Multiple interacting circular nano-inhomogeneities with surface/interface effects

A two-dimensional problem of multiple interacting circular nano-inhomogeneities or/and nano-pores is considered. The analysis is based on the Gurtin and Murdoch model [Gurtin, M.E., Murdoch, A.I., 1975. A continuum theory of elastic material surfaces. Arch. Ration. Mech. Anal. 57, 291–323.] in which the interfaces between the nano-inhomogeneities and the matrix are regarded as material surfaces that possess their own mechanical properties and surface tension. The precise component forms of Gurtin and Murdoch's three-dimensional equations are derived for interfaces of arbitrary shape to provide a basis for critical review of various modifications used in the literature. The two-dimensional specification of these equations is considered and their representation in terms of complex variables is provided. A semi-analytical method is proposed to solve the problem. Solutions to several example problems are presented to: (i) examine the difference between the results obtained with the original and modified Gurtin and Murdoch's equations, (ii) compare the results obtained using Gurtin and Murdoch's model and those for a problem of nano-inhomogeneities with thin membrane-type interphase layers, and (iii) demonstrate the effectiveness of the approach in solving problems with multiple nano-inhomogeneities.     

Dynamic interaction between a sub-interface crack and the interface in a bi-material: time-domain BEM analysis

Summary Transient response of a sub-interface crack in a bi-material is studied with emphasis on the dynamic interaction between the crack and the interface, by combining the traditional time-domain displacement boundary element method (BEM) and the non-hypersingular traction BEM. Computations are performed for an unbounded bi-material with a crack subjected to impact tensile loading on its faces or incident impact waves and a bounded rectangular bi-material plate under remote impact tensile loading. Numerical results of the dynamic stress intensity factors (DSIFs) and dynamic interface tractions are presented for various material combinations and crack locations. It is shown that pronounced increases in DSIFs and the interface tractions may be caused in some cases because of the dynamic interaction between the crack and the interface.This work was initialized during the second author's stay at Institute of Mechanics, TU Darmstadt, Germany under the support of the Alexander von Humboldt Foundation. Discussion on the BEM formulation with Dr. Seelig is gratefully acknowledged. The first two authors are also grateful for the partial support by the China National Natural Science Foundation under Grant No. 10025211 and the NJTU Scientific Paper Fund (PD195).     

Numerical simulation of the hydrodynamic interaction between a sedimenting particle and a neutrally buoyant particle

A new method for the simulation of the translational and rotational motions of a system containing a sedimenting particle interacting with a neutrally buoyant particle has been developed. The method is based on coupling the quasi-static Stokes equations for the fluid with the rigid body equations of motion for the particles. The Stokes equations are solved at each time step with the boundary element method. The stresses are then integrated over the surface of each particle to determine the resultant forces and moments. These forces and moments are inserted into the rigid body equations of motion to determine the translational and rotational motions of the particles. Unlike many other simulation techniques, no restrictions are placed on the shape of the particles. Superparametric boundary elements are employed to achieve accurate geometric representations of the particles. The simulation method is able to predict the local fluid velocity, resolve the forces and moments exerted on the particles, and track the particle trajectories and orientations.     

Periodic array of traction-free interface cracks subjected to far-field uniform heat flow

A periodic array of interface cracks is subjected to a uniform heat flow in the far field. The crack opening displacements and complex stress intensity factors are determined, using analytic function theory, for the case that the upper half-space is less distortive than the lower half-space.     

Analysis of matching conditions at the boundary surface of a fluid-saturated porous solid and a bulk fluid: the use of Lagrange multipliers

The compatibility conditions matching macroscopic mechanical fields at the contact surface between a fluid-saturated porous solid and an adjacent bulk fluid are considered. The general form of balance equations at that discontinuity surface are analyzed to obtain the compatibility conditions for the tangent and normal components of the velocity and the stress vector fields. Considerations are based on the procedure similar to that used in the phenomenological thermodynamics for derivation of constitutive relations, where the entropy inequality and the concept of Lagrange multipliers are applied. This procedure made possible to derive the compatibility conditions for the viscous fluid flowing tangentially and perpendicularly to the boundary surface of the porous solid and to formulate the generalized form of the so called slip condition for the fluid velocity field, postulated earlier by Beavers and Joseph, J. Fluid. Mech. 30, 197–207 (1967). PACS 47.55.Mh Communicated by Y.D. Shikhmurzaev     

Surface waves at the interface between an inviscid fluid and a dipolar gradient solid

This paper is about the dispersion analysis of surface waves propagating at the interface between an inviscid fluid and a higher gradient homogeneous elastic solid modelled as a dipolar gradient continuum. In order to compare the results, a second gradient model is also evaluated. The analysis is carried out by finding the roots of the secular equation, and by carefully studying their physical meaning. As it is well known, higher gradient continua are dispersive, i.e. phase and group velocities are frequency dependent. As a consequence, the existence of surface waves will indeed depend on frequency. In order to investigate the behaviour of surface waves in this specific fluid–solid configuration, a complete dispersion analysis is performed, with a particular focus on the frequency range in which the phase velocity of shear waves is lower than the speed of waves of the fluid. Surface waves of the type Leaky Rayleigh and Scholte–Stoneley are observed in this frequency range. This work extends the knowledge on surface waves in the case of higher gradient solids and applications of these results can be found in the field of non-destructive damage evaluation in micro structured materials, composites, metamaterials and biological tissues.     

Energy Approach to the Formulation of Boundary Problems of Nonlinear Thermomechanics for Elastic Systems

An energy approach is proposed to derive the physical constitutive equations of nonlinear thermomechanics for inertial elastic systems. A potential of local inertial thermodynamic state and a potential of thermoelastic energy dissipation are introduced. The variational formulation of nonlinear boundary problems of thermoelasticity is implemented on the basis of the Hamiltonian energy functional. Sufficient conditions for the convexity of the functional are formulated __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 9, pp. 52–59, September 2005.     

Flutter instability of a fluid-conveying fluid-immersed pipe affixed to a rigid body

A set of simplified boundary conditions for a flexible beam connected to a rigid body at one end and free at the other end is presented and applied to the case of a fluid-conveying, fluid-immersed pipe. These boundary conditions represent an analytically tractable approximation to those of a submersible which uses a combination of jet action and flutter instability induced tail motion to produce thrust. The boundary conditions are made non-dimensional, and the effect of the non-dimensional mass of the rigid body on system stability is assessed. The neutral stability of this system is determined within a two-parameter space consisting of the velocity of the fluid within the tail, and the forward speed of the submersible. Equations in the literature, derived using slender-body theory, were used to compute the sign of the thrust produced by the tail and the tail's Froude efficiency for the neutrally stable waveforms of the beam.     

Thermomechanics of a heterogeneous fluctuating chain

In this paper we present a theory to efficiently calculate the thermo-mechanical properties of fluctuating heterogeneous rods and chains. The central problem is to evaluate the partition function and free energy of a general heterogeneous chain under the assumption that its energy can be expressed as a quadratic function in the kinematic variables that characterize the configurations of the chain. We analyze the effects of various types of boundary conditions on the fluctuations of the rods and chains and show that our results are in agreement with recent work on homogeneous rods. The results for the heterogeneous chains are verified through Monte Carlo simulations. Finally, we consider a special heterogeneous chain with only two bending moduli and use it as a model to interpret experiments on partially unfolded protein oligomers.     

On 3-d analog of the second basic problem of the theory of elasticity for a cylindrical solid

We formulate and solve the 3-d analog of the second basic problem for a cylindrical elastic solid.     

On 3-d strains in a thin coat of a plane domain

We formulate and solve the boundary value problem for a thin coat of a plane domain.     

Dynamic behaviour of a bubble near an elastic infinite interface

This paper presents a study to describe the behaviour of a non-equilibrium bubble in a fluid (Fluid 1) that is in contact with another fluid (Fluid 2). Fluid 2 is assumed to incorporate some elastic properties, which are modelled through a pressure term at the fluid–fluid interface. The Laplace equation is assumed to be valid in both fluids and the boundary integral method is employed to simulate the dynamics of the bubble and the fluid–fluid interface. Interesting characteristic phenomena concerning bubble oscillations and the deformation of the fluid–fluid interface are studied for a range of parameters (distance from the fluid–fluid interface, density ratios of the two fluids and elastic properties of Fluid 2). Some of the phenomena observed are jet formation in the bubble, bubble splitting, a ring bubble separating from the main bubble, mushroom-shaped bubbles and the dynamic elevation of the elastic interface. Most of these phenomena are only observed when Fluid 2 possesses some elastic properties (besides the usual formation of a high speed liquid jet). Comparisons with experimental observations confirm the validity of our simulations.     

Non-linear free surface flows and an application of the Orlanski boundary condition

The focus of this paper is the analysis of spatially two-dimensional non-linear free surface problems. The critical aspects of the problem concern the treatment of the non-linear free surface, the body boundary condition for large motions and the imposition of suitable radiation conditions. To address such complexities, time domain simulation was chosen as the method of analysis. With the use of a finite domain for simulation, a major concern is with the radiation condition to be applied at the open or truncation boundary. For the two-dimensional problem at hand, no theoretical radiation conditions are known to exist. An extension of the Orlanski open boundary condition, based on phase velocity determination at the free surface, is proposed. Three categories of problems were analysed using numerical simulation-namely, freely moving steep waves, waves over a submerged body and forced body motion. Simulation results have been compared with linear theory and experiments.     

Investigation on the choice of boundary conditions and shape functions for flexible multi-body system

The objective of this investigation is to examine the correctness and efficiency of the choice of boundary conditions when using assumed mode approach to simulate flexible multi-body systems. The displacement field due to deformation is approximated by the Rayleigh-Ritz assumed modes in floating frame of reference (FFR) formulation. The deformations obtained by the absolute nodal coordinate (ANC) formulation which are transformed by two sets of reference coordinates are introduced as a criterion to verify the accuracy of the simulation results by using the FFR formulation. The relationship between the deformations obtained from different boundary conditions is revealed. Numerical simulation examples demonstrate that the assumed modes with cantilevered-free, simply-supported and freefree boundary conditions without inclusion of rigid body modes are suitable for simulation of flexible multi-body system with large over all motion, and the same physical deformation can be obtained using those mode functions, differ only by a coordinate transformation. It is also shown that when using mode shapes with statically indeterminate boundary conditions, significant error may occur. Furthermore, the slider crank mechanism with rigid crank is accurate enough for investigating boundary condition problem of flexible multi-body system, which cost significant less simulating time.     

g-Jitter free convection flow in the stagnation-point region of a three-dimensional body

A numerical solution of the effect of a small fluctuating gravitational field characteristic of g-jitter is presented. Specifically the problem of free convection boundary layer flow near a three-dimensional stagnation point of attachment resulting from a step change in its constant surface temperature is considered. The transformed non-similar boundary layer equations are solved using the Keller-box method, which is essentially an implicit finite-difference scheme. Numerical results are given for a value of the Prandtl number, Pr = 0.72 with the forcing amplitude, ε, and the forcing frequency, Ω. It is shown that g-jitter affects considerably the flow characteristics, namely the skin friction and the rate of heat transfer. Comparison with earlier results for the case of constant gravity field show very good agreement.     

Electrodynamics and Thermomechanics of Material Bodies

We consider a material body emersed in space and, relative to an aether frame, the balance laws which govern its interaction with an electromagnetic, thermal and mechanical environment. A detailed formulation of a non-relativistic theory for studying thermomechanical–electromagnetic processes in deformable media is presented and certain invariance issues are discussed. The idea of an isolated process in a given aether frame is introduced and we identify a related non-increasing Lyapunov function for such processes. This function suggests the structure of a class of minimization problems within the statical theory and we discuss a typical problem within the area of elastic dielectrics.      

On the no-slip boundary conditions for squeeze flow of viscous fluids

A typical class of boundary conditions for squeeze flow problems in lubrication approximation is the one in which the squeezing rate and the width between the squeezing plates are constant. This hypothesis is justified by claiming that the plates moves so slowly that they can be considered static. In this short note we prove that this assumption leads to a contradiction and hence cannot be used.     

On boundary conditions and plastic strain-gradient discontinuity in lower-order gradient plasticity

Through linearized analysis and computation, we show that lower-order gradient plasticity is compatible with boundary conditions, thus expanding its predictive capability. A physically motivated gradient modification of the conventional Voce hardening law is shown to lead to a convective stabilizing effect in 1-D, rate-independent plasticity. The partial differential equation is genuinely nonlinear and does not arise as a conservation law, thus making the task of inferring plausible boundary conditions a delicate matter. Implications of wave-type behavior in rate-independent plastic response (under conditions of static equilibrium) are analyzed with a discussion of an appropriate numerical algorithm. Example problems are solved numerically, showing the robustness and simplicity of physically motivated lower-order gradient plasticity. The 3-D case and rate-dependent constitutive assumptions are also discussed.     

An inviscid model for vortex shedding from a deforming body

An inviscid vortex sheet model is developed in order to study the unsteady separated flow past a two-dimensional deforming body which moves with a prescribed motion in an otherwise quiescent fluid. Following Jones (J Fluid Mech 496, 405–441, 2003) the flow is assumed to comprise of a bound vortex sheet attached to the body and two separate vortex sheets originating at the edges. The complex conjugate velocity potential is expressed explicitly in terms of the bound vortex sheet strength and the edge circulations through a boundary integral representation. It is shown that Kelvin’s circulation theorem, along with the conditions of continuity of the normal velocity across the body and the boundedness of the velocity field, yields a coupled system of equations for the unknown bound vortex sheet strength and the edge circulations. A general numerical treatment is developed for the singular principal value integrals arising in the solution procedure. The model is validated against the results of Jones (J Fluid Mech 496, 405–441, 2003) for computations involving a rigid flat plate and is subsequently applied to the flapping foil experiments of Heathcote et al. (AIAA J, 42, 2196–2204, 2004) in order to predict the thrust coefficient. The utility of the model in simulating aquatic locomotion is also demonstrated, with vortex shedding suppressed at the leading edge of the swimming body.      

On the numerical computation of laminar boundary layers at a phase-changing,gas-liquid interface

The two-dimensional, laminar boundary-layer equations of heat, mass and momentum at a smooth, phase-changing, gas-liquid interface are solved numerically by the Keller Box method. The gas and liquid regimes are embedded in a single marching scheme which computes interfacial parameters implicitly. Results of both self-similar and non-similar boundary-layer computations are presented and effects of mild pressure gradient, a mean current in the liquid, and free-stream vapour concentration on the interfacial parameters are analysed. In order to assess the accuracy of the method, several self-similar problems are solved by Runge-Kutta integration and results are compared to those obtained by the finite-difference scheme. Agreement is excellent in all cases.