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Research Papers

J. Appl. Mech. 2018;85(6):061001-061001-7. doi:10.1115/1.4039456.

The subject of this investigation is the plane strain elasticity problem of a finite width semi-infinite strip with its end pressed against a half-plane of the same material with friction. From the existing integral equation solution for a perfect bond, it is shown that the length of the zone of frictional slip and the value of the slip displacement can both be inferred. It is further shown how this method allows a finite element stress analysis of a structure, obtained with the simple assumption of a perfect bond, to be used instead of the more complicated finite element structural analysis with frictional slip. Nonetheless, the results of this simpler finite element analysis can be used to infer the length of the frictional slip zone and the magnitude of the slip displacement. It is expected that this method will be valuable in the analysis of the mechanics of fretting. Damage due to fretting fatigue is initiated due to frictional slip near the edges of the interface between two connected materials. The stress analysis of structures, which includes these frictional slip zones, is considerably more complicated than it is for a perfect bond, often making it impractical to include in a comprehensive finite element model of the complete structure. Thus, the methodology used in this paper should allow the size of the frictional slip zones and the frictional slip displacements to be inferred directly from the stress analysis for a perfect bond.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2018;85(6):061002-061002-10. doi:10.1115/1.4039457.

Buckling of multilayer graphene sheets (MLGSs) subjected to an axial compressive load in plane-strain condition is studied. Closed-form solutions for buckling load of MLGSs are obtained based on a continuum model for MLGSs. Two different kinematic assumptions, which lead to MLGS beam, which was recently proposed by the authors, and the Euler beam, are used to obtain the buckling loads. The obtained solutions yield significantly different buckling loads when the axial length is small. To validate obtained results, molecular dynamics (MD) simulations are conducted, and they show that the MLGS beam model well captures the buckling load of MLGSs. The buckling solution of MLGS beam model provides two interesting facts. First, the buckling load of MLGSs coincides with the Euler buckling load when the length is large. Second, when the number of layers is large, the buckling strain converges to a finite value, and could be expressed as a linear combination of the buckling strain of single-layer graphene and the ratio between the shear rigidity of interlayer and the tensile rigidity of graphene layer. We validate the asymptotic behavior of buckling strain through MD simulations and show that buckling occurs even when the overall thickness is larger than the axial length. Finally, we present a diagram that contains buckling strain of MLGSs according to the boundary conditions, the number of layers, and the axial length.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2018;85(6):061003-061003-10. doi:10.1115/1.4039437.

An approximate mathematical treatise is proposed to improve the accuracy of multiscale models for nonlinear mechanics of two-dimensional (2D) nanomaterials by taking into account the contribution of dihedral energy term in the nonlinear constitutive model for the generalized deformation (three nonzero components of each strain and curvature tensors) of the corresponding continuum. Twelve dihedral angles per unit cell of graphene sheet are expressed as functions of strain and curvature tensor components. The proposed model is employed to study the bending modulus of graphene sheets under finite curvature. The atomic interactions are modeled using first- and second-generation reactive empirical bond order (REBO) potentials with the modifications in the former to include dihedral energy term for accurate prediction of bending stiffness coefficients. The constitutive law is obtained by coupling the atomistic and continuum deformations through Cauchy–Born rule. The present model will facilitate the investigations on the nonlinear mechanics of graphene sheets and carbon nanotubes (CNTs) with greater accuracy as compared to those reported in the literature without considering dihedral energy term in multiscale modeling.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2018;85(6):061004-061004-9. doi:10.1115/1.4039620.

The membrane structure has been applied throughout different fields such as civil engineering, biology, and aeronautics, among others. In many applications, large deflections negate linearizing assumptions, and linear modes begin to interact due to the nonlinearity. This paper considers the coupling effect between vibration modes and develops the theoretical analysis of the free vibration problem for orthotropic rectangular membrane structures. Von Kármán theory is applied to model the nonlinear dynamics of these membrane structures with sufficiently large deformation. The transverse displacement fields are expanded with both symmetric and asymmetric modes, and the stress function form is built with these coupled modes. Then, a reduced model with a set of coupled equations may be obtained by the Galerkin technique, which is then solved numerically by the fourth-order Runge–Kutta method. The model is validated by means of an experimental study. The proposed model can be used to quantitatively predict the softening behavior of amplitude–frequency, confirm the asymmetric characters of mode space distribution, and reveal the influence of various geometric and material parameters on the nonlinear dynamics.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2018;85(6):061005-061005-11. doi:10.1115/1.4039573.

Failure by steady-state kink band propagation in layered materials is analyzed using three substantially different models. A finite element model and an analytical model are developed and used together with a previously introduced constitutive model. A novel methodology for simulating an infinite kink band is used for the finite element model using periodic boundary conditions on a skewed mesh. The developed analytical model results in a transcendental equation for the steady-state kink band propagation state. The three models are mutually in good agreement and results obtained using the models correlate well with the previous experimental findings.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2018;85(6):061006-061006-8. doi:10.1115/1.4039575.

In this work, we develop an optoelectronic system for in situ observation and measurement in hypervelocity flows. The system has the advantages of strong radiation resistance and self-adaptive exposure time of the cameras. Thermal ablation test using flat plate thermal protection system material was carried out in an arc jet. Real-time ablation images were captured and analyzed to understand the thermal ablation mechanism. Through the modified algorithms of particle image velocity (PIV) and image feature detection, the surface recession rate and the velocity distribution of the melted droplets flowing on the sample surface were obtained. The experimental results demonstrate vast potential for using this in situ measuring technique in various engineering applications. Finally, the formation and merging of the melted droplets was analyzed based on energy theory, and the numerical simulation results showed good agreement with the actual experimental results.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2018;85(6):061007-061007-8. doi:10.1115/1.4039574.

The indentation of plant cells by a conical indenter is modeled. The cell wall is represented as a spherical shell consisting of a relatively stiff thin outer layer and a softer thicker inner layer. The state of the interior of the cell is idealized as a specified turgor pressure. Attention is restricted to axisymmetric deformations, and the wall material is characterized as a viscoelastic solid with different properties for the inner and outer layers. Finite deformation, quasi-static calculations are carried out. The effects of outer layer stiffness, outer layer thickness, turgor pressure, indenter sharpness, cell wall thickness, and loading rate on the indentation hardness are considered. The calculations indicate that the small indenter depth response is dominated by the cell wall material properties, whereas for a sufficiently large indenter depth, the value of the turgor pressure plays a major role. The indentation hardness is found to increase approximately linearly with a measure of indenter sharpness over the range considered. The value of the indentation hardness is affected by the rate of indentation, with a much more rapid decay of the hardness for slow loading, because there is more time for viscous relaxation during indentation.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2018;85(6):061008-061008-7. doi:10.1115/1.4039619.

This paper presents the results of analytical and numerical investigations into stress behavior in the vicinity of different types of singular points on two-dimensional (2D) elastic bodies made of functionally graded materials (FGMs). A variant of constructing eigensolutions for plane FGM wedges, where the elastic properties are represented as a series expansion with respect to the radial coordinates, was considered. It was shown that, in the vicinity of singular points, the stress behavior is determined by solving the problem for the corresponding homogeneous wedge, where the elastic characteristics coincide with the characteristics of FGMs at the wedge vertex. Numerical investigations were carried out to evaluate the stress state of elastic bodies containing FGM elements at singular points, where the type of boundary conditions changes or where dissimilar materials come into contact. The results of the calculations showed that the behavior of stresses in FGMs in the vicinity of singular points can also be determined from an analysis of the eigensolutions for the corresponding homogeneous wedges, where the elastic properties coincide with the elastic constants of FGMs at singular points and that the functionally graded properties are dependent on one or two polar coordinates.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2018;85(6):061009-061009-5. doi:10.1115/1.4039621.

An elastic sphere adheres to a rigid substrate in the presence of moisture. The adhesion–detachment trajectory is derived based on the Hertz contact theory that governs the contact mechanics and Laplace–Kelvin equation that governs the water meniscus at the interface. The intersurface attraction is solely provided by the Laplace pressure within the meniscus. Interrelation between the applied load, contact radius, and approach distance is derived based on a force balance. The resulting “pulloff” force to detach the sphere exceeds the critical load in the Derjaguin–Muller–Toporov (DMT) limit which only holds at saturated moisture. The new model accounts for the finite size of water molecules that is missing in virtually all classical models.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2018;85(6):061010-061010-10. doi:10.1115/1.4039435.

A novel algorithm for the estimation of rigid-body angular velocity and attitude—the most challenging part of pose-and-twist estimation—based on isotropic accelerometer strapdowns, is proposed in this paper. Quaternions, which employ four parameters for attitude representation, provide a compact description without the drawbacks brought about by other representations, for example, the gimbal lock of Euler angles. Within the framework of quaternions for rigid-body angular velocity and attitude estimation, the proposed methodology automatically preserves the unit norm of the quaternion, thus improving the accuracy and efficiency of the estimation. By virtue of the inherent nature of isotropic accelerometer strapdowns, the centripetal acceleration is filtered out, leaving only its tangential counterpart, to be estimated and updated. Meanwhile, using the proposed integration algorithm, the angular velocity and the quaternion, which are dependent only on the tangential acceleration, are calculated and updated at appropriate sampled instants for high accuracy. This strategy, which brings about robustness, allows for relatively large time-step sizes, low memory demands, and low computational complexity. The proposed algorithm is tested by simulation examples of the angular velocity and attitude estimation of a free-rotating brick and the end-effector of an industrial robot. The simulation results showcase the algorithm with low errors, as estimated based on energy conservation, and high-order rate of convergence, as compared with other algorithms in the literature.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2018;85(6):061011-061011-10. doi:10.1115/1.4039671.

This paper presents a novel application of multiparameter spectral theory to the study of structural stability, with particular emphasis on aeroelastic flutter. Methods of multiparameter analysis allow the development of significant new solution and analysis algorithms for aeroelastic flutter problems; including direct solvers for polynomial problems of arbitrary order and size, and a pseudospectral method for characterizing the nature of the flutter point and its local modal damping gradient. Two variants of the flutter point direct solver are presented, their computational characteristics are compared, and an efficient hybrid method of direct spectral solution and iterative pseudospectral solution is developed. This method is well suited to the analysis of problems arising in reduced-order modeling and preliminary design optimization and has the advantage of computing all the system flutter points and their characteristics with minimal user oversight. The aeroelastic inverse problem, with applications in parameter identification and system optimization, is also shown to be solvable via multiparameter analysis. Extensions and improvements to this new conceptual framework and associated solvers are discussed.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2018;85(6):061012-061012-7. doi:10.1115/1.4039755.

Artificial periodic structures are used to control spatial and spectral properties of acoustic or elastic waves. The ability to exploit band gap structure creatively develops a new route to achieve excellently manipulated wave properties. In this study, we introduce a paradigm for a type of real-time band gap modulation technique based on parametric excitations. The longitudinal wave of one-dimensional (1D) spring-mass systems that undergo transverse periodic vibrations is investigated, in which the high-frequency vibration modes are considered as parametric excitation to provide pseudo-stiffness to the longitudinal elastic wave in the propagating direction. Both analytical and numerical methods are used to elucidate the versatility and efficiency of the proposed real-time dynamic modulating technique.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2018;85(6):061013-061013-9. doi:10.1115/1.4039814.

A series of stress-controlled uniaxial cyclic tension-unloading tests are discussed to investigate the ratchetting of a filled rubber at room temperature. It is shown that obvious ratchetting occurs and depends apparently on the applied stress level, stress rate, and stress history. Based on the experimental observations, a damage-coupled hyper-viscoelastic-plastic constitutive model is then developed to describe the ratchetting of the filled rubber, which consists of three branches in parallel, i.e., a hyperelastic, a viscoelastic, and a plastic one. The damage is assumed to act equally on three branches and consists of two parts, i.e., the Mullins-type damage caused by the initial tensile deformation and the accumulated damage occurred during the cyclic deformation. The developed model is validated by comparing the predicted results with the experimental data.

Commentary by Dr. Valentin Fuster

Errata

J. Appl. Mech. 2018;85(6):067001-067001-1. doi:10.1115/1.4039623.

The authors regret that Fig. 7 in page 7 should be replaced by the picture which contains two subfigures as follows:

Commentary by Dr. Valentin Fuster

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