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Research Papers

J. Appl. Mech. 2017;84(4):041001-041001-9. doi:10.1115/1.4035522.

High-frequency mechanical excitation has been shown to generate heat within composite energetic materials and even induce reactions in single energetic crystals embedded within an elastic binder. To further the understanding of how wave scattering effects attributable to the presence of an energetic crystal can result in concentrated heating near the inclusion, an analytical model is developed. The stress and displacement solutions associated with the scattering of compressional plane waves by a spherical obstacle (Pao and Mow, 1963, “Scattering of Plane Compressional Waves by a Spherical Obstacle,” J. Appl. Phys., 34(3), pp. 493–499) are modified to account for the viscoelastic effects of the lossy media surrounding the inclusion (Gaunaurd and Uberall, 1978, “Theory of Resonant Scattering From Spherical Cavities in Elastic and Viscoelastic Media,” J. Acoust. Soc. Am., 63(6), pp. 1699–1712). The results from this solution are then utilized to estimate the spatial heat generation due to the harmonic straining of the material, and the temperature field of the system is predicted for a given duration of time. It is shown that for certain excitation and sample configurations, the elicited thermal response near the inclusion may approach, or even exceed, the decomposition temperatures of various energetic materials. Although this prediction indicates that viscoelastic heating of the binder may initiate decomposition of the crystal even in the absence of defects such as initial voids or debonding between the crystal and binder, the thermal response resulting from this bulk heating phenomenon may be a precursor to dynamic events associated with such crystal-scale effects.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2017;84(4):041002-041002-6. doi:10.1115/1.4035858.

Mechanics of tympanic membrane (TM) is crucial for investigating the acoustic transmission through the ear. In this study, we studied the wrinkling behavior of tympanic membrane when it is exposed to mismatched air pressure between the ambient and the middle ear. The Rayleigh–Ritz method is adopted to analyze the critical wrinkling pressure and the fundamental eigenmode. An approximate analytical solution is obtained and validated by finite element analysis (FEA). The model will be useful in future investigations on how the wrinkling deformation of the TM alters the acoustic transmission function of the ear.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2017;84(4):041003-041003-11. doi:10.1115/1.4035785.

This paper extends the approach for determining the three-dimensional global displaced shape of slender structures from a limited set of scalar surface strain measurements. It is an exhaustive approach that captures the effect of curvature, shear, torsion, and elongation. The theory developed provides both a determination of the uniaxial strain (in a given direction) anywhere in the structure and the deformed shape, given a set of strain values. The approach utilizes Cosserat rod theory and exploits a localized linearization approach that helps to obtain a local basis function set for the displacement solution in the Cosserat frame. For the assumed deformed shape (both the midcurve and the cross-sectional orientation), the uniaxial value of strain in any given direction is obtained analytically, and this strain model is the basis used to predict the shape via an approximate local linearized solution strategy. Error analysis due to noise in measured strain values and in uncertainty in the proximal boundary condition is performed showing uniform convergence with increased sensor count.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2017;84(4):041004-041004-11. doi:10.1115/1.4035523.

Knowledge of the subcritical crack growth (SCG) in cement-based materials subject to concurrent physical and chemical attacks is of great importance for understanding and mitigating the chemomechanical deterioration in concrete structural members. In this study, the SCG in hardened cement pastes is investigated experimentally by a novel test approach aided with microcharacterization. In the test, specimens of negative geometry are designed, which enable the use of load control to trigger stable crack propagation in hardened cement pastes. Multiple specimens, cast from the same batch of mixture, are exposed to the same chemical condition and loaded at the same age. With the aid of a high-resolution microscopy system, which is used to trace the crack tip, the average trend and the associated variation of the dependence of crack velocity v on the stress intensity factor K at the crack tip are obtained. Different from static fatigue, three distinctive regions are captured in the K–v curves of specimens experiencing chemomechanical deterioration. With the help of advanced techniques including scanning electron microscopy (SEM), atomic-force microscopy (AFM), and Raman spectroscopy, the microstructure destruction and chemical composition change induced by the imposed chemomechanical attack are characterized at different stages. In addition to the physical insights for deeper understanding of the coupled effect of chemomechanical attack, these experimental results provide important macro- and microscopic benchmarks for the theoretical modeling and numerical investigation in the future studies.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2017;84(4):041005-041005-10. doi:10.1115/1.4035930.

An analytical study is presented of the covariance kernels of a damped, linear, two-degrees-of-freedom (2DOF) system which resembles a primary system that is provided with an auxiliary mass damper (AMD), in addition to an “inerter” (a device that imparts additional inertia to the vibration damper, hence magnifying its effectiveness without a significant damper mass addition). The coupled 2DOF system is subjected to nonstationary stochastic excitation consisting of a modulated white noise. An exponential function, resembling the envelope of a typical earthquake, is considered. Results of the analysis are used to determine the dependence of the peak transient mean-square response of the system on the damper/inerter tuning parameters, and the shape of the deterministic intensity function. It is shown that, under favorable dynamic environments, a properly designed auxiliary damper, encompassing an inerter with a sizable mass ratio, can significantly attenuate the response of the primary system to broad band excitations; however, the dimensionless “rise-time” of the nonstationary excitation substantially reduces the effectiveness of such a class of devices (even when optimally tuned) in attenuating the peak dynamic response of the primary system.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2017;84(4):041006-041006-10. doi:10.1115/1.4035932.

Due to the oscillatory singular stress field around a crack tip, interface fracture has some peculiar features. This paper is focused on two of them. One can be reflected by a proposed paradox that geometrically similar structures with interface cracks under similar loadings may have different failure behaviors. The other one is that the existing fracture parameters of the oscillatory singular stress field, such as a complex stress intensity factor, exhibit some nonobjectivity because their phase angle depends on an arbitrarily chosen length. In this paper, two objective and independent fracture parameters are proposed which can fully characterize the stress field near the crack tip. One parameter represents the stress intensity with classical unit of stress intensity factors. It is interesting to find that the loading mode can be characterized by a length as the other parameter, which can properly reflect the phase of the stress oscillation with respect to the distance to the crack tip. This is quite different from other crack tip fields in which the loading mode is usually expressed by a phase angle. The corresponding failure criterion for interface cracks does not include any arbitrarily chosen quantity and, therefore, is convenient for comparing and accumulating experimental results, even existing ones. The non-self-similarity of the stress field near an interface crack tip is also interpreted, which is the major reason leading to many differences between the interfacial fracture and the fracture in homogenous materials.

Commentary by Dr. Valentin Fuster

Technical Brief

J. Appl. Mech. 2017;84(4):044501-044501-5. doi:10.1115/1.4035931.

The principals of interfacial fracture mechanics and modified Gibbs adsorption equation are utilized to provide a predictive correlation for the macroscopic (effective) fracture toughness of polymer-based adhesive interfaces, exposed to varying level of contaminant concentration. The macroscopic fracture toughness measurement by double cantilever beam test exhibits a progressive deterioration with the increase of the contaminant surface concentration. The associated variation of fracture surface morphology exhibits ductile-to-brittle failure transition, caused by the contamination-induced suppression of plastic deformation within the adhesive layer. The corresponding intrinsic interfacial surface energy is extracted by finite-element simulation, employing surface-based cohesive elements. The modified Gibbs adsorption equation is utilized to correlate the contamination-induced degradation of the interfacial surface energy as a function of contaminant surface concentration. Interfacial fracture mechanics principals are applied to extend the correlation to the macroscopic fracture toughness of the interface. With additional examination of other systems, the proposed correlation may provide the basis for nondestructive evaluation of bond line integrity, exposed to different levels of contaminant.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2017;84(4):044502-044502-9. doi:10.1115/1.4035857.

A round elevator traveling cable is modeled using a singularity-free beam formulation. Equilibria of the traveling cable with different elevator car positions are studied. Natural frequencies and the corresponding mode shapes of the traveling cable are calculated and they are in excellent agreement with those calculated by abaqus. In-plane natural frequencies of the traveling cable do not change much with the car position compared with its out-of-plane ones. Dynamic responses of the traveling cable are calculated and they are in good agreement with those from commercial multibody dynamics software recurdyn. Effects of vertical motion of the car on free responses of the traveling cable and those of in-plane and out-of-plane building sways on forced responses are investigated.

Commentary by Dr. Valentin Fuster

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