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Research Papers

J. Appl. Mech. 2018;86(3):031001-031001-12. doi:10.1115/1.4041964.

The nonlinear extremely large-amplitude oscillation of a cantilever subject to motion constraints is examined for the first time. In order to be able to model the large-amplitude oscillations accurately, the equation governing the cantilever centerline rotation is derived. This allows for analyzing motions of very large amplitude even when tip angle is larger than π/2. The Euler–Bernoulli beam theory is employed along with the centerline inextensibility assumption, which results in nonlinear inertial terms in the equation of motion. The motion constraint is modeled as a spring with a large stiffness coefficient. The presence of a gap between the motion constraint and the cantilever causes major difficulties in modeling and numerical simulations, and results in a nonsmooth resonance response. The final form of the equation of motion is discretized via the Galerkin technique, while keeping the trigonometric functions intact to ensure accurate results even at large-amplitude oscillations. Numerical simulations are conducted via a continuation technique, examining the effect of various system parameters. It is shown that the presence of the motion constraints widens the resonance frequency band effectively which is particularly important for energy harvesting applications.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2018;86(3):031002-031002-9. doi:10.1115/1.4042101.

We experimentally study the dynamic behavior of a belt-drive system to explore the effect of loading conditions, driving speed, and system inertia on both the frequency and amplitude of the observed frictional and rotational instabilities. A self-excited oscillation is reported whereby local detachment events in the belt–pulley interface serve as harmonic forcing of the pulley, leading to angular velocity oscillations that grow in time. Both the frictional instabilities and the pulley oscillations depend strongly on operating conditions and system inertia, and differ between the driver and driven pulleys. A larger net torque applied to the pulley generally intensifies Schallamach waves of detachment in the driver case but has little influence on other measured response quantities. Higher driving speeds accelerate the occurrence of frictional instabilities as well as pulley oscillations in both cases. Increasing the system's inertia does not affect the behavior of contact instabilities, but does lead to a steadier rotation of the pulley and more pronounced fluctuations in the belt tension. A simple dynamic model of the belt-drive system demonstrates good agreement with the experimental results and provides strong evidence that frictional instabilities are the primary source of the system's self-oscillation.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2018;86(3):031003-031003-12. doi:10.1115/1.4042134.

The deployment dynamics of a simplified solar sail quadrant consisting of two Euler–Bernoulli beams and a flexible membrane are studied. Upon prescribing the in-plane motion and modeling the tension field based on linearly increasing stresses assumed on the attached boundaries, the coupled equations of motion that describe the system's transverse deflections are obtained. Based on these equations and their boundary conditions (BCs), deployment stability is studied by deriving simplified analytic expressions for the rate of change of system energy. It is shown that uniform extension and retraction result in decreasing and increasing energy, respectively. The motion equations are discretized using expansions in terms of “time-varying quasi-modes” (snapshots of the modes of a cantilevered beam and a clamped membrane), and the integrals needed for the resulting system matrices are rendered time-invariant via a coordinate transformation. Numerical simulation results are provided to illustrate a sample deployment and validate the analytic energy rate expressions.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2018;86(3):031004-031004-12. doi:10.1115/1.4042136.

Compared to robots and devices made of rigid components, soft robots and flexible devices driven by soft active materials possess various advantages including high adaptability under extreme environment and compatibility with a human. Dielectric elastomer (DE) membrane, which is commonly used in building soft actuators, can achieve large actuation by the combined loadings of voltage-induced Maxwell stress and fluidic pressures (pneumatic and hydraulic pressure). This paper proposes a pneumatic–hydraulic coupled electromechanical actuator (PHCEA), which exhibits strong coupling effect of electromechanical actuation (the Maxwell stress on DE membrane), pneumatic and hydraulic pressures. Considering the moving boundary and state transition, a computational model has been developed to investigate the coupling behaviors of the PHCEA. The numerical result by this model is in accordance with the experimental measurements. The combination of experimental data and the theoretical result indicates that the state transition and moving boundary separate the potential region of electrical breakdown and mechanical damage. This model can be utilized as a practical method to characterize the performance and guide the design of soft devices. The experimental setup and computational method of the PHCEA bring new insights into the fabrication and characterization of soft robots, adaptive optics, and flexible bio-medical devices. The PHCEA possesses wide applications in underwater robots, soft muscles, and microfluidics systems. It can serve as the gas bladder of soft swimming robots, the soft actuator of hydraulic–pneumatic coupling systems, and the gas–liquid valve of flexible microfluidics systems.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2018;86(3):031005-031005-8. doi:10.1115/1.4042135.

This study reconstructs a two-dimensional stress field from measured strain data. The advantage of using stress functions is that the stress equilibrium and strain compatibility are automatically satisfied. We use the complex stress functions given by the finite series of polynomials. Then, we find the proper set of coefficients required to make the best fit to the measured strain data. Numerical examples represent the stress concentration problems around a hole(s) in a plate. It is demonstrated that the present method reconstructs the stress field around the hole(s), and the estimated stress agrees with the finite element (FE) analysis result.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2019;86(3):031006-031006-11. doi:10.1115/1.4042216.

Tensegrities have exhibited great importance and numerous applications in many mechanical, aerospace, and biological systems, for which symmetric configurations are preferred as the tensegrity prototypes. Besides the well-known prismatic tensegrities, another ingenious group of tensegrities with high symmetry is the truncated regular polyhedral (TRP) tensegrities, including Z-based and rhombic types. Although Z-based TRP tensegrities have been widely studied in the form-finding and application issues, rhombic TRP tensegrities have been much less reported due to the lack of explicit solutions that can produce their symmetric configurations. Our former work presented a unified solution for the rhombic TRP tensegrities by involving the force-density method which yet cannot control structural geometric sizes and may produce irregular shapes. Here, using the structural equilibrium matrix-based form-finding method, we establish some analytical equations, in terms of structural geometric parameters and force-densities in elements, to directly construct the self-equilibrated, symmetric configurations of rhombic TRP tensegrities, i.e., tetrahedral, cubic/octahedral, and dodecahedral/icosahedral configurations. Moreover, it is proved, both theoretically and numerically, that all of our obtained rhombic TRP tensegrities are super-stable and thus can be stable for any level of the force-densities without causing element material failure, which is beneficial to their actual construction. This study helps to readily design rhombic tensegrities with high symmetry and develop novel biomechanical models, mechanical metamaterials, and advanced mechanical devices.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2019;86(3):031007-031007-6. doi:10.1115/1.4042217.

The modeling of the different mechanical behaviors of brittle and quasi-brittle materials in tension and compression leads to partitioning of the strain (or stress) tensor into a positive part and a negative part. In this study, applying a recently proposed general method to the two-dimensional (2D) strain and stress tensors, closed-form coordinate-free expressions are obtained for their decompositions which are orthogonal in the sense of an inner product where the forth-order elastic stiffness or compliance acts as a metric. The orthogonal decompositions are given analytically and explicitly for all possible 2D elastic symmetries, i.e., isotropic, orthotropic, square, and totally anisotropic elastic materials. These results can be directly used, for example, in developing phase field methods for modeling and simulating the fracture of isotropic and anisotropic brittle and quasi-brittle materials.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2019;86(3):031008-031008-7. doi:10.1115/1.4042289.

In this investigation, we consider a crack close to and perpendicular to a bimaterial interface. If the crack tip is at the interface then, depending on material properties, the order of the stress singularity will be equal to, less than, or greater than one-half. However, if the crack tip is located any finite distance away from the interface the stress field is square-root singular. Thus, as the crack tip approaches the interface, the stress intensity factor approaches zero (for cases corresponding to a singularity of order less than one-half) or infinity (for a singularity of order greater than one-half). The implication of this behavior is that for a finite applied pressure the crack will either never reach the interface or will reach the interface with vanishing small applied pressure. In this investigation, a cohesive zone model is used in order to model the crack behavior. It is found that the aforementioned anomalous behavior for the crack without a cohesive zone disappears and that the critical value of the applied pressure for the crack to reach the interface is finite and depends on the maximum stress of the cohesive zone model, as well as on the work of adhesion and the Dundurs' parameters.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2019;86(3):031009-031009-11. doi:10.1115/1.4042320.

A new design has been proposed and numerically analyzed for the polydimethylsiloxane (PDMS) substrate of gallium arsenide (GaAs) photovoltaics. A stack structure is realized by inserting a cube between island and basement, and thus, a support structure of basement-cube-island is formed. Numerical analyses show that, as the deformation of GaAs layer and interfacial stresses are concerned, the height of the stack structure of only island and cube has direct effect on deformation isolation. Especially, the length of the inserted cube can dramatically increase this effect. Therefore, when a cube is inserted between island and basement, a thin photovoltaic film can be realized with reliable performance. As stretch is applied to the film, the thickness of encapsulation is still the dominant factor on deformation of GaAs layer and interfacial stresses, and the length of cube only has slight effect on the influence.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2019;86(3):031010-031010-9. doi:10.1115/1.4042321.

Predeformation simultaneously changes the effective material stiffness as well as the geometric configuration and therefore may be utilized to tune wave propagation in soft phononic crystals (PCs). Moreover, the band gaps of soft PCs, as compared with those of the hard ones, are more sensitive to the external mechanical stimuli. A one-dimensional tunable soft acoustic diode based on soft functionally graded (FG) PCs is proposed. The two-way asymmetric propagation behavior is studied at the resonant frequency within the band gap. Numerical results show that the operating frequency (i.e., the resonant peak) of the soft graded acoustic diode can be altered by adjusting the mechanical biasing fields (including the longitudinal prestress and the lateral equibiaxial tension). The adjustment becomes significant when the strain-stiffening effect of the Gent hyperelastic material is properly harnessed. Furthermore, the prestress or equibiaxial tension can affect the two-way filtering of the soft FG PC in a separate and different manner. In addition, it is much easier to realize the tunable acoustic diode by exploiting soft FG materials with stronger compressibility. It is shown that the introduction of acoustic impedance is beneficial for predicting the tunable effects. The simulations and conclusions should provide a solid guidance for the design of tunable two-way unidirectional acoustic diodes made from soft hyperelastic materials.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2019;86(3):031011-031011-6. doi:10.1115/1.4042290.

Inorganic stretchable electronics based on the island-bridge layout have attracted great attention in recent years due to their excellent electrical performance under the extreme condition of large deformations. During the mechanics design of interconnects in such devices, the major task is not only to maximize the elastic stretchability of device but also to smoothen the whole deformation process of interconnects. In this work, a novel design strategy is proposed for free-standing fractal serpentine interconnects to improve their elastic performance comprehensively without reducing the areal coverage of functional/active components of device. By modifying the classical design slightly, the new strategy can achieve a larger elastic stretchability, a smaller maximum out-of-plane displacement, and most strikingly, a smoother post-buckling deformation. This study will provide helpful guidance to the mechanics design of stretchable electronics with free-standing interconnects.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2019;86(3):031012-031012-6. doi:10.1115/1.4042138.

The load–displacement curves of an aluminum alloy and tantalum were determined using a hat-type specimen in the compression test. Based on the results of finite element analysis, the employed geometry of the hat-type specimen was found to yield a load–displacement curve that is nearly independent of the friction between the specimen and the platen. The flow stress–strain curves of the alloy and tantalum were modeled using the Ludwik and Voce constitutive laws, respectively; furthermore, simulation of the compression event of the hat-type specimen was performed by assuming appropriate constitutive parameters. The constitutive parameters were varied via an optimization function built in matlab until the simulated load–displacement curves reasonably fit the experimental curve. The optimized constitutive parameters obtained in this way were then used to construct friction-free flow stress–strain curves of the two materials.

Commentary by Dr. Valentin Fuster

Technical Brief

J. Appl. Mech. 2019;86(3):034501-034501-5. doi:10.1115/1.4042288.

The existing regular hexagonal cellular substrate for stretchable electronics minimizes the disruptions to the natural diffusive or convective flow of bio-fluids. Its anisotropy is insignificant, which is not ideal for mounting on skins that involve directional stretching. This paper proposes an irregular hexagonal cellular substrate with large anisotropy to minimize the constraints on the natural motion of the skin, and establishes an analytic model to study its stress–strain relation under finite stretching.

Commentary by Dr. Valentin Fuster

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