A recently developed transfer printing technique, laser-driven noncontact microtransfer printing, which involves laser-induced heating to initiate the separation at the interface between the elastomeric stamp (e.g., polydimethylsiloxane (PDMS)) and hard micro/nanomaterials (e.g., Si chip), is valuable to develop advanced engineering systems such as stretchable and curvilinear electronics. The previous thermomechanical model has identified the delamination mechanism successfully. However, that model is not valid for small-size Si chip because the size effect is ignored for simplification in the derivation of the crack tip energy release rate. This paper establishes an accurate interfacial fracture mechanics model accounting for the size effect of the Si chip. The analytical predictions agree well with finite element analysis. This accurate model may serve as the theoretical basis for system optimization, especially for determining the optimal condition in the laser-driven noncontact microtransfer printing.

Accurate modeling of collagen molecules including their stiffness is essential for our understanding of mechanics of collagen fibers and tissues where these fibers play a prominent role. Studies of mechanical properties of collagen molecules employing various experimental methods and molecular dynamics (MD) simulations yield a broad range of values of the modulus of elasticity. The effect of nonlocal elasticity on the molecule stiffness derived from experiments and simulations is assessed in this brief. The estimate of the correction accounting for the nonlocal effect utilizes the exact solution of the nonlocal elasticity theory for one-dimensional elastic bars. It is demonstrated that the effect of nonlocal elasticity on the stiffness of collagen molecules can be neglected.

An effective yield function is derived for a porous ductile solid near a state of failure by microvoid coalescence. Homogenization theory combined with limit analysis are used to that end. A cylindrical cell is taken to contain a coaxial cylindrical void of finite height. Plastic flow in the intervoid matrix is described by J2 theory while regions above and below the void remain rigid. Velocity boundary conditions are employed which are compatible with an overall uniaxial straining for the cell, a postlocalization kinematics that is ubiquitous during the coalescence of neighboring microvoids in rate-independent solids. Such boundary conditions are not of the uniform strain rate kind, as is the case for Gursonlike models. A similar limit analysis problem for a square-prismatic cell containing a square-prismatic void was posed long ago (Thomason, P. F., 1985, “Three-Dimensional Models for the Plastic Limit–Loads at Incipient Failure of the Intervoid Matrix in Ductile Porous Solids,” Acta Metallurgica, 33, pp. 1079–1085). However, to date a closed-form solution to this problem has been lacking. Instead, an empirical expression of the yield function proposed therein has been widely used in the literature. The fully analytical expression derived here is intended to be used concurrently with a Gursonlike yield function in numerical simulations of ductile fracture.

Recent numerical cell-model studies have revealed the ductile failure mechanism in shear to be governed by the interaction between neighboring voids, which collapse to micro-cracks and continuously rotate and elongate until coalescence occurs. Modeling this failure mechanism is by no means trivial as contact comes into play during the void collapse. In the early studies of this shear failure mechanism, Tvergaard (2009, “Behaviour of Voids in a Shear Field,” Int. J. Fract., 158 , pp. 41-49) suggested a pseudo-contact algorithm, using an internal pressure inside the void to resemble frictionless contact and to avoid unphysical material overlap of the void surface. This simplification is clearly an approximation, which is improved in the present study. The objective of this paper is threefold: (i) to analyze the effect of fully accounting for contact as voids collapse to micro-cracks during intense shear deformation, (ii) to quantify the accuracy of the pseudo-contact approach used in previous studies, and (iii) to analyze the effect of including friction at the void surface with the main focus on its effect on the critical strain at coalescence. When accounting for full contact at the void surface, the deformed voids develop into shapes that closely resemble micro-cracks. It is found that the predictions using the frictionless pseudo-contact approach are in rather good agreement with corresponding simulations that fully account for frictionless contact. In particular, good agreement is found at close to zero stress triaxiality. Furthermore, it is shown that accounting for friction at the void surface strongly postpones the onset of coalescence, hence, increasing the overall material ductility. The changes in overall material behavior are here presented for a wide range of initial material and loading conditions, such as various stress triaxialities, void sizes, and friction coefficients.

A micromechanics approach for assessing the impact of an interfacial thermal resistance, also known as the Kapitza resistance, on the effective thermal conductivity of carbon nanotube-polymer nanocomposites is applied, which includes both the effects of the presence of the hollow region of the carbon nanotube (CNT) and the effects of the interactions amongst the various orientations of CNTs in a random distribution. The interfacial thermal resistance is a nanoscale effect introduced in the form of an interphase layer between the CNT and the polymer matrix in a nanoscale composite cylinder representative volume element to account for the thermal resistance in the radial direction along the length of the nanotube. The end effects of the interfacial thermal resistance are accounted for in a similar manner through the use of an interphase layer between the polymer and the CNT ends. Resulting micromechanics predictions for the effective thermal conductivity of polymer nanocomposites with randomly oriented CNTs, which incorporate input from molecular dynamics for the interfacial thermal resistance, demonstrate the importance of including the hollow region in addition to the interfacial thermal resistance, and compare well with experimental data.

Hydrated biological soft tissue consists of a porous extracellular matrix (ECM) and an interstitial fluid. The poroelastic theory (Biot, 1962), which was originally developed for soil mechanics, has been widely used for mathematical modeling of such hydrated biological tissue. This theory assumes that the ECM is incompressible and purely elastic, and that the interstitial fluid is incompressible and inviscid. The overall viscoelasticity of the tissue is expressed as a result of the frictional interaction between the elastic porous matrix and the interstitial fluid. The poroelastic theory, also known as the biphasic theory (Mow et al., 1980) in the biomechanics field, has served well over the past 20 years as an excellent modeling tool for the interstitial fluid flow-dependent viscoelastic response of hydrated soft tissue. It has been demonstrated that hydrated soft tissue also possesses a significant intrinsic viscoelasticity, independent of the interstitial fluid flow. The biphasic poroviscoelastic (BPVE) theory, which was first introduced by Mak (1986a and 1986b), incorporates a viscoelastic relaxation function into the effective solid stress of the poroelastic theory thus accounting for both intrinsic fluid flow-independent and fluid flow-dependent viscoelasticity. The objective of the present study is to investigate the biphasic poroviscoelastic characteristics of hydrated soft tissue, with an emphasis on the relative contribution of fluid flow-dependent and fluid flow-independent viscoelasticity to the overall viscoelastic behavior of soft tissues.

In this paper, we present a simple and accurate model for the normal force-displacement (NFD) relation for contacting spherical particles, accounting for the effects of plastic deformation. This NFD model, based on the formalism of the continuum theory of elastoplasticity, is to be used in granular flow simulations involving thousands of particles; the efficiency of the model is thus a crucial property. The accuracy of the model allows for an accurate prediction of the contact force level in the plastic regime. In addition to being more accurate than previously proposed NFD models, the proposed NFD model also leads to more accurate coefficient of restitution that is a function of the approaching velocity of two particles in collision. The novelty of the present NFD model is the additive decomposition of the contact-area radius, and the correction of the curvature of the particles at the contact point due to plastic flow. The accuracy of the proposed model is validated against nonlinear finite element results involving plastic flow in both loading and unloading conditions. [S0021-8936(00)03102-0]

A linear bifurcation analysis is presented for pressure sensitive elastoplastic hollow cylinders under radial surface loads. Material response is modeled by flow and deformation theories of the Drucker-Prager solid accounting for arbitrary hardening. Sample calculations are given for cylinders that deform in axially symmetric patterns under uniform radial pressure applied at the boundaries. No bifurcation points were found with flow theory in the realistic range of stress though the primary equilibrium path is nearly identical for both theories. For thick-walled cylinders the dominant bifurcation mode predicted by deformation theory appears to be a circumferential surface instability. Deformation theory results for bifurcations are apparently not sensitive to deviations from associativity.

The focus of this paper is the development of linear, asymptotically correct theories for inhomogeneous orthotropic plates, for example, laminated plates with orthotropic laminae. It is noted that the method used can be easily extended to develop nonlinear theories for plates with generally anisotropic inhomogeneity. The development, based on variational-asymptotic method, begins with three-dimensional elasticity and mathematically splits the analysis into two separate problems: a one-dimensional through-the-thickness analysis and a two-dimensional “plate” analysis. The through-the-thickness analysis provides elastic constants for use in the plate theory and approximate closed-form recovering relations for all truly three-dimensional displacements, stresses, and strains expressed in terms of plate variables. In general, the specific type of plate theory that results from variational-asymptotic method is determined by the method itself. However, the procedure does not determine the plate theory uniquely, and one may use the freedom appeared to simplify the plate theory as much as possible. The simplest and the most suitable for engineering purposes plate theory would be a “Reissner-like” plate theory, also called first-order shear deformation theory. However, it is shown that construction of an asymptotically correct Reissner-like theory for laminated plates is not possible in general. A new point of view on the variational-asymptotic method is presented, leading to an optimization procedure that permits a derived theory to be as close to asymptotical correctness as possible while it is a Reissner-like. This uniquely determines the plate theory. Numerical results from such an optimum Reissner-like theory are presented. These results include comparisons of plate displacement as well as of three-dimensional field variables and are the best of all extant Reissner-like theories. Indeed, they even surpass results from theories that carry many more generalized displacement variables. Although the derivation presented herein is inspired by, and completely equivalent to, the well-known variational-asymptotic method, the new procedure looks different. In fact, one does not have to be familiar with the variational-asymptotic method in order to follow the present derivation.

The ultimate effects of the entrance region on startup flow are considered by one-dimensional steady-state analysis. By roughly accounting for the entrance loss, semiempirical formulas for the average velocity and the hydrodynamic entrance length in terms of a startup flow parameter and an entrance effect coefficient are provided. The startup flow parameter M = gHD 4 /2048v 2 L 2 is identified as the fundamental parameter of the problem. While Szymanski’s solution is recovered in the long pipe limit, i.e., M → 0, the steady-state volume flux through short pipes (M > 0.05) is significantly reduced due to entrance region effects.

A numerical solution is presented for the laminar start-up flow in a circular pipe. It is an extension of the Szymanski solution to include a parameter accounting for the head that must be devoted to the acceleration of the flow. Velocity profiles, wall shear stress, mean velocity history, and start-up time constants are given as a function of the new parameter.

The title problem is solved by estimating the maximum strain rate field in a circular membrane associated with a modal velocity condition when one-half the kinetic energy in the system has been dissipated. The radial stress may only vary in the radial direction, but is taken as a constant with time at any given location. Internal plastic energy absorbed during the large deformation is found by integrating while accounting for rate sensitivity effects; this absorbed energy is equated to the initial kinetic energy in the system to obtain the final deformed configuration. Correlation of analytically determined results with a series of experiments reported elsewhere is very good. The procedure described here is potentially extendable to any planform membrane shape as well as to axisymmetric shells. The method is applicable to plate problems when membrane effects dominate over bending, that is for deformations of the order of two thicknesses or more. A simple general formula for final plate deformation is devised and also agrees well with experimental results.

A method is given for representing analytically defined or data-based covariance kernels of arbitrary random processes in a compact form that results in simplified, analytical, random-vibration transmission studies. The method uses two-dimensional orthogonal functions to represent the covariance kernel of the underlying random process. Such a representation leads to a relatively simple analytical expression for the covariance kernel of the linear system response which consists of two independent groups of terms: one reflecting the input characteristics, and the other accounting for the transmission properties of the excited dynamic system. The utility of the method is demonstrated by application to a covariance kernel widely used in random-vibration studies.

An analytical continuation form of the viscoelastic correspondence principle is presented accounting for frequency dependent complex Lame´ constants. This formulation is especially useful when the elastic frequency response function is available only in numerical form.

A theoretical investigation into the linear, spatial stability of plane laminar jets is presented. The three cases studied are: 1. Inviscid stability of Sato’s velocity profile. 2. Viscous stability of the Bickley’s jet using parallel-flow stability theory. 3. Viscous stability of the Bickley’s jet using a theory modified to account for the inflow terms. The integration of stability equations is started from the outer region of the jet toward the jet axis using the solution of the asymptotic forms of the governing equations. An eigenvalue search technique is employed to find the number of eigenvalues and their approximate location in a closed region of the complex eigenvalue plane. The accurate eigenvalues are obtained using secant method. The inviscid spatial stability theory is found to give results that are in better agreement with Sato’s experimental results than those obtained by him after transformation of the temporal theory results. For the viscous case the critical Reynolds number found by using the theory accounting for inflow is in better agreement with the experimental value than that given by the parallel-flow theory, implying thereby that the parallel-flow approximation for a jet is erroneous for the stability analysis.

The steady-state (ss) stochastic theory of convergent, cohesionless particle flow under gravity toward an orifice in the floor of a semi-infinite bed, based on the statistics of random flight and assuming instantaneous propagation of flow disturbances throughout the bed, is extended to nonsteady-state flow and time lag effects. The new theory, of which the ss theory is a special case, assumes flow to be restricted to an expanding zone, surmounting the orifice (opened at t = 0), of particle density ρ ss , separated from the rest of the bed of the original particle density ρ 0 = ρ ss + Δρ (Δρ > 0) by a boundary whose elements advance with a velocity v n = −(1/Δρ)J n where J n is the normal component of the particle flux on the inside of the boundary due to flow (assumed to be ss) within the zone. Detailed equations describing the flow zone boundary as a function of time and the flow within the zone are developed; the equations depend on two material parameters (Δρ/ρ ss , and α of ss theory) and on the quantity of material drained out. Corrections are derived for the analysis of the z 2 and z 3/2 plots of layer data previously made on the basis of the ss theory. A comparison of the new predictions with one piece of flow data shows the theory capable of accounting for lag effects and for details of the flow pattern in that case. Values of Δρ/ρ ss and α are deduced, the latter being the order of the particle size in conformity to the expectations of the statistical theory.

An experimental and analytical investigation is presented for simultaneous stress relaxation in tension and creep in torsion of polyurethane in the nonlinear range of stresses. The method employed a multiple integral approach with an assumed product form of kernel function to describe creep behavior. The required constants were determined from pure creep experiments on polyurethane. The tension stress and shearing strain versus time for simultaneous stress relaxation and creep were computed from results of these pure creep tests alone, and the results were compared with experiments on the same polyurethane under simultaneous stress relaxation and creep. In the method of analysis, direct inversion of the equation for creep was used as a first approximation for relaxation. Means for obtaining successive approximations and for accounting for cross effects are described. The second approximation was found to be adequate to describe the observed behavior very satisfactorily.

The equations describing the flow of simple non-Newtonian oils in short journal bearings are solved approximately for low eccentricity ratios and small viscosity variations with temperature. An approximate method for predicting the temperature distribution is compared with available experiments and appears to give realistic results. It is also shown that the reduction in friction coefficient observed by Dubois, Ocvirk, and Wehe in experiments with non-Newtonian fluids cannot be explained by accounting for through-film viscosity variations.

In a previous paper the authors proposed constitutive equations for the analytical description of gelling incompressible materials. This set of equations is used to predict the steady-state Couette-type flow between concentric cylinders under relative rotation. The solution for the thixotropic material is given in terms of five material parameters accounting for the phenomena of “breakdown” and “recovery” in rigidity. Analysis shows that dependence of the solution on the loading history occurs if a certain inequality is satisfied by the five material parameters.

A previous analysis of the annular damper was based on the hypothesis that the motion at any instant could be regarded as quasi-steady. This analysis is revised in the present paper by accounting for all accelerations. The decay times are found to be substantially greater (damping less) than those predicted in the previous analysis. A general result for the dissipation in the laminar boundary layer of a liquid oscillating over a rigid wall is developed.