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Research Papers

J. Appl. Mech. 2017;84(12):121001-121001-6. doi:10.1115/1.4037885.

Interfaces such as grain boundaries are ubiquitous in crystalline materials and have provided a fertile area of research over decades. Their importance stems from the numerous critical phenomena associated with them, such as grain boundary sliding, migration, and interaction with other defects, that govern the mechanical properties of materials. Although these crystalline interfaces exhibit small out-of-plane fluctuations, statistical thermodynamics of membranes has been effectively used to extract relevant physical quantities such as the interface free energy, grain boundary stiffness, and interfacial mobility. In this perspective, we advance the viewpoint that thermal fluctuations of crystalline interfaces can serve as a computational microscope for gaining insights into the thermodynamic and kinetic properties of grain boundaries and present a rich source of future study.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2017;84(12):121002-121002-8. doi:10.1115/1.4037968.

For the title problem, the punch is assumed to be pressed vertically into the horizontal upper surface of the half space, then slide horizontally sideways. A range of such configurations is identified that permit Shtaerman’s solution for the contact pressure for a rigid frictionless punch to be modified so that it applies to a deformable punch and also yields the contact stresses when the punch slides in the presence of friction. Closed-form expressions are obtained for the peak edge-of-contact stresses. These edge-of-contact stresses can fluctuate significantly with even modest amounts of sliding.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2017;84(12):121003-121003-12. doi:10.1115/1.4037933.

The analytical model of a mechanism for regulating the thermally induced axial force and displacement in a fixed–fixed microbeam is presented in this article. The mechanism which consists of a set of parallel chevron beams replaces one of the fixed ends of the microbeam. The thermomechanical behavior of the system is modeled using Castigliano’s theorem. The effective coefficient of thermal expansion is used in the analytical model. The analytical model takes into account both the axial and bending deformations of the chevron beams. The model provides a closed-form equation to determine the thermally induced axial force and displacement in the microbeam. In addition, the model is used to derive the equations for the sensitivities of the microbeam’s axial force and displacement to the variations of the design parameters involved. Moreover, the model produces the stiffness of the chevron beams. The effect of the stiffness of the chevron beams on the dynamic behavior of the microbeam is discussed. The analytical model is verified by finite element modeling using a commercially available software package. Using the analytical model, two special cases are highlighted: a system with thermally insensitive axial force and a system with thermally insensitive axial displacement. The main application of the model presented in this article is in the design of sensors and resonators that require robustness against changes of temperature in the environment. The analytical model and the sensitivity equations can be easily integrated into optimization algorithms.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2017;84(12):121004-121004-11. doi:10.1115/1.4038064.

Piezoresponse force microscopy (PFM) extends the conventional nano-indentation technique and has become one of the most widely used methods to determine the properties of small scale piezoelectric materials. Its accuracy depends largely on whether a reliable analytical model for the corresponding properties is available. Based on the coupled theory and the image charge model, a rigorous analysis of the film thickness effects on the electromechanical behaviors of PFM for piezoelectric films is presented. When the film is very thick, analytical solutions for the surface displacement, electric potential, image charge, image charge distance, and effective piezoelectric coefficient are obtained. For the infinitely thin (IT) film case, the corresponding closed-form solutions are derived. When the film is of finite thickness, a single parameter semi-empirical formula agreeing well with the numerical results is proposed for the effective piezoelectric coefficient. It is found that if the film thickness effect is not taken into account, PFM can significantly underestimate the effective piezoelectric coefficient compared to the half space result. The effects of the ambient dielectric property on PFM responses are also explored. Humidity reduces the surface displacement, broadens the radial distribution peak, and greatly enlarges the image charge, resulting in reduced effective piezoelectric coefficient. The proposed semi-empirical formula is also suitable to describe the thickness effects on the effective piezoelectric coefficient of thin films in humid environment. The obtained results can be used to quantitatively interpret the PFM signals and enable the determination of intrinsic piezoelectric coefficient through PFM measurement for thin films.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2017;84(12):121005-121005-9. doi:10.1115/1.4038063.

We study the buckling of hemispherical elastic shells subjected to the combined effect of pressure loading and a probing force. We perform an experimental investigation using thin shells of nearly uniform thickness that are fabricated with a well-controlled geometric imperfection. By systematically varying the indentation displacement and the geometry of the probe, we study the effect that the probe-induced deflections have on the buckling strength of our spherical shells. The experimental results are then compared to finite element simulations, as well as to recent theoretical predictions from the literature. Inspired by a nondestructive technique that was recently proposed to evaluate the stability of elastic shells, we characterize the nonlinear load-deflection mechanical response of the probe for different values of the pressure loading. We demonstrate that this nondestructive method is a successful local way to assess the stability of spherical shells.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2017;84(12):121006-121006-10. doi:10.1115/1.4038141.

Benefits of a functionally graded core increasing wrinkling stability of sandwich panels have been demonstrated in a recent paper (Birman, V., and Vo, N., 2017, “Wrinkling in Sandwich Structures With a Functionally Graded Core,” ASME J. Appl. Mech., 84(2), p. 021002), where a several-fold increase in the wrinkling stress was achieved, without a significant weight penalty, using a stiffer core adjacent to the facings. In this paper, wrinkling is analyzed in case where the facings are subject to biaxial compression and/or in-plane shear loading, and the core is arbitrary graded through the thickness. Two issues addressed are the effect of biaxial or in-plane shear loads on wrinkling stability of panels with both graded and ungraded core, and the verification that functional grading of the core remains an effective tool increasing wrinkling stability under such two-dimensional (2D) loads. As follows from the study, biaxial compression and in-plane shear cause a reduction in the wrinkling stress compared to the case of a uniaxial compression in all grading scenarios. Accordingly, even sandwich panels whose mode of failure under uniaxial compression was global buckling, the loss of strength in the facings or core crimpling may become vulnerable to wrinkling under 2D in-plane loading. It is demonstrated that a functionally graded core with the material distributed to increase the local stiffness in the interface region with the facings is effective in preventing wrinkling under arbitrary in-plane loads compared to the equal weight homogeneous core.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2017;84(12):121007-121007-7. doi:10.1115/1.4038146.

Flexural propagation behavior of a metamaterial beam with circular membrane-mass structures is presented. Each cell is comprised of a base structure containing circular cavities filled by an elastic membrane with a centrally loaded mass. Numerical results show that there exist two kinds of bandgaps in such a system. One is called Bragg bandgap caused by structural periodicity; the other is called locally resonant (LR) bandgap caused by the resonant behavior of substructures. By altering the properties of the membrane-mass structure, the location of the resonant-type bandgap can be easily tuned. An analytical model is proposed to predict the lowest bandgap location. A good agreement is seen between the theoretical results and finite element (FE) results. Frequencies with negative mass density lie in the resonant-type bandgap.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2017;84(12):121008-121008-11. doi:10.1115/1.4038186.

The analytic response for the Cauchy extra stress in large amplitude oscillatory shear (LAOS) is computed from a constitutive model for isotropic incompressible materials, including viscoelastic contributions, and relaxation time. Three cases of frame invariant derivatives are considered: lower, upper, and Jaumann. In the first two cases, the shear stress at steady-state includes the first and third harmonics, and the difference of normal stresses includes the zeroth, second, and fourth harmonics. In the Jaumann case, the stress components are obtained in integral form and are approximated with a Fourier series. The behavior of the coefficients is studied parametrically, as a function of relaxation time and constitutive parameters. Further, the shear stress and the difference of normal stresses are studied as functions of shear strain and shear rate, and are visualized by means of the elastic and viscous Lissajous–Bowditch (LB) plots. Sample results in the Pipkin plane are reported, and the influence of the constitutive parameters in each case is discussed.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2017;84(12):121009-121009-7. doi:10.1115/1.4037881.

Double and triple network (TN) elastomers can be made by infusing monomers into a single network (SN) polymer, causing it to swell, and then polymerizing and cross-linking the monomers. The result is a double network (DN) elastomer in which one network is stretched and the other is in hydrostatic compression. TN systems are made by repeating the process starting with the DN material. The multinetwork (MN) elastomers exhibit a Mullins effect in which softening occurs upon a first cycle of loading, with the elastomer stiffness recovered above the previous maximum strain. The Mullins effect is attributed to rupture of the stretched network, eliminating the constraint on the compressed network, thereby motivating straining at the lower stiffness of the remaining material. A model for this process is developed, based on the previous work of Horgan et al. (2004, “A Theory of Stress Softening of Elastomers Based on Finite Chain Extensibility,” Proc. R. Soc. A, 460(2046), pp. 1737–1754). In the proposed model, a composite stiffness for the MN system is developed and a damage process introduced to degrade the contribution of the stretched network. The damage model is designed to account for the progressive elimination of chains that are most highly loaded in the stretched network, so that the undamaged stiffness is restored when the strain rises above levels previously experienced. The proposed model reproduces the behavior of the Mullins effect in the MN system.

Topics: Elastomers , Stress , Chain , Damage
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2017;84(12):121010-121010-10. doi:10.1115/1.4038173.

Stretchable electronics based on inorganic materials are an innovative technology with potential applications for many emerging electronic devices, due to their combination of stretchable mechanics and high electronic performance. The compliant elastomeric substrate, on which the brittle electronic components are mounted, plays a key role in achieving stretchability. However, conventional elastomeric substrates can undergo excessive mechanical deformation, which can lead to active component failure. Here, we introduce a simple and novel strategy to produce failure-resistant stretchable electronic platforms by bonding a thin film of stiff material, patterned into a serpentine network layout, to the elastomeric substrate. No prestraining of the substrate is required, and these systems offer sharp bilinear mechanical behavior and high ratio of tangent-to-elastic moduli. We perform comprehensive theoretical, numerical, and experimental studies on the nonbuckling-based prestrain-free design, and we analyze the key parameters impacting the mechanical behavior of a strain-limiting substrate. As a device-level demonstration, we experimentally fabricate and characterize skin-mountable stretchable copper (Cu) electrodes for electrophysiological monitoring. This study paves the way to high performance stretchable electronics with failure-resistant designs.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2017;84(12):121011-121011-7. doi:10.1115/1.4038174.

It is an interesting open question how to achieve large actuation of a dielectric elastomer (DE). In many previous works, in order to harness snap-through instability to achieve large deformation, a reservoir was employed to assist the dielectric elastomer actuator (DEA) to optimize its loading condition/path, which makes the whole actuation system bulky and heavy. In this paper, we explore large actuation of a DE balloon with applications to a soft flight system. The balloon consists of two separate DEAs: The inner one is stiffer while the outer one is softer. The whole actuation system has a small volume and a low weight, but can achieve large actuation by harnessing dielectric breakdown of the inner elastomer. The volume induced by dielectric breakdown is more than 20 times the voltage-induced volume change of DEAs. The experiments demonstrate a soft flight system, which can move effectively in air by taking advantage of large actuation of this DE balloon. This project also shows that failure of materials can be harnessed to achieve useful functionalities.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2017;84(12):121012-121012-12. doi:10.1115/1.4038195.

The use of large-deflection springs, tabs, and other compliant systems to provide integral attachment, joining, and retention is well established and may be found throughout nature and the designed world. Such systems present a challenge for mechanical analysis due to the interaction of contact mechanics with large-deflection analysis. Interlocking structures experience a variable reaction force that depends on the cantilever angle at the contact point. This paper develops the mathematical analysis of interlocking cantilevers and provides verification with finite element analysis and physical measurements. Motivated by new opportunities for nanoscale compliant systems based on ultrathin films and two-dimensional (2D) materials, we created a nondimensional analysis of retention tab systems. This analysis uses iterative and elliptic integral solutions to the moment–curvature elastica of a suspended cantilever and can be scaled to large-deflection cantilevers of any size for which continuum mechanics applies. We find that when a compliant structure is bent backward during loading, overlap increases with load, until a force maximum is reached. In a force-limited scenario, surpassing this maximum would result in snap-through motion. By using angled cantilever restraint systems, the magnitude of insertion force relative to retention force can vary by 50× or more. The mathematical theory developed in this paper provides a basis for fast analysis and design of compliant retention systems, and expands the application of elliptic integrals for nonlinear problems.

Commentary by Dr. Valentin Fuster

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