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Research Papers

J. Appl. Mech. 2017;85(3):031001-031001-10. doi:10.1115/1.4038718.

Guided by the experimental observations in the literature, this paper discusses two possible modes of defect growth in soft solids for which the size-dependent fracture mechanics is not always applicable. One is omni-directional growth, in which the cavity expands irreversibly in all directions; and the other is localized cracking along a plane. A characteristic material length is introduced, which may shed light on the dominant growth mode for defects of different sizes. To help determine the associated material properties from experimental measurement, the driving force of defect growth as a function of the remote load is calculated for both modes accordingly. Consequently, one may relate the measured critical load to the critical driving force and eventually to the associated material parameters. For comprehensiveness, the calculations here cover a class of hyperelastic materials. As an application of the proposed hypothesis, the experimental results (Cristiano et al., 2010, “An Experimental Investigation of Fracture by Cavitation of Model Elastomeric Networks,” J. Polym. Sci. Part B: Polym. Phys., 48(13), pp. 1409–1422) from two polymers with long and short chain elastomeric network are examined. The two polymers seem to be susceptible to either of the two dominating modes, respectively. The results are interpreted, and the material characteristic length and other growth parameters are determined.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2018;85(3):031002-031002-10. doi:10.1115/1.4038749.

A comprehensive study is reported herein for the evaluation of Lagrangian functions for linear systems possessing symmetric or nonsymmetric coefficient matrices. Contrary to popular beliefs, it is shown that many coupled linear systems do not admit Lagrangian functions. In addition, Lagrangian functions generally cannot be determined by system decoupling unless further restriction such as classical damping is assumed. However, a scalar function that plays the role of a Lagrangian function can be determined for any linear system by decoupling. This generalized Lagrangian function produces the equations of motion and it contains information on system properties, yet it satisfies a modified version of the Euler–Lagrange equations. Subject to this interpretation, a solution to the inverse problem of linear Lagrangian dynamics is provided.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2018;85(3):031003-031003-10. doi:10.1115/1.4038719.

Penny-shaped fluid-driven cracks are often detected in many fluid–solid interaction problems. We study the combined effect of pressure and shear stress on the crack propagation in an impermeable elastic full space. Boundary integral equations are presented, by using the integral transform method, for a penny-shaped crack under normal and shear stresses. The crack propagation criterion of stress intensity factor is examined with the strain energy release rate. Dominant regimes are obtained by using a scaling analysis. Asymptotic solution of the toughness-dominant regime is derived to show the effect of shear stress on the crack opening, crack length, and pressure distribution. The results indicate that a singular shear stress can dominate the asymptotic property of the stress field near the crack tip, and the stress intensity factor cannot be calculated even though the energy release rate is finite. Shear stress leads to a smaller crack opening, a longer crack, and a slightly larger wellbore pressure. A novel dominant-regime transition between shear stress and pressure is found. Unstable crack propagation occurs in the shear stress-dominant regime. This study may help in understanding crack problems under symmetrical loads and modeling fluid–solid interactions at the crack surfaces.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2018;85(3):031004-031004-16. doi:10.1115/1.4038770.

Soft electroactive materials can undergo large deformation subjected to either mechanical or electrical stimulus, and hence, they can be excellent candidates for designing extremely flexible and adaptive structures and devices. This paper proposes a simple one-dimensional soft phononic crystal (PC) cylinder made of dielectric elastomer (DE) to show how large deformation and electric field can be used jointly to tune the longitudinal waves propagating in the PC. A series of soft electrodes, which are mechanically negligible, are placed periodically along the DE cylinder, and hence, the material can be regarded as uniform in the undeformed state. This is also the case for the uniformly prestretched state induced by a static axial force only. The effective periodicity of the structure is then achieved through two loading paths, i.e., by maintaining the longitudinal stretch and applying an electric voltage over any two neighboring electrodes or by holding the axial force and applying the voltage. All physical field variables for both configurations can be determined exactly based on the nonlinear theory of electroelasticity. An infinitesimal wave motion is further superimposed on the predeformed configurations, and the corresponding dispersion equations are derived analytically by invoking the linearized theory for incremental motions. Numerical examples are finally considered to show the tunability of wave propagation behavior in the soft PC cylinder. The outstanding performance regarding the band gap (BG) property of the proposed soft dielectric PC is clearly demonstrated by comparing with the conventional design adopting the hard piezoelectric material. One particular point that should be emphasized is that soft dielectric PCs are susceptible to various kinds of failure (buckling, electromechanical instability (EMI), electric breakdown (EB), etc.), imposing corresponding limits on the external stimuli. This has been carefully examined for the present soft PC cylinder such that the applied electric voltage is always assumed to be less than the critical voltage except for one case, in which we illustrate that the snap-through instability of the axially free PC cylinder made of a generalized Gent material may be used to efficiently trigger a sharp transition in the BGs.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2018;85(3):031005-031005-5. doi:10.1115/1.4038884.

Knowledge of the ideal shear strength of solid single crystals is of fundamental importance. However, it is very hard to determine this quantity at finite temperatures. In this work, a theoretical model for the temperature-dependent ideal shear strength of solid single crystals is established in the view of energy. To test the drawn model, the ideal shear properties of Al, Cu, and Ni single crystals are calculated and compared with that existing in the literature. The study shows that the ideal shear strength first remains approximately constant and then decreases almost linearly as temperature changes from absolute zero to melting point. As an example of application, the “brittleness parameter” of solids at elevated temperatures is quantitatively characterized for the first time.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2018;85(3):031006-031006-6. doi:10.1115/1.4038809.

Scar structures of natural animals can reinforce the wounds both mechanically and biologically to maintain the functions of the injured muscle and skin. Inspired by the scar structure, we present a dielectric elastomer (DE) with silver nanowire electrodes possessing the scar-like ability. This DE membrane can tolerate the failures by both electric breakdown and mechanical rupture. The DE actuator (DEA) can maintain their performances of force and displacement output after multiple failures. Scanning electronic microscope (SEM) images show that the scar-like structures accumulate around the electromechanical failure locations on the DE membrane as the stiffened and insulated regions, which prevent further short current and membrane rupture. J-integrals and stress distribution around the failure location have been calculated by finite element analysis to verify the mechanical reinforcements of the scar-like structures over crack propagation.

Commentary by Dr. Valentin Fuster

Technical Brief

J. Appl. Mech. 2018;85(3):034501-034501-4. doi:10.1115/1.4038808.

Configurational forces acting on two-dimensional (2D) elastic line singularities are evaluated by path-independent J-, M-, and L-integrals in the framework of plane strain linear elasticity. The elastic line singularities considered in this study are the edge dislocation, the line force, the nuclei of strain, and the concentrated couple moment that are subjected to far-field loads. The interaction forces between two similar parallel elastic singularities are also calculated. Self-similar expansion force, M, evaluated for the line force shows that it is exactly the negative of the strain energy prelogarithmic factor as in the case for the well-known edge dislocation result. It is also shown that the M-integral result for the nuclei of strain and the L-integral result for the line force yield interesting nonzero expressions under certain circumstances.

Topics: Stress , Dislocations
Commentary by Dr. Valentin Fuster

Design Innovation Paper

J. Appl. Mech. 2018;85(3):035001-035001-9. doi:10.1115/1.4038697.

The models of normal and tangential oil film damping are established by modeling the viscous-elastic fluid as massless damping elements. The central pressure and film thickness distributions, friction coefficient, and maximum temperature rise with or without considering thermal effect indicate the proposed damping models and the solutions to the damping are valid. Thereafter, the thermal effect on oil film damping is discussed and the effects of contact force, rotation speed, and tooth number of spur gears in line contact non-Newtonian transient thermal elastohydrodynamic lubrication (EHL) on the oil film damping are investigated. The results imply that the larger damping in the normal direction is beneficial to meshing impact resistance and vibration reduction, whereas the smaller damping in the tangential direction is very helpful for fluidity enhancement and friction heat inhibition.

Commentary by Dr. Valentin Fuster

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