International Journal of Applied Mechanics

Filled with certain amount of magnetic particles, an elastomer can be made magneto active for numerous applications. When a magneto-active elastomer (MAE) is subject to a homogeneous magnetic field, both magnetostriction and field-stiffening effect can be observed. Inspired by experimental observations and microstructure simulations in the literature, this paper presents a simplified phenomenological model for MAEs by considering a uniaxial deformation state. The model hypothesizes the field-stiffening effect to be a direct consequence of the inverse magnetostriction, i.e., the strain-dependent magnetization, in the context of finite deformation. By taking the elastic energy to be independent of magnetic field and the magnetization energy to be strain dependent, the model can capture both magnetostriction and field stiffening of an MAE. The functional form of the strain-dependent magnetization energy is determined by the underlying microstructure. MAEs with different microstructures exhibit different magnetostriction and field-stiffening behaviors. To predict the behavior of a specific MAE, one only needs to measure the effective permeability of an MAE as a function of the axial strain. The mathematical simplicity of the model could enable simulation and optimization of MAE-based devices under complex loading conditions.

Based on the theory of elasticity, bending and free vibrational analyses of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) beam embedded in piezoelectric layers are carried out, using the state-space differential quadrature method (DQM). Applying the DQM to the governing differential equations and boundary conditions along the longitudinal directions, new state equations about state variables at discrete points are derived. By using the state-space technique across the thickness direction, semi- analytical closed form solutions are derived. The method is validated by comparing numerical results for beams without piezoelectric layers. Both the direct and the inverse piezoelectric effects are investigated and the influence of piezoelectric layers on the mechanical behavior of beam is studied. Furthermore, the effects of CNT volume fraction, kind of CNT distribution, length to thickness ratio and edge boundary conditions on the mechanical behavior of the beams are examined.

A semi-analytic solution is presented for multiple inhomogeneous inclusions and cracks in a half-space under elastohydrodynamic lubrication contact. In formulating the governing equations, each inhomogeneous inclusion embedded under the contacting surfaces is modeled as a homogeneous inclusion with initial eigenstrains plus unknown equivalent eigenstrains by employing Eshelby's equivalent inclusion method, while each crack of mixed modes I and II is treated as a distribution of climb and glide dislocations with unknown densities according to the dislocation distribution technique. Such a treatment converts the problem into a homogeneous lubricated contact with disturbed deformation due to the inclusions and cracks. The unknowns in the governing equations are integrated by a numerical algorithm and determined iteratively by utilizing a modified conjugate gradient method. The iterative process is performed until the convergence of the half-space surface displacements, which involve the displacements due to the inhomogeneous inclusions and cracks as well as the fluid pressure. Samples are presented to demonstrate the generality of the solution.

In the present study, the defect was introduced in the form of missing strut for the individual cell. The effect of defect on the compressive response of carbon-fiber pyramidal truss cores sandwich panel was investigated through experimental and theoretical methods. A series of sandwich panel sample with or without defect was fabricated, and compressive tests were performed at ambient temperature. Scanning electron microscopy (SEM) was conducted on the samples to evaluate the carbon-fiber distribution and failure mode. A revised theoretical model was proposed to predict the effect of defect considering the strut bending and shear behavior. Our results revealed that the compressive moduli of sandwich panel decrease linearly with the fraction of missing struts. Comparing with open-cell foams and honeycombs, the pyramidal truss has better defect tolerance. The theoretical result calculated by the proposed model was in general agreement with experimental result.

In this paper, the bi-axial stretching effects on the electrical conductivity of carbon nanotube (CNT)-polymer composites are studied by a mixed micromechanics model with the consideration of the electrical conductive mechanisms. The bi-axial stretching effects are characterized by volume expansion of composite, re-orientation of CNTs and change of conductive networks. Simulation results demonstrate that the bi-axial stretching decreases the electrical conductivity of the composites due to the dominant role of the stretching-induced change in conductive networks, i.e., the increase in the percolation threshold, the separation distance among CNTs and the breakdown of the networks. It is also found that the bi-axial stretching enhances the decreasing rate of the electrical conductivity and increases the distribution randomness of the CNTs in the bi-axial stretching plane, as compared to a uni-axial stretching case. Furthermore, the dependency of the variation of electrical conductivity on the CNT concentration and sizes is also investigated. Possible reasons for the variation trends are interpreted. The study in this paper is expected to provide an increased understanding on the stretching effects upon the electrical conductivity of CNT-polymer composites.

In this paper, a fourth-order compact stencil finite difference scheme is developed for solving elliptic Poisson equation. The scheme presented here is based on a modular approach using a linear combination of compact difference algorithms that results in different discrete formulation than the well-known Mehrstellen scheme. An adjoint optimal V-cycle multigrid (MG) iterative solver are developed, implemented, and tested. The robustness of the adjoint Poisson solver is illustrated by solving incompressible Navier–Stokes equations in vorticity-stream function formulation. Using a fully implicit factorized delta-scheme algorithm for the time integration, benchmark quality results of the cavity flow problem are presented and compared to existing literature for various Reynolds numbers.

A study of multimodal galloping is carried out on an iced transmission line with thin ice accretions. The partial differential governing equations of iced transmission line are established to describe the nonlinear interactions between the in-plane, out-of-plane and torsional vibration, in which geometrical and aerodynamic nonlinearities are considered. The transformation of modal galloping with the continuous variations of parameters and modal interactions are analyzed based on the reduced model obtained by employing Galerkin spatial discretization. Eigenvalue analysis is applied on linear system to determine the switch of different modal galloping in plane U -l, where Hopf bifurcation occurs and mono-modal, bi-modal and multi-modal galloping are observed. Various numerical procedures are implemented to capture the outstanding nonlinear dynamic features of every regional galloping in plane U -l. Internal resonance is observed and investigated to interpret the phenomenon of modal transition which is also analyzed by accounting for the influence of initial conditions on galloping with either symmetric or anti-symmetric modes.

A new first-order shear deformation theory (FSDT) with pure bending deflection and shearing deflection as two independent variables is presented in this paper for free vibrations of rectangular plate. In this two-variable theory, the shearing deflection is regarded as the only fundamental variable by which the total deflection and bending deflection can be expressed explicitly. In contrast with the conventional three-variable first-order shear plate theory, present variationally consistent theory derived by using Hamiltonian variational principle can uniquely define the bending and the shearing deflections, and give two rotations by the differentiations of bending deflection. Due to more restrictive geometrical constraints on rotations and boundary conditions, the obtained natural frequencies are equal to or higher than those by conventional FSDT for the rectangular plate with at least one pair of opposite edges simply supported. This new theory is of considerable significance in theoretical sense for giving a simple two-variable FSDT which is variational consistent and involve rotary inertia and shear deformation. The relation and differences of present theory with conventional FSDT and other relative formulations are discussed in detail.

The problem of the shape optimization of acoustic enclosures is investigated in this paper. A general procedure, comprising a Wavelet–Garlerkin formulation and a so-called vertex-driven shape optimization is proposed to deal with the general problem of internal sound field prediction and the optimization of the boundary shape. It is shown that, owing to the compactly supported orthogonal property and the remarkable fitting ability, Daubechies Wavelet can be used as a global basis to approximate the unknown sound field on a relatively large interval globally instead of piecewise approximation like most of element based methods do. This feature avoids meshing the boundary of the enclosure, although vertex points are needed to define the boundary shape, whose positions keep updating during the shape optimization process. A rectangular enclosure is used as benchmark to assess and validate the proposed formulation, by investigating the influence of some key parameters involved in the formulation. It was shown that the sound pressure along the entire boundary of the rectangular enclosure can be accurately approximated without meshing. The same enclosure with an inner rigid acoustic screen is then used to reduce the sound pressure level within a chosen area through optimizing the shape of the screen, which shows the remarkable potentials of the proposed approach as a shape optimal tool for inner sound field problems.

Molecular dynamics simulations (MDSs) are carried on to examine the effects of liquid–nanoparticle (NP) interaction strength, size and number of nanoparticles on the aggregation process in liquid-based nanofluid flowing inside nanochannel. The results show that the increase in liquid–NP interaction strength leads to the reduction of aggregation rate. In addition, the increase in the size and number of NPs leads to more aggregation rate. Predicted results for aggregation trend are in good agreement with experimental data. Likewise, variations of velocity profile and density distribution of liquid particles inside nanochannel are explored.

A general visco-hyperelastic model for dielectric elastomers (DE) is presented in this paper, derived from the Quasi-Linear Viscoelastic (QLV) framework. To gain a physical insight into the time-dependent constitutive relation and solve it efficiently, a complex frequency representation of the convolution integral equation, with the legible form of block-scheme, is specifically constructed, in which the viscoelastic stress is interpreted considering the instantaneous response (depicted by Yeoh strain energy potential) as a signal filtered by a linear system (superposition of characteristic modes of the time relaxation function, i.e., Prony series). By incorporating the effects of electrostatic pressure, the model is further extended to the electromechanical coupling state, which can be expediently implemented by the general software, MATLAB/Simulink. Comparisons of the theoretical predictions from the proposed model with the experimental results previously reported (for VHB elastomers) show good agreements over a wide range of stretch rates (from 10^-4 to ~ 1 s^-1), whether the membrane is only subjected to large mechanical deformations, or undergoes electric loads simultaneously.

In the present paper, for linear elastic materials, effects of couple stresses on micro/nanosolids are physically discussed and mathematically represented in the context of the classical, the modified and the consistent couple–stress theories. Then, an evaluation is provided showing the validity and the limit of applicability of each one of these theories. At first, the possible couple stress effects on mechanics of particles and on continuum mechanics are represented. Then, a reasoning comparison with examples is performed to discuss and evaluate the way that each one of these theories represents the couple stress effects.

In the context of the classical couple–stress theory, two higher-order material constants are introduced in addition to the conventional ones to capture the microstructure rigid rotation effects. Recently, two alternative theories, the modified couple–stress and the consistent couple–stress theories, with only one additional material constant are introduced with contradictory points of view. Authors of these two alternative theories gave apparently strong motivations for their opposed points of view. Therefore, through the present paper, it will be convenient to analyze the essential points of view based on which these alternative theories are proposed since they lead to exactly opposed conclusions. Thus their essential points of view are discussed and evaluated showing their consistency with the fundamental concepts of the couple stress effects.

It has been shown that the scientific bases of these two alternative theories are not consistent with the representation of the couple–stress effects on micro/nanocontinua. Based on discussions and results through the paper, both the modified theory and the consistent theory represent, only, simplifications for the classical couple–stress theory but they did not able to well represent the possible effects of couple stresses and they are limited for only two categories of linear elastic materials problems. This demolishes the scientific points of view based on which the two theories are proposed.

In this paper, an analytical model is developed to investigate sound transmission loss characteristic of adhesively bonded metal sandwich panels with pyramidal lattice truss cores based on 3D elasticity theory. Meanwhile, practical specimen is fabricated to conduct corresponding sound insulation experiment test via a standing wave tube method. The effective elastic constant of truss cores is derived using one homogenization theory on account of equivalent strain energy. It is found that satisfactory agreement is achieved between theoretical solutions and experiment results, and damping effect of adhesive bonding interface between facesheets and core has a great impact on transmission loss. Further parameter investigations demonstrate the significant effect of the elevation and azimuth angles of the pyramidal cores, which can be conveniently changed to tailor the acoustic performance of the sandwich panels in the whole frequency range.

In this paper, we present a mathematical model for the peristaltic flow of a Newtonian fluid in an axisymmetric channel with small aspect ratio. In particular, we study the effects of the wave length of the wall oscillation distinguishing between long wave length (same order of the vessel's length) and short wave length (same order of the vessel's radius). We prove that the oscillation produces flow even in the absence of a pressure gradient in case of long wave. In case of short wave length, peristalsis does not affect the flow. We also prove that, in both cases, the tube resistance increases as the oscillation amplitude increases.

Single-molecule dynamic force spectroscopy (DFS) is a powerful tool for studying mechanical forces of molecular interactions. Recently, the important role of bond rebinding in DSF experiments was recognized, which intrigued mounting researches in this direction. In this work, we study how the bond rebinding influences the strength of single-molecular bonds using Brownian dynamics (BD) simulations and theoretical modeling. Our results show that bond rebinding significantly enhances the strength of single-molecular bond at ultralow loading rates. The rebinding behavior strongly depends on the loading stiffness, suggesting that the strength of single-molecular bond is not only dependent on its intrinsic property, but also the stiffness of loading device. By connecting our new model with conventional theories that did not consider the rebinding effect and are only applied to high loading rates, we propose a unified scheme to predict the rupture forces in a full range of loading rate in DSF experiments and simulations.