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Research Papers

J. Appl. Mech. 2017;84(10):101001-101001-14. doi:10.1115/1.4037409.

The stationary response of multidegree-of-freedom (MDOF) strongly nonlinear system to fractional Gaussian noise (FGN) with Hurst index 1/2 < H < 1 is studied. First, the system is modeled as FGN-excited and -dissipated Hamiltonian system. Based on the integrability and resonance of the associated Hamiltonian system, the system is divided into five classes: partially integrable and resonant, partially integrable and nonresonant, completely integrable and resonant, completely integrable and nonresonant, and nonintegrable. Then, the averaged fractional stochastic differential equations (SDEs) for five classes of quasi-Hamiltonian systems with lower dimension and involving only slowly varying processes are derived. Finally, the approximate stationary probability densities and other statistics of two example systems are obtained by numerical simulation of the averaged fractional SDEs to illustrate the application and compared with those from original systems to show the advantages of the proposed procedure.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2017;84(10):101002-101002-5. doi:10.1115/1.4037410.

A plastic liquid such as toothpaste and butter deforms like an elastic solid under a small stress and like a plastic solid under a large stress. Recently, plastic liquids have been used as compliant electrodes for elastomeric transducers. Here, we study the deformation of a plastic liquid adherent on an elastomer when the elastomer is stretched monotonically. We observe that deformation in the plastic liquid localized into shear bands and necks. We further observe that the plastic liquid slips near the interface between the plastic liquid and the elastomer. Each pulling edge of the plastic liquid develops a shear tail, a thin layer of the plastic liquid adherent to the elastomer. As the elastomer is stretched, the tail conforms to the deformation of the elastomer, and the plastic liquid above the tail slips. Finite element simulations confirm that localization occurs even for a relatively simple elastic–plastic model, but require a boundary condition that allows the near-interface slip.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2017;84(10):101003-101003-13. doi:10.1115/1.4037551.

Explicit, closed-form, exact analytical expressions are derived for the covariance kernels of a multi degrees-of-freedom (MDOF) system with arbitrary amounts of viscous damping (not necessarily proportional-type), that is equipped with one or more auxiliary mass damper-inerters placed at arbitrary location(s) within the system. The “inerter” is a device that imparts additional inertia to the vibration damper, hence magnifying its effectiveness without a significant damper mass addition. The MDOF system is subjected to nonstationary stochastic excitation consisting of modulated white noise. Results of the analysis are used to determine the dependence of the time-varying mean-square response of the primary MDOF system on the key system parameters such as primary system damping, auxiliary damper mass ratio, location of the damper-inerter, inerter mass ratio, inerter node choices, tuning of the coupling between the damper-inerter and the primary system, and the excitation envelope function. Results of the analysis are used to determine the dependence of the peak transient mean-square response of the system on the damper/inerter tuning parameters, and the shape of the deterministic intensity function. It is shown that, under favorable dynamic environments, a properly designed auxiliary damper, encompassing an inerter with a sizable mass ratio, can significantly attenuate the response of the primary system to broad band excitations; however, the dimensionless “rise-time” of the nonstationary excitation substantially reduces the effectiveness of such a class of devices (even when optimally tuned) in attenuating the peak dynamic response of the primary system.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2017;84(10):101004-101004-5. doi:10.1115/1.4037412.

An applications methodology is synthesized from the research-based development of failure theory for orthotropic fiber composite laminates. In effect, this work continues and completes the work of Christensen (2017, “Lamination Theory for the Strength of Fiber Composite Materials,” ASME J. Appl. Mech., 84(7), p. 071007). This failure theory applies for the condition of fiber-dominated behavior, appropriate to carbon fiber—polymeric matrix composites and such similar systems. A lamination theory for stiffness and a separate lamination theory for strength are the outcomes derived here. Final forms are given for 0, 90, ± 45 type orthotropic laminates, with the four lamina orientation volume fractions to be specified in any particular application of interest. Many examples are given of using the new methodology in specific design cases.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2017;84(10):101005-101005-11. doi:10.1115/1.4037503.

Thin metal-polymer laminates make excellent materials for use in inflatable space structures. By inflating a stowed envelope using pressurized gas and by increasing the internal pressure slightly beyond the yield point of the metal films, the shell rigidizes in the deployed shape. Structures constructed with such materials retain the deployed geometry once the inflation gas has either leaked away, or it has been intentionally vented. For flight, these structures must be initially folded and stowed. This paper presents a numerical method for predicting the force required to achieve a given fold radius in a three-ply metal-polymer-metal laminate and to obtain the resultant springback. A coupon of the laminate is modeled as a cantilever subject to an increasing tip force. Fully elastic, elastic–plastic, relaxation, and springback stages are included in the model. The results show good agreement when compared with experimental data at large curvatures.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2017;84(10):101006-101006-9. doi:10.1115/1.4037589.

Current studies on tailoring the coefficient of thermal expansion (CTE) of materials focused on either exploring the composition of the bulk material or the design of composites which strongly depend on a few negative CTE materials or fibers. In this work, an approach to achieve a wide range of tailorable CTEs through a dual-constituent triangular lattice material is studied. Theoretical analyses explicitly reveal that through rational arrangement of commonly available positive CTE constituents, tailorable CTEs, including negative, zero, and large positive CTEs can be easily achieved. We experimentally demonstrate this approach through CTE measurements of the specimens, which were exclusively fabricated from common alloys. The triangular lattice material fabricated from positive CTE alloys is shown to yield large positive (41.6 ppm/°C), near-zero (1.9 ppm/°C), and negative (−32.9 ppm/°C) CTEs. An analysis of the collapse strength and stiffness ensures the robust mechanical properties. Moreover, hierarchal triangular lattice material is proposed, and with certain constituents, wide range of tailorable CTEs can be easily obtained through the rationally hierarchal structure design. The triangular lattice material presented here integrates tailorable CTEs, lightweight characteristic, and robust mechanical properties, and is very promising for engineering applications where precise control of thermally induced expansion is in urgently needed.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2017;84(10):101007-101007-8. doi:10.1115/1.4037552.

The flexoelectric effect is an electromechanical phenomenon that is universally present in all dielectrics and exhibits a strong size-dependency. Through a judicious exploitation of scale effects and symmetry, flexoelectricity has been used to design novel types of structures and materials including piezoelectric materials without using piezoelectric. Flexoelectricity links electric polarization with strain gradients and is rather difficult to estimate experimentally. One well-acknowledged approach is to fabricate truncated pyramids and/or cones and examine their electrical response. A theoretical model is then used to relate the measured experimental response to estimate the flexoelectric properties. In this work, we revisit the typical model that is used in the literature and solve the problem of a truncated cone under compression or tension. We obtained closed-form analytical solutions to this problem and examine the size and shape effects of flexoelectric response of the aforementioned structure. In particular, we emphasize the regime in which the existing models are likely to incur significant error.

Commentary by Dr. Valentin Fuster

Technical Brief

J. Appl. Mech. 2017;84(10):104501-104501-4. doi:10.1115/1.4037346.

Interfacial wave solutions for a planar interface between two finite layers have been obtained within the framework of antiplane elasticity. Solutions are found to exist both for slipping contact and for bonded contact at the interface. Both the slip and bonded contact waves are found to be dispersive and multivalued. One family of slip and bonded contact waves is found with phase velocity in between the shear wave speeds of the two solids. It is also found that two families of slip and bonded contact waves exist with phase velocity greater than the shear wave speed of both solids.

Topics: Waves
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2017;84(10):104502-104502-5. doi:10.1115/1.4037347.

Controlled formation of complex three-dimensional (3D) geometries has always attracted wide interest especially in micro/nanoscale where traditional fabrication techniques fail to apply. Recent advances employed buckling as a promising complementary assembling technique and the method can be used for high-performance electronics materials, such as silicon. This paper describes a new buckling pattern generated by joining multiple prestrained and unstrained elastomeric strips. After releasing, periodic twisting of the system along the releasing direction is generated and bilinear force–displacement relationship is revealed from finite element analysis (FEA). The finding enriches the classes of geometries that can be achieved from structural buckling. Also, compared to other buckling phenomena, the lateral dimension of the system does not change during the buckling process, which makes the structure perfect for elastic spring elements that can be arranged closely to each other without interference.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2017;84(10):104503-104503-4. doi:10.1115/1.4037317.

The interlaminar stress in angle-ply and cross-ply composite laminates subjected to twisting deformation are investigated. Two mechanisms of interlaminar load transfer have been developed by studying the angle-ply laminate and the cross-ply laminate subjected to uniform axial extension, thermoelastic deformation and anticlastic bending deformation. In the present, these mechanisms are investigated in laminates subjected to twisting deformation. It is shown that the mechanisms of interlaminar load transfer in twisting deformation are identical to those previously investigated, though they arise from different causes. Furthermore, a unified treatment of the mechanisms of interlaminar load transfer is presented for the angle-ply laminate and the cross-ply laminate subjected to the four aforementioned modes of deformation.

Commentary by Dr. Valentin Fuster

Errata

J. Appl. Mech. 2017;84(10):107001-107001-1. doi:10.1115/1.4037411.

Figure 2, the evolution of the crack half-length, in the published paper misrepresents the solution of Bunger et al. (Ref. [26] in the published paper) owing to wrong coordinate origin. The corrected Fig. 2 is given below.

Commentary by Dr. Valentin Fuster

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