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Research Papers

J. Appl. Mech. 2017;84(8):081001-081001-13. doi:10.1115/1.4036940.

Structures of thin films bonded on thick substrates are abundant in biological systems and engineering applications. Mismatch strains due to expansion of the films or shrinkage of the substrates can induce various modes of surface instabilities such as wrinkling, creasing, period doubling, folding, ridging, and delamination. In many cases, the film–substrate structures are not flat but curved. While it is known that the surface instabilities can be controlled by film–substrate mechanical properties, adhesion and mismatch strain, effects of the structures’ curvature on multiple modes of instabilities have not been well understood. In this paper, we provide a systematic study on the formation of multimodal surface instabilities on film–substrate tubular structures with different curvatures through combined theoretical analysis and numerical simulation. We first introduce a method to quantitatively categorize various instability patterns by analyzing their wave frequencies using fast Fourier transform (FFT). We show that the curved film–substrate structures delay the critical mismatch strain for wrinkling when the system modulus ratio between the film and substrate is relatively large, compared with flat ones with otherwise the same properties. In addition, concave structures promote creasing and folding, and suppress ridging. On the contrary, convex structures promote ridging and suppress creasing and folding. A set of phase diagrams are calculated to guide future design and analysis of multimodal surface instabilities in curved structures.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2017;84(8):081002-081002-16. doi:10.1115/1.4036612.

A new one-dimensional high-order sandwich panel theory for curved panels is presented and compared with the theory of elasticity. The theory accounts for the sandwich core compressibility in the radial direction as well as the core circumferential rigidity. Two distinct core displacement fields are proposed and investigated. One is a logarithmic (it includes terms that are linear, inverse, and logarithmic functions of the radial coordinate). The other is a polynomial (it consists of second and third-order polynomials of the radial coordinate), and it is an extension of the corresponding field for the flat panel. In both formulations, the two thin curved face sheets are assumed to be perfectly bonded to the core and follow the classical Euler–Bernoulli beam assumptions. The relative merits of these two approaches are assessed by comparing the results to an elasticity solution. The case examined is a simply supported curved sandwich panel subjected to a distributed transverse load, for which a closed-form elasticity solution can be formulated. It is shown that the logarithmic formulation is more accurate than the polynomial especially for the stiffer cores and for curved panels of smaller radius.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2017;84(8):081003-081003-19. doi:10.1115/1.4036942.

We study cross-flow vortex-induced vibration (VIV) of a linearly sprung circular cylinder equipped with a dissipative oscillator with cubic stiffness nonlinearity, restrained to move in the direction of travel of the cylinder. The dissipative, essentially nonlinear coupling between the cylinder and the oscillator allows for targeted energy transfer (TET) from the former to the latter, whereby the oscillator acts as a nonlinear energy sink (NES) capable of passively suppressing cylinder oscillations. For fixed values of the Reynolds number (Re = 48, slightly above the fixed-cylinder Hopf bifurcation), cylinder-to-fluid density ratio, and dimensionless cylinder spring constant, spectral-element simulations of the Navier–Stokes equations coupled to the rigid-body motion show that different combinations of NES parameters lead to different long-time attractors of the dynamics. We identify four such attractors which do not coexist at any given point in the parameter space, three of which lead to at least partial VIV suppression. We construct a reduced-order model (ROM) of the fluid–structure interaction (FSI) based on a wake oscillator to analytically study those four mechanisms seen in the high-fidelity simulations and determine their respective regions of existence in the parameter space. Asymptotic analysis of the ROM relies on complexification-averaging (CX-A) and slow–fast partition of the transient dynamics and predicts the existence of complete and partial VIV-suppression mechanisms, relaxation cycles, and Hopf and Shilnikov bifurcations. These outcomes are confirmed by numerical integration of the ROM and comparisons with spectral-element simulations of the full system.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2017;84(8):081004-081004-12. doi:10.1115/1.4036939.

Flexoelectricity (FE) refers to the two-way coupling between strain gradients and the electric field in dielectric materials, and is universal compared to piezoelectricity, which is restricted to dielectrics with noncentralsymmetric crystalline structure. Involving strain gradients makes the phenomenon of flexoelectricity size dependent and more important for nanoscale applications. However, strain gradients involve higher order spatial derivate of displacements and bring difficulties to the solution of flexoelectric problems. This dilemma impedes the application of such universal phenomenon in multiple fields, such as sensors, actuators, and nanogenerators. In this study, we develop a mixed finite element method (FEM) for the study of problems with both strain gradient elasticity (SGE) and flexoelectricity being taken into account. To use C0 continuous elements in mixed FEM, the kinematic relationship between displacement field and its gradient is enforced by Lagrangian multipliers. Besides, four types of 2D mixed finite elements are developed to study the flexoelectric effect. Verification as well as validation of the present mixed FEM is performed through comparing numerical results with analytical solutions for an infinite tube problem. Finally, mixed FEM is used to simulate the electromechanical behavior of a 2D block subjected to concentrated force or voltage. This study proves that the present mixed FEM is an effective tool to explore the electromechanical behaviors of materials with the consideration of flexoelectricity.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2017;84(8):081005-081005-7. doi:10.1115/1.4036943.

We proposed an eccentric ellipse criterion to describe the failure of amorphous materials under a combination of normal stress σ and shear stress τ. This criterion can reflect a tension–compression strength asymmetry, and unify four previous failure criteria in the σ–τ stress space, including von Mises criterion, Drucker–Prager criterion, Christensen criterion, and ellipse criterion. We examined the validity of the eccentric ellipse criterion in the tensile-shear failure regimes using the results from our atomistic simulations for two typical amorphous CuZr and LiSi, and recent tension–torsion experiments on metallic glasses. The predictions from the eccentric ellipse criterion agree well with these results from atomistic simulations and experiments. It indicates that this eccentric ellipse criterion is essential for the tensile-shear failure of amorphous materials.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2017;84(8):081006-081006-12. doi:10.1115/1.4036937.

A novel tetrachiral and antitetrachiral hybrid metastructure is proposed, and its in-plane mechanical properties are studied through strain energy analysis. Based on rigid ring rotation assumption, the analytical expression for the in-plane modulus of anisotropic tetrachiral and antitetrachiral hybrid metastructure is derived, and in-plane tensile experimental test and finite element simulation are performed and compared with the theoretical models. The corresponding in-plane anisotropic mechanical properties can be tuned with three independent dimensionless geometrical parameters, and effects of dimensionless geometrical parameters on the in-plane mechanical properties are studied systematically. Finally, an innovative tetrachiral and antitetrachiral hybrid metastructure stent is designed, and its mechanical behaviors under uniaxial tensile loading are investigated. It is found that the designed tetrachiral and antitetrachiral hybrid stent shows negative Poisson ratio properties, and the axial and circumferential deformation can be controlled through adjusting the spacing of unit cell along axial and circumferential directions.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2017;84(8):081007-081007-6. doi:10.1115/1.4036938.

Intrinsic driving mechanism is of particular significance to nanoscale mass delivery and device design. Stiffness gradient-driven directional motion, i.e., nanodurotaxis, provides an intrinsic driving mechanism, but an in-depth understanding of the driving force is still required. Based on molecular dynamics (MD) simulations, here we investigate the motion behavior of a graphene flake on a graphene substrate with a stiffness jump. The effects of the temperature and the stiffness configuration on the driving force are discussed in detail. We show that the driving force is almost totally contributed by the unbalanced edge force and increases with the temperature and the stiffness difference but decreases with the stiffness level. We demonstrate in particular that the shuttle behavior of the flake between two stiffness jumps on the substrate can be controlled by the working temperature and stiffness configuration of the system, and the shuttle frequency can be well predicted by an analytical model. These findings may have general implications for the design of nanodevices driven by stiffness jumps.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2017;84(8):081008-081008-12. doi:10.1115/1.4036941.

In the present work, a new approach for designing graded lattice structures is developed under the moving morphable components/voids (MMC/MMV) topology optimization framework. The essential idea is to make a coordinate perturbation to the topology description functions (TDF) that are employed for the description of component/void geometries in the design domain. Then, the optimal graded structure design can be obtained by optimizing the coefficients in the perturbed basis functions. Our numerical examples show that the proposed approach enables a concurrent optimization of both the primitive cell and the graded material distribution in a straightforward and computationally effective way. Moreover, the proposed approach also shows its potential in finding the optimal configuration of complex graded lattice structures with a very small number of design variables employed under various loading conditions and coordinate systems.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2017;84(8):081009-081009-10. doi:10.1115/1.4036988.

Symmetrical load on the crack surfaces is found in many fluid–solid problems. The combined effect of symmetrical normal and shear stresses is investigated, which impacts on the displacement and stress fields and the predictions of crack initiation and deflection. The boundary integral equations of displacement and stress fields are formulated using the integral-transform method. The equations of the displacement and stress are reduced using the Abel integral equations. The analytical solution of the full space for uniform normal and shear stresses is obtained. The asymptotic solution of the displacement of the crack surface is obtained near the crack tip under specific normal and shear stresses. Results show that shear stress tends to inhibit the crack, and the predictions of crack initiation and deflection could be inappropriate for a slit crack under a singular shear stress. This study may be useful for future investigations of the fluid–solid problems and help to understand the hydraulic fracturing.

Commentary by Dr. Valentin Fuster

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