Research Papers

J. Appl. Mech. 2019;86(6):061001-061001-12. doi:10.1115/1.4042572.

This paper presents an analytical method to investigate the effects of symmetric and asymmetric elastic supports on the nonlinear equilibria and buckling responses of shallow arches. It is found that arches with symmetric elastic supports can bifurcate into secondary paths with high-order symmetric modes. When a small asymmetry exists in the elastic supports, the equilibria of the arch may abruptly split and lead to the occurrence of remote unconnected equilibria. Such unconnected equilibria can be obtained experimentally or numerically using typical path following controls only with prior knowledge of location of these paths. A small asymmetry in the elastic supports may also make a secondary branch shrink into points connecting surrounding equilibria, resulting in the appearance of more limit points. The analytical solutions are also derived to directly calculate critical loads. We find that the magnitude of the stiffness of symmetric elastic supports has no influence on limits loads and bifurcation loads at branching into secondary paths with symmetric configurations, but greatly affect the bifurcation loads of secondary paths with asymmetric configurations. All critical loads are very sensitive to the degree of asymmetry in the elastic supports. The asymmetry in the supports reduces the top values of all pairs of critical loads compared to the case of symmetric elastic supports. The results obtained from the analytical derivations are confirmed using finite element analysis (FEA).

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2019;86(6):061002-061002-15. doi:10.1115/1.4042681.

This paper presents an innovative approach of stress attenuation through a continuous impedance-graded material system for high strain-rate events. High energetic dynamic events such as blasts and impact could cause stress waves—in the form of elastic, plastic, and shock—to propagate in a solid material. An impedance-graded composite is created by arranging different metallic alloys in the reducing order of their impedance through the system. Impedance, which is the product of volumetric mass density and wave velocity, is chosen as the function as it plays a governing role in elastic, plastic, and shock waves. An analytical framework to quantify the stress wave propagation through an impedance-graded multimaterial system is developed based on the principles of shock and elastic wave theories. The numerical simulations carried out using nonlinear finite element code, LS-DYNA, were able to capture and quantify the elastic, plastic, and shock waves and their reflections at different interfaces. It was identified that the final transmitted stress wave, which could comprise elastic, plastic, and shock waves, as well as the reflected tensile elastic wave at each material interface, needs to be controlled in order to develop a robust multimaterial system.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2019;86(6):061003-061003-8. doi:10.1115/1.4042764.

A soft adhesive layer bonded between two rigid substrates, which are being pulled apart, may exhibit diverse instability phenomena before failure, such as cavitation, fingering, and fringe instability. In this study, by subdividing the soft layers into different numbers of disconnected smaller parts, we achieve desired instability modes and mechanical responses of the layer. The partition process not only retains the monotonicity on the tensile curve but also tunes the modulus and stretchability of the adhesive layer. Meanwhile, cavitation in layers of large aspect ratios is suppressed, and the hysteresis during cyclic loading is reduced. This study provides a guideline for the structural design of soft joints and adhesive layers.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2019;86(6):061004-061004-7. doi:10.1115/1.4042895.

Epidermal electronics mounted on the body provides the robust and noninvasive interfaces to monitor the electrophysiological signals of human body. The contact characteristic of the epidermal electronics with the skin affects the accuracy of the measured signals. In this paper, ionic polymer–metal composite is used to regulate the interface force for the consistency of the contact performance. The patterns of the ionic polymer–metal composite are designed for the flexibility and the contact characteristic of the epidermal electronics with the skin. This study provides an approach for the adjustment of the contact characteristic, which is very valuable for the longtime accurate monitoring of the epidermal electronics attached on the skin.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2019;86(6):061005-061005-8. doi:10.1115/1.4043073.

Wrinkling is a common phenomenon in natural and engineering film structures. The wrinkles influence the geometry and dynamic response of these structures. In this work, we investigate the wrinkling of a stretched thin film containing engineered microstructures and its derived functionality on controlling the propagation of bending waves. The underlying mechanism is revealed and the effect of wrinkles on the bandgap of bending waves is systematically evaluated via numerical simulations based on the Bloch wave theory. We show that wrinkles with a customized wavelength can be triggered in the microstructured film due to the mismatched deformation in the film. The bandgap of the wrinkled film can be finely tuned via applied stretching, resulting in the controllable propagation of bending waves in thin films. Our work provides fundamental insights into wave propagation in wrinkled films and potential applications for dynamic control of the wave propagation in engineering film structures.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2019;86(6):061006-061006-5. doi:10.1115/1.4042762.

The transfer matrix method for linear multibody systems is capable of providing precise solutions for the dynamics of various mechanical systems, but it may also suffer from numerical instability in some cases, where serial chains with a large number of mechanical elements are involved or high-frequency harmonic responses are computed. Combining such a transfer strategy with the Riccati transformation yields the Riccati transfer matrix method (RTMM), which can help improve the numerical stability. According to the existing method, the conventional transfer matrices of all the mechanical elements should be obtained first; in other words, the existence of conventional transfer matrices is a prerequisite for the application of the RTMM. Thus, it seems that the RTMM is incapable of performing the dynamics analysis of linear multibody systems with indeterminate in-span conditions due to the nonexistence of the corresponding conventional transfer matrices. Observe that, for any state variables with indeterminate input–output relationships, the complementary state variables (the complementary state variable of a displacement is the corresponding internal force and vice versa) are identically equal to zero, and that the dimension of the Riccati transfer equation is only half of that of the conventional transfer equation. It reveals that the Riccati transfer equations for the connection points associated with indeterminate in-span conditions can be formulated directly, and that there is no need to rely on the conventional transfer equation. Two numerical examples are simulated and the computational results are compared with those obtained by the finite element method, which verifies the proposed method.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2019;86(6):061007-061007-7. doi:10.1115/1.4043141.

In applying the Udwadia–Kalaba equation for constrained mechanical systems, a direct proof of the equivalence of first integrals and nonholonomic constraints is given, and it is demonstrated that the generalized force of the system is equivalent to the constraint force derived by all first integrals of the nonholonomic constraints. Furthermore, depending on whether complete information is included in the subsets of the first integrals or not, the concept of “multiple kernel” of the system is introduced, and then the core groups of the first integrals and the folding index, which reveals the “simplicity” of the system, are defined. Finally, the onefold system is discussed in detail, and the judgment method is given. To verify the feasibility of this method and illustrate the application of the multiple kernel theory, three examples are considered. The new concepts and results presented in this paper help reveal the inner structure of the general mechanical system, which forms the foundation of control theory of constraint motions, and the multiple kernel analysis of the complex systems can be a new research area of analytic mechanics in the future.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2019;86(6):061008-061008-11. doi:10.1115/1.4042996.

Electrically driven dielectric elastomers (DEs) suffer from an electromechanical instability (EMI) when the applied potential difference reaches a critical value. A majority of the past investigations address the mechanics of this operational instability by restricting the kinematics to homogeneous deformations. However, a DE membrane comprising both active and inactive electric regions undergoes inhomogeneous deformation, thus necessitating the solution of a complex boundary value problem. This paper reports the numerical and experimental investigation of such DE actuators with a particular emphasis on the EMI in quasistatic mode of actuation. The numerical simulations are performed using an in-house finite element framework developed based on the field theory of deformable dielectrics. Experiments are performed on the commercially available acrylic elastomer (VHB 4910) at varying levels of prestretch and proportions of the active to inactive areas. In particular, two salient features associated with the electromechanical response are addressed: the effect of the flexible boundary constraint and the locus of the dielectric breakdown point. To highlight the influence of the flexible boundary constraint, the estimates of the threshold value of potential difference on the onset of electromechanical instability are compared with the experimental observations and with those obtained using the lumped parameter models reported previously. Additionally, a locus of localized thinning, near the boundary of the active electric region, is identified using the numerical simulations and ascertained through the experimental observations. Finally, an approach based on the Airy stress function is suggested to justify the phenomenon of localized thinning leading to the dielectric breakdown.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2019;86(6):061009-061009-5. doi:10.1115/1.4043142.

Directional motion is one of the most fundamental motions in the nature, which is driven by specific types of gradients. The transition metal dichalcogenides graded lateral heterostructure is a valuable semiconductor playing crucial roles in electronic and optoelectronic devices. This lateral heterostructure has a graded composition and is thus a promising candidate to drive possible directional motions. Here, we perform molecular dynamics simulations to demonstrate the directional motion of a graphene sheet on top of the MoS2–WSe2 graded lateral heterostructure. It is quite interesting that the direction for the diffusion is sensitive to the graphene sheet’s initial location, which is in two different regions. The graphene sheet diffuses in opposite directions for the initial location that falls in different regions. We derive an analytic formula for the interlayer coupling potential, which discloses the underlying mechanism for the dependence of the directional motion on the initial location of the graphene sheet. These results shall be varifiable by present experimental set ups and may be valuable for the application of the transition metal dichalcogenides graded lateral heterostructure in practical electronic devices.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2019;86(6):061010-061010-10. doi:10.1115/1.4042995.

Porous bulk metallic glasses (BMGs) exhibit an excellent combination of superior mechanical properties such as high strength, high resilience, large malleability, and energy absorption capacity. However, a mechanistic understanding of their response under diverse states of stress encountered in practical load-bearing applications is lacking in the literature. In this work, this gap is addressed by performing three-dimensional finite element simulations of porous BMGs subjected to a wide range of tensile and compressive states of stress. A unit cell approach is adopted to investigate the mechanical behavior of a porous BMG having 3% porosity. A parametric study of the effect of stress triaxialities T = 0, ±1/3, ±1, ±2, ±3, and ±∞, which correspond to stress states ranging from pure deviatoric stress to pure hydrostatic stress under tension and compression, is conducted. Apart from the influence of T, the effects of friction parameter, strain-softening parameter and Poisson’s ratio on the mechanics of deformation of porous BMGs are also elucidated. The results are discussed in terms of the simulated stress-strain curves, pore volume fraction evolution, strain to failure, and development of plastic deformation near the pore. The present results have important implications for the design of porous BMG structures.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2019;86(6):061011-061011-11. doi:10.1115/1.4042836.

A general formula of Jacobian matrix is derived in an incremental harmonic balance (IHB) method for general nonlinear delay differential equations (DDEs) with multiple discrete delays, where the fast Fourier transform is used to calculate Fourier coefficients of partial derivatives of residuals. It can be efficiently and automatically implemented in a computer program, and the only manual work is to derive the partial derivatives, which can be a much easier task than derivation of Jacobian matrix. An advantage of the IHB method in stability analysis is also revealed here. A direct construction method is developed for stability analysis of nonlinear differential equations with use of a relationship between Jacobian matrix in the IHB method and the system matrix of linearized equations. Toeplitz form of the system matrix can be directly constructed, and Hill’s method is used to calculate Floquet multipliers for stability analysis. Efficiency of stability analysis can be improved since no integration is needed to calculate the system matrix. Period-doubling bifurcations and period-p solutions of a delayed Mathieu–Duffing equation are studied to demonstrate use of the general formula of Jacobian matrix in the IHB method and the direct construction method in stability analysis. Its solution is the same as that from the numerical integration method using the spectral element method in the DDE toolbox in matlab, and it has a high convergence rate for solving a delayed Van der Pol equation.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2019;86(6):061012-061012-12. doi:10.1115/1.4043074.

This is the first study to develop an empirical formulation to predict fretting wear (volume removal) under frictional conditions for plane-strain line contacts as borne out by the finite element analysis (FEA). The contact is between a deformable half-cylinder rubbing against a deformable flat block. The FEA is guided by detailed physical conceptions, with results that subsequently lead to the methodical modeling of fretting wear. The materials in contact are first set to steel/steel, then to Alloy617/Alloy617, and finally to copper/copper. Various coefficients of friction (COFs) and the Archard Wear Model are applied to the interface. Initially, pure elastic conditions are investigated. The theoretical predictions for the wear volume at the end of the partial slip condition in unidirectional sliding contact agree very well with the FEA results. The empirical formulation for the initial gross slip distance is constructed, again revealing results that are in good agreement with those obtained from the FEA for different materials and for various scales. The Timoshenko beam theory and the tangential loading analysis of a half elastic space are used to approximate the deflection of the half-cylinder and the flat block, respectively. That theory supports well the empirical formulation, matching closely the corresponding FEA results. The empirical formulation of the wear volume for a general cycle under fretting motion is then established. The results are shown to be valid for different materials and various COFs when compared with the FEA results. Finally, plasticity is introduced to the model, shown to cause two phenomena, namely junction growth and larger tangential deformations. Wear is shown to either increase or decrease depending on the combined influences of these two phenomena.

Commentary by Dr. Valentin Fuster

Technical Brief

J. Appl. Mech. 2019;86(6):064501-064501-5. doi:10.1115/1.4042994.

The efficiency of the critical plane model of Smith, Watson, and Topper in estimating fatigue life for loaded notched shape memory alloy members undergoing thermal cycling is demonstrated. The field intensity approach is adopted, which characterizes fatigue damage over a critical notch root region rather than at a critical point.

Commentary by Dr. Valentin Fuster

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