speeds than current technology allows. The primary novelty of this technology is the two-stage harvesting system. In these energy harvesting systems, input mechanical energy from the environment such as wind or ocean waves is stored in a primary sub-system (stage) as potential energy. When the level of potential energy reaches a certain predetermined level, it is released into a secondary sub-system (stage). The secondary sub-system converts the stored mechanical energy into electrical energy. The secondary sub-system is preferably designed as vibrating mass-spring type energy harvester to achieve relatively high and nearly constant natural frequency and use piezoelectric or magnet and coil type generators to convert stored mechanical energy of vibration to electrical energy.

For morphing wing skin applications, low in-plane stiffness is advantageous to reduce the cost of actuation and high out-of-plane stiffness is required to withstand the aerodynamic loads. A proposed solution is to engineer a composite material made of a honeycomb support combined with a multi-state infill that can reduce the Young’s modulus for a low in-plane stiffness. Assuming thin beam theory and using the potential energy formulation, equivalent in-plane Young’s moduli can be calculated for a range of honeycomb cell geometries. The out-of-plane deflection of a representative plate fixed on all edges is calculated using flat plate theory and used to assess the performance of the skin system. To optimize the cell geometry for a given application, the out-of-plane deflection is constrained and the honeycomb cell geometry varied to investigate the design space. Results show that a skin can be designed to have in-plane Young’s moduli similar to the polymer infill and still have a low out-of-plane deflection. However, these results come at the expense of increased skin weight. Further analysis to obtain a more realistic design is done by imposing weight and geometric constraints.

Morphing aircraft and other shape-changing structures are well suited to McKibben-like flexible composite actuators. These actuators, made from fiber-reinforced elastomeric composites, are extremely efficient in converting potential energy (pressurized air) into mechanical energy. Such actuators are promising for use in micro air vehicles, prosthetics and robotics because they offer excellent force-to-weight ratios and behave similar to biological muscle. Use of an incompressible pressurizing fluid instead of compressible air may also offer higher actuator stiffness, better control, and compatibility with existing actuation systems. Using incompressible fluids also allows the actuator to serve as a variable stiffness element which can be modulated by opening and closing valves that constrain or allow fluid flow. The effect of an incompressible fluid (water) on the performance of Rubber Muscle Actuators (RMA), with varying diameters, lengths and segment lengths, was experimentally investigated in the current work. Upon pressurization with air or water, past an activation threshold, overall force and stroke increased with increasing actuation length and diameter. Actuation force when pressurized with water is slightly greater than with air. Both air and water-pressurized actuation force and strain decrease significantly when segment length is less than a minimum critical length. Closed valve actuator stiffness (modulus) of actuators at full length, when pressurized with an incompressible fluid is up to 60× greater than the open valve stiffness of the same actuator. Air-filled RMAs with equal parameters only see a 10× increase. Incompressible fluid-filled RMAs have great potential to provide needed high actuation forces within adaptive material systems. Design guidelines are given to aid additional RMA use.