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Journal of Applied Mechanics
Journal Prestige (SJR): 1.133 Citation Impact (citeScore): 2 Number of Followers: 197 Subscription journal ISSN (Print) 0021-8936 - ISSN (Online) 1528-9036 Published by ASME International [25 journals] |
- Probing the Force Field to Identify Potential Energy
- Authors: Xu Y; Virgin LN.
Abstract: A small ball resting on a curve in a gravitational field offers a simple and compelling example of potential energy. The force required to move the ball, or to maintain it in a given position on a slope, is the negative of the vector gradient of the potential field: the steeper the curve, the greater the force required to push the ball up the hill (or keep it from rolling down). We thus observe the turning points (horizontal tangency) of the potential energy shape as positions of equilibrium (in which case the “restoring force” drops to zero). In this paper, we appeal directly to this type of system using both one- and two-dimensional shapes: curves and surfaces. The shapes are produced to a desired mathematical form generally using additive manufacturing, and we use a combination of load cells to measure the forces acting on a small steel ball-bearing subject to gravity. The measured forces, as a function of location, are then subject to integration to recover the potential energy function. The utility of this approach, in addition to pedagogical clarity, concerns extension and applications to more complex systems in which the potential energy would not be typically known a priori, for example, in nonlinear structural mechanics in which the potential energy changes under the influence of a control parameter, but there is the possibility of force probing the configuration space. A brief example of applying this approach to a simple elastic structure is presented.
PubDate: Mon, 05 Aug 2019 00:00:00 GMT
- Authors: Xu Y; Virgin LN.
- Determining Prestrains in an Elastomer Through Elliptical Indentation
- Authors: Zheng Y; Cai S.
Abstract: Residual stresses or prestrains could strongly affect the properties and functionalities of soft materials and tissues. However, non-destructive measurements of residual stresses or prestrains in materials are generally challenging. Previous studies have shown that residual stresses or prestrains can affect indentation tests of different materials, including metals, glassy polymers, soft elastomers, and gels. Nevertheless, an indentation method for determining the state of residual stresses or prestrains of large magnitude in an elastomer is not yet available. In this article, we propose to use elliptical indentation to measure large prestretches in a Neo-Hookean elastomer. We have analytically derived the relationship between the indentation force and indentation depth for both a flat-ended elliptical indenter and an ellipsoidal indenter. We have further shown that such a relationship greatly depends on the rotational angle of the indenter with respect to the direction of principle stretches in the elastomer. Based on the derived analytical results, we construct two diagrams for the flat-ended elliptical indenter and ellipsoidal indenter, respectively, which can be directly used to determine quantitatively large prestrains in an elastomer.
PubDate: Mon, 05 Aug 2019 00:00:00 GMT
- Authors: Zheng Y; Cai S.
- Modeling the Compressive Buckling Strain as a Function of the
Nanocomposite Interphase Thickness in a Carbon Nanotube Sheet Wrapped
Carbon Fiber Composite- Authors: Wang X; Xu T, Zhang R, et al.
Abstract: Polymer matrix composites have high strengths in tension. However, their compressive strengths are much lower than their tensile strengths due to their weak fiber/matrix interfacial shear strengths. We recently developed a new approach to fabricate composites by overwrapping individual carbon fibers or fiber tows with a carbon nanotube sheet and subsequently impregnate them into a matrix to enhance the interfacial shear strengths without degrading the tensile strengths of the carbon fibers. In this study, a theoretical analysis is conducted to identify the appropriate thickness of the nanocomposite interphase region formed by carbon nanotubes embedded in a matrix. Fibers are modeled as an anisotropic elastic material, and the nanocomposite interphase region and the matrix are considered as isotropic. A microbuckling problem is solved for the unidirectional composite under compression. The analytical solution is compared with finite element simulations for verification. It is determined that the critical load at the onset of buckling is lower in an anisotropic carbon fiber composite than in an isotropic fibfer composite due to lower transverse properties in the fibers. An optimal thickness for nanocomposite interphase region is determined, and this finding provides a guidance for the manufacture of composites using aligned carbon nanotubes as fillers in the nanocomposite interphase region.
PubDate: Thu, 18 Jul 2019 00:00:00 GMT
- Authors: Wang X; Xu T, Zhang R, et al.
- A Comparative Study of Cohesive Law Shapes in Analytical Modeling of
Interfacial Debonding in Lithium-Ion Battery Electrodes- Authors: Lu B; Ning C, Zhao Y, et al.
Abstract: To determine the impact of cohesive law shapes on the modeling of interfacial debonding in lithium-ion battery electrodes, analytical methods based on different cohesive models for the debonding process have been developed individually. Three different cohesive laws, namely, triangular, trapezoidal, and rectangular laws, have been employed. To ensure comparability, the cohesive strength and the fracture toughness have been set to be identical for different cohesive laws. The evaluation of debonding onset has suggested that the cohesive law shape affects the modeling results only when the interface is ductile. The largest possible difference for the triangular law and the rectangular law on the debonding onset has been estimated. A discussion for specific electrodes has also been provided.
PubDate: Wed, 17 Jul 2019 00:00:00 GMT
- Authors: Lu B; Ning C, Zhao Y, et al.
- Investigating the Self-Healing of Dynamic Covalent Thermoset Polyimine and
Its Nanocomposites- Authors: Shi C; Zou Z, Lei Z, et al.
Abstract: Self-healable and recyclable materials and electronics can improve the reliability and repairability and can reduce environmental pollution; therefore, they promise very broad applications. In this study, we investigated the self-healing performance of dynamic covalent thermoset polyimine and its nanocomposites based on the dynamic covalent chemistry. Heat press was applied to two laminating films of polyimine and its nanocomposites to induce self-healing. The effects of heat press time, temperature, and load on the interfacial shear strength of the rehealed films were investigated. The results showed that increasing the heat press time, temperature, and load can significantly improve the interfacial shear strength and thus the self-healing effect. For polyimine nanocomposites, increasing the heat press time, temperature, and load led to the improved electrical conductivity of the rehealed films.
PubDate: Wed, 17 Jul 2019 00:00:00 GMT
- Authors: Shi C; Zou Z, Lei Z, et al.
- On Incompressibility Constraint and Crack Direction in Soft Solids
- Authors: Mythravaruni PP; Volokh KY.
Abstract: Most soft materials resist volumetric changes much more than shape distortions. This experimental observation led to the introduction of the incompressibility constraint in the constitutive description of soft materials. The incompressibility constraint provides analytical solutions for problems which, otherwise, could be solved numerically only. However, in the present work, we show that the enforcement of the incompressibility constraint in the analysis of the failure of soft materials can lead to somewhat nonphysical results. We use hyperelasticity with energy limiters to describe the material failure, which starts via the violation of the condition of strong ellipticity. This mathematical condition physically means inability of the material to propagate superimposed waves because cracks nucleate perpendicular to the direction of a possible wave propagation. By enforcing the incompressibility constraint, we sort out longitudinal waves, and consequently, we can miss cracks perpendicular to longitudinal waves. In the present work, we show that such scenario, indeed, occurs in the problems of uniaxial tension and pure shear of natural rubber. We also find that the suppression of longitudinal waves via the incompressibility constraint does not affect the consideration of the material failure in equibiaxial tension and the practically relevant problem of the failure of rubber bearings under combined shear and compression.
PubDate: Wed, 17 Jul 2019 00:00:00 GMT
- Authors: Mythravaruni PP; Volokh KY.
- Formulation of Statistical Linearization for M-D-O-F Systems Subject to
Combined Periodic and Stochastic Excitations- Authors: Spanos PD; Zhang Y, Kong F.
Abstract: A formulation of statistical linearization for multi-degree-of-freedom (M-D-O-F) systems subject to combined mono-frequency periodic and stochastic excitations is presented. The proposed technique is based on coupling the statistical linearization and the harmonic balance concepts. The steady-state system response is expressed as the sum of a periodic (deterministic) component and of a zero-mean stochastic component. Next, the equation of motion leads to a nonlinear vector stochastic ordinary differential equation (ODE) for the zero-mean component of the response. The nonlinear term contains both the zero-mean component and the periodic component, and they are further equivalent to linear elements. Furthermore, due to the presence of the periodic component, these linear elements are approximated by averaging over one period of the excitation. This procedure leads to an equivalent system whose elements depend both on the statistical moments of the zero-mean stochastic component and on the amplitudes of the periodic component of the response. Next, input–output random vibration analysis leads to a set of nonlinear equations involving the preceded amplitudes and statistical moments. This set of equations is supplemented by another set of equations derived by ensuring, in a harmonic balance sense, that the equation of motion of the M-D-O-F system is satisfied after ensemble averaging. Numerical examples of a 2-D-O-F nonlinear system are considered to demonstrate the reliability of the proposed technique by juxtaposing the semi-analytical results with pertinent Monte Carlo simulation data.
PubDate: Wed, 17 Jul 2019 00:00:00 GMT
- Authors: Spanos PD; Zhang Y, Kong F.
- Two-Way Coupling Fluidâ€“Structure Interaction Analysis and Tests of Shaft
Vibration and Clearance Flow Across Plain Annular Seal- Authors: Miyake K; Inoue T, Watanabe Y.
Abstract: Shaft vibration caused by rotor dynamic (RD) fluid force generated by the seal clearance flow has caused several problems. Because such vibration is a coupled phenomenon of clearance flow and shaft vibration, a coupling analysis is essential to solve these problems. In this study, a two-way coupling fluid–structure interaction (FSI) analysis of the seal clearance flow and shaft vibration of a rotor system was conducted and verified through experiments. The rotor system used was a vertical, flexible rotor system with a plain annular seal. In the numerical analysis of the seal clearance flow, the continuity equation and momentum equations, which were averaged across the film thickness, were numerically solved. To suppress the numerical instability, which is unique to the coupling analysis, and improve its numerical stability, a method of successively correcting pressure and shaft acceleration values was adopted so that the continuity equation and rotor equations of motion could be satisfied at every time step. By performing the coupling simulation, the frequency response characteristics of whirling amplitude and leakage flow were investigated. In regard to the stability of the system, the rotational speeds at which self-excited vibration occurs (onset speed of instability: OSI) in its increasing condition and ceases (onset speed of dropdown: OSD) in its decreasing condition were investigated. The coupling analysis results reasonably agree with the experimental results, which demonstrate the validity of the analysis method. In addition, the influence of static eccentricity and whirling amplitude on stability (OSI and OSD) was clarified, which are useful in the design stage of turbomachinery.
PubDate: Wed, 17 Jul 2019 00:00:00 GMT
- Authors: Miyake K; Inoue T, Watanabe Y.
- Belt-Drive Mechanics: Friction in the Absence of Sliding
- Authors: Wu Y; Leamy MJ, Varenberg M.
Abstract: Recent studies have shown that steady and unsteady operation of a belt drive may exhibit regimes absent of sliding at the belt–pulley interface, where instead detachment waves serve to relax stress in the so-called “slip” arc. To explore this finding further, herein we present an experimental and theoretical investigation into frictional mechanics in a simple belt drive system. To estimate friction experimentally, we perform a stress analysis based on spatio-temporal measurements of the belt tension, traction, and contact area evolution. Subsequently, we develop a model taking into account both bulk and surface hysteretic losses to explain the experimental observations. Our results show that the shear strain at the belt–pulley interface differs significantly between the driver and the driven pulleys, resulting in much larger mechanical losses in the driver case. The shear strain drops at the transition from the adhesion to the slip arc, and, in contrast to accepted theories, the slip arc contributes little to nothing to the power transmission. Our model reveals that the contact area evolution correlates to the shear traction changes and that viscoelastic shear and stretching dominate in the belt rolling friction. A significant contribution of detachment waves to the energy dissipation explains the higher mechanical losses observed in the driver case.
PubDate: Thu, 27 Jun 2019 00:00:00 GMT
- Authors: Wu Y; Leamy MJ, Varenberg M.