0

IN THIS ISSUE

### Research Papers

J. Appl. Mech. 2016;83(12):121001-121001-7. doi:10.1115/1.4034461.
OPEN ACCESS

Accurate estimation and tuning of frictional damping are critical for proper design, safety, and reliability of assembled structures. In this study, we investigate how surface geometry and boundary conditions affect frictional energy dissipation under microslip contact situations. In particular, we investigate the frictional losses of a two-dimensional (2D) deformable wavy surface in contact with rigid plate under specific normal and tangential loading. We also propose a dissipation tuning mechanism by tension-induced wrinkling of a composite surface. This surface is made of stiff strips printed on a compliant substrate. We show that the contact geometry of wrinkling surfaces can be altered significantly by tensile loading and design of the composite surface. Using this, we present frictional dissipation maps as functions of applied tension and one of the geometric parameters in the composite design; spacing between stiff strips. Those maps illustrate the dissipation tuning capability of wrinkled surfaces, and thus present a unique mean of damping control.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2016;83(12):121002-121002-12. doi:10.1115/1.4034520.

Three-dimensional transient deformations of clamped flat and doubly curved polycarbonate (PC) panels impacted by a rigid smooth hemispherical-nosed circular cylinder have been numerically studied by the finite-element (FE) method to delineate effects of the panel radius of curvature to its thickness ratio on their penetration resistance. The PC is modeled as thermoelastoviscoplastic with the effective plastic strain rate depending upon the hydrostatic pressure. The effective plastic strain of 3.0 at failure is ascertained by matching for one set of flat panels the computed and the experimental minimum perforation speeds. It is found that a negative curvature (i.e., the center of curvature toward the impactor) of a panel degrades its penetration performance, and the positive curvature enhances it especially for thin panels with thickness/radius of curvature of 0.01. However, the benefit is less evident for panels with the panel thickness/radius of curvature of 0.04 or more. For positively curved thin panels, an elastic hinge forms around the central impacted area during an early stage of deformations, and subsequent deformations occur within this region. No such hinge is observed for flat plates, negatively curved panels of all the thicknesses, and positively curved thick panels. Furthermore, the maximum effective stress induced in regions surrounding the impacted area is less for positively curved panels than that for flat panels. The dominant failure mechanism is found to be the deletion of failed elements due to the effective plastic strain in them exceeding 3.0 rather than due to plug formation. For an example problem, the dependence of the effective plastic strain rate upon the hydrostatic pressure and the consideration of the Coulomb friction at the contact surfaces exhibited minimal effects on the penetration characteristics. This information should be useful for designers of impact-resistant transparent armor, such as an airplane canopy, automobile windshield, and goggles.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2016;83(12):121003-121003-9. doi:10.1115/1.4034460.

In this paper, an approximate semi-analytical approach is developed for determining the first-passage probability of randomly excited linear and lightly nonlinear oscillators endowed with fractional derivative elements. The amplitude of the system response is modeled as one-dimensional Markovian process by employing a combination of the stochastic averaging and the statistical linearization techniques. This leads to a backward Kolmogorov equation which governs the evolution of the survival probability of the oscillator. Next, an approximate solution of this equation is sought by resorting to a Galerkin scheme. Specifically, a convenient set of confluent hypergeometric functions, related to the corresponding linear oscillator with integer-order derivatives, is used as orthogonal basis for this scheme. Applications to the standard viscous linear and to nonlinear (Van der Pol and Duffing) oscillators are presented. Comparisons with pertinent Monte Carlo simulations demonstrate the reliability of the proposed approximate analytical solution.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2016;83(12):121004-121004-7. doi:10.1115/1.4034562.

The destabilization of the steady-state regime of two semi-infinite half-spaces of different elastic coefficients sliding upon each other has been theoretically investigated when a rate-and-state friction constitutive law controls the sliding. In the framework of linear and isotropic elastodynamics, the effect of the frictional constitutive law has been investigated onto the development of self-excited oscillations as well as the influence of the shear modulus difference between the two materials. The possibility of existence of a stick–slip regime and the conditions for the loss-of-contact are finally discussed.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2016;83(12):121005-121005-11. doi:10.1115/1.4034563.

In this paper, a compressive-mode wideband vibration energy harvester using a combination of bistable and flextensional mechanisms is proposed. The structure consists of a cantilever with a magnet fixed at its free end, and a flextensional actuator with a magnet fixed at its free end. A theoretical model is developed to characterize the compressive-mode wideband vibration energy harvester. Both simulations and experiments are carried out to validate the design and analysis of the compressive-mode wideband vibration energy harvester. The results show that the device can work in broadband, and the piezoelectric constant d31 can be enlarged 134 times. The experimental results also indicate that the harvester can generate the power about 31 μW with the resistive load 390 kΩ, while the magnetic pressure is 2.9 N. A developed design including two flextensional actuators symmetrically arranged is also presented. The experimental results show that the two flextensional actuators in the developed design can harvest more energy than one flextensional actuator in the primal design.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2016;83(12):121006-121006-9. doi:10.1115/1.4034564.
OPEN ACCESS

We perform atomistic simulations of nanoindentation on Lennard–Jones 2D hexagonal crystals. In this work, we find a new spatially extended buckling-like mode of instability, which competes with the previously known instability governed by dislocation-dipole nucleation. The geometrical parameters governing these instabilities are the lattice constant, a, the radius of curvature of the indenter, R, and the thickness of the indenter layer, Ly. Whereas dislocation nucleation is a saddle-node bifurcation governed by R/a, the buckling-like instability is a pitchfork bifurcation (like classical Euler buckling) governed by $R/Ly$. The two modes of instability exhibit strikingly different behaviors after the onset of instability. The dislocation nucleation mode results in a stable final configuration containing a surface step and a stable dislocation at some depth beneath the surface, while the buckling modes are always followed immediately by subsequent nucleation of many dislocation dipoles. We show that this subsequent dislocation nucleation is also observed immediately after buckling in free standing rods, but only for rods which are of sufficiently wide aspect ratio, while thinner rods exhibit stable buckling followed only later by dislocation nucleation in the buckled state. Finally, we study the utility of several recently proposed local and quasi-local stability criteria in detecting the buckling mode. We find that the so-called Λ criterion, based on the stability of a representative homogeneously deformed lattice, is surprisingly useful in detecting the transition from dislocation-type instability to buckling-type instability.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2016;83(12):121007-121007-10. doi:10.1115/1.4034704.
OPEN ACCESS

The incorporation of real-time structural health monitoring has the potential to substantially reduce the inspection burden of advanced composite rotor blades, particularly if impacts can be detected and characterized using operational data. Data-driven impact identification techniques, such as those applied in this work, require that a structural dynamic model of blade frequency response functions (FRFs) be developed for the operational environment. However, the operational characteristics of the rotor system are not accurately described by a model developed and validated in a nonrotating environment. The discrepancies are predominately due to two sources: the change in the blade root boundary condition and the presence of a centrifugal force. This research demonstrates an analytical methodology to compensate for the first of these effects. Derivations of this method are included, as well as analytical and experimental results. Additionally, the theory and experimental results are presented for an approach by which planar impact area and impactor stiffness may be estimated. Applying these techniques, impact location estimation accuracy was improved from 51.6% to 94.2%. Impacts produced by objects of 2–in. diameter were demonstrated to be distinguishable from those of 1 in. or less diameter. Finally, it was demonstrated that the impacts by objects of metallic material were distinguishable from those of rubber material, and that such differentiation was robust to impactor size and impact force magnitude.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2016;83(12):121008-121008-8. doi:10.1115/1.4034620.

This paper presents an improved model for the critical impact yaw (or simply the critical yaw) in long-rod penetration with considering the deceleration and rotation of the rod and the crater shape of the target. Two critical yaws, $θc1$ and $θc2$, under normal impact were identified, below which there is no contact between the rod and crater sidewall (for $θc1$) and between the rod and the crater entrance (for $θc2$) during the entire penetration process. Contact functions and iterative algorithms were proposed in order to obtain these two critical yaws numerically. The influences of four dominant nondimensional numbers (i.e., the ratio of the target resistance to the rod strength $λ$, Johnson's damage number of the rod $ς$, square root of the target–projectile density ratio $μ$, and the diameter–length ratio of the rod $ψ$) on two critical yaws were studied for three typical rod–target systems (tungsten alloy rods penetrating steel targets, steel rods penetrating aluminum alloy targets, and steel rods penetrating steel targets). The relationship between two critical yaw angles was also discussed. A new empirical formula for the critical yaw $θc2$ was proposed based on the parametric study results and dominant nondimensional numbers, which extends the valid application range of the existing empirical formula.

Topics: Steel , Rods , Yaw , Shapes , Tungsten alloys
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2016;83(12):121009-121009-8. doi:10.1115/1.4034783.

By directly solving the prescribed differential equations, an analytical method based on the cohesive model has been developed to investigate the interfacial debonding process induced by lithiation in an axisymmetric thin film electrode where an elastic active layer is bonded on a rigid substrate. The assumption of rigid substrate has been proved acceptable for high-modulus substrates such as copper and aluminum which are common materials for current collectors in lithium-ion batteries. For the case where the weak interface is assumed and the radial concentration gradient is neglected, an extremely simplified solution has been obtained. The simplified solution which has acceptable accuracy provides a good guidance for understanding and predicting the interfacial debonding.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2016;83(12):121010-121010-12. doi:10.1115/1.4034705.

The celebrated solution of the Eshelby ellipsoidal inclusion has laid the cornerstone for many fundamental aspects of micromechanics. A well-known difficulty of this classical solution is to determine the elastic field outside the ellipsoidal inclusion. In this paper, we first analytically present the full displacement field of an ellipsoidal inclusion subjected to uniform eigenstrain. It is demonstrated that the displacements inside inclusion are linearly related to the coordinates and continuous across the interface of inclusion and matrix. The exterior displacement, which is less detailed in existing literatures, may be expressed in a more compact, explicit, and simpler form through utilizing the outward unit normal vector of an auxiliary confocal ellipsoid. Other than many practical applications in geological engineering, the displacement solution can be a convenient starting point to derive the deformation gradient, and subsequently in a straightforward manner to accomplish the full-field solutions of the strain and stress. Following Eshelby's definition, a complete set of the Eshelby tensors corresponding to the displacement, deformation gradient, strain, and stress are expressed in explicit analytical form. Furthermore, the jump conditions to quantify the discontinuities across the interface are discussed and a benchmark problem is provided to validate the present formulation.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2016;83(12):121011-121011-10. doi:10.1115/1.4034829.

The properties and behavior of a surface as well as its interaction with surrounding media depend on the inherent material constituency and the surface topography. Structured surface topography can be achieved via surface wrinkling. Through the buckling of a thin film of stiff material bonded to a substrate of a softer material, wrinkled patterns can be created by inducing compressive stress states in the thin film. Using this same principle, we show the ability to create wrinkled topologies consisting of a highly structured gradient in amplitude and wavelength, and one which can be actively tuned. The mechanics of graded wrinkling are revealed through analytical modeling and finite element analysis, and further demonstrated with experiments.

Commentary by Dr. Valentin Fuster

### Technical Brief

J. Appl. Mech. 2016;83(12):124501-124501-4. doi:10.1115/1.4034619.

The air flow that crosses the cylinderhead of a low-capacity engine is studied both theoretically and experimentally in the steady regime. We analyze the dependence of both the discharge coefficient and swirl number on the Reynolds number and valve lift. The formation of the turbulent vortex in the cylinder is described by measuring the 2D velocity distribution over several cylinder cross sections. The integration of the Reynolds-averaged Navier–Stokes (RANS) equations reproduces satisfactorily the experimental data, especially the swirl number values.

Commentary by Dr. Valentin Fuster

### Announcement

J. Appl. Mech. 2016;83(12):128001-128001-3. doi:10.1115/1.4034462.

From March 16 to 18, 2016, International Union of Theoretical and Applied Mechanics (IUTAM) Symposium on Mechanics of Stretchable Electronics, hosted by Zhejiang University, was held in Hangzhou, China.

Commentary by Dr. Valentin Fuster