Bulk strain energy density in randomly reinforced polymer composites with antifriction dispersed additives

Bulk strain energy density was numerically simulated for epoxy-phenol-based composites randomly reinforced with short polyimide fibers, with antifriction dispersed polytetrafluoroethylene (PTFE) additives. A mathematical model was constructed using the notion of a stress concentration operator (fourth-rank tensor) that relates volume averaged, or external, stresses within a heterogeneous material with their local values within an individual heterogeneity. The simulation was based on a generalized singular approximation of random field theory used to solve a stochastic differential equation of equilibrium of an elastic medium. This approximation yields an explicit expression for stress concentration in a composite material. The explicit expression allows one to analyze the distribution of bulk strain energy density depending on the composition, structure, volume and mass fraction of heterogeneities, and on the type and value of applied load. We studied how the considered energy characteristic depends on the type of external mechanical loading and concentration of isotropic components in the model composites. It is shown that with the increasing concentration of polyimide fibers at a fixed concentration of PTFE inclusions, the bulk strain energy density values of all components decrease and approach each other independently of the type of external loading. The form of these dependences is nonlinear. A change in the mass fraction of dispersed PTFE inclusions in the model composites exerts little effect on local energy values of all components under any of the considered applied external loads.     

Free energies of supercritical solvation from molecular dynamics simulation and integral equation studies

We present here molecular dynamics (MD) simulation and integral equation (IE) studies on free energies of solvation of a non-polar solute in a dilute supercritical solvent to estimate the contribution of inhomogeneities in solvent density to the free energy of solvation. The solvation of a Xe-like solute in an Ne-like solvent as well as that of naphthalene in CO₂ have been investigated. At state points in the compressible region in the neighborhood of the solvent critical point, we have utilized the IE estimates of free energies to model the ideal situation where local density inhomogeneities would be absent. The difference between the free energies in the presence (as derived from MD simulation) and in the absence (from IE) of local density inhomogeneities was studied as a function of density along an isotherm close to the critical point. Although for low density supercritical solvents, a marked difference is observed, a study of the density dependence of this difference across the critical density does not directly reveal any signature of local density enhancement on the thermodynamics of solvation.     

A BBGKY-based density gradient approximation of interparticle forces: Application for discrete Boltzmann methods

The force term accounting for interparticle interactions, with application to discrete Boltzmann simulation methods, is derived using a density gradient expansion of the BBGKY collision operator. It is shown that previous calculations, based on essentially the same mean-field-theory philosophy, do not apply the density gradient approximation in a self consistent fashion. Thus these previous models have errors in the second virial coefficient as well as coefficients associated with gradient terms in the pressure tensor. This new treatment corrects these shortcomings.     

振动驱动颗粒气体体系的局域态本构关系的实验验证

对准二维、水平边界振动驱动的颗粒气体体系的流体力学 参量进行了局域态本构关系的实验研究. 实验观测结果与经典动力学理论预测进行了比较.由于颗粒气体空间分布的不均匀性, 颗粒体系的整体本构关系不成立, 有必要对局域态进行分析. 局域态本构关系是指颗粒系统的局域温度、局域压强和局域数密度之间的关系. 通过颗粒速度的方向变化, 可以得到颗粒的碰撞点. 因此在计算压力张量的对角线项时, 除了动力学部分之外, 我们计入了颗粒碰撞的影响, 得到了一个约为常数的压力张量迹, 即颗粒压强的空间分布, 与流体力学理论预测以及分子动力学模拟结果相符合; 但是颗粒温度和数密度的空间分布, 在振动的正反两个方向的分量出现差异, 并且温度、压强和数密度之间的局域本构关系, 无论在低密度或高密度区域, 实验与理论预测在定性上一致, 但定量上都有较大差别. 因此经典流体力学理论在描述这样的体系时需加以修正. 关键词： 颗粒气体 态方程 流体力学     

Charged dilaton,energy, momentum and angular-momentum in teleparallel theory equivalent to general relativity

We apply the energy-momentum tensor to calculate energy, momentum and angular-momentum of two different tetrad fields. This tensor is coordinate independent of the gravitational field established in the Hamiltonian structure of the teleparallel equivalent of general relativity (TEGR). The spacetime of these tetrad fields is the charged dilaton. Our results show that the energy associated with one of these tetrad fields is consistent, while the other one does not show this consistency. Therefore, we use the regularized expression of the gravitational energy-momentum tensor of the TEGR. We investigate the energy within the external event horizon using the definition of the gravitational energy-momentum. PACS 04.70.Bw; 04.50.+h; 04.20.-Jb     

Optical momentum transfer to absorbing mie particles

The momentum transfer to absorbing particles is derived from the Lorentz force density without prior assumption of the momentum of light in media. We develop a view of momentum conservation rooted in the stress tensor formalism that is based on the separation of momentum contributions to bound and free currents and charges consistent with the Lorentz force density. This is in contrast with the usual separation of material and field contributions. The theory is applied to predict a decrease in optical momentum transfer to Mie particles due to absorption, which contrasts the common intuition based on the scattering and absorption by Rayleigh particles.     

Electromagnetic angular momentum flux tensor in a medium

Electromagnetic angular momentum describes the ability of electromagnetic field to impose torque on matter. We show that for an electromagnetic field ?C such as an optical beam field ?C in a medium, the torque density is determined by two fundamental quantities: the angular momentum flux tensor and the angular momentum density of the field. It is remarkable that the tensor alone gives the full picture of the angular momentum transfer between the field and the medium in all stationary electromagnetic phenomena. We derive a general expression for this tensor and apply the theory to several important examples without resorting to the classical paraxial approximation.     

Complete determination of the stress tensor of a polarization-maintaining fiber by photoelastic tomography

The use of photoelastic tomography to obtain the two-dimensional axial stress profile of a polarization-maintaining (PM) fiber with high resolution and accuracy is described. We illustrate, for what is believed to be the first time, the two-dimensional distribution of the local principal axes of the fiber's cross section, which is directly related to the fiber's PM ability. We demonstrate that the stress-induced anisotropy as well as all the stress tensor components of the fiber can be fully determined.     

On the calculation of forces and total energy changes via the quantum mechanical stress field

Many-electron systems are within density functional theory described in terms of an appropriately defined local stress tensor. The differential equation for its exchange and correlation part is solved also for the case of density gradient dependent exchange and correlation energy. Formulae are given (i) for the direct calculation of the global stress tensor of a homogeneously strained crystal via surface integrals of the local stress tensor along intercell boundaries, and (ii) similarly for the energy change of inhomogeneously strained crystals.     

Theory of surface tension and its application to simple fluids

We consider a liquid-vapor interface in thermal equilibrium. The tangential component of the pressure tensor is supposed to depend explicitly upon the position and the density profile. Under this hypothesis the mechanical definition of surface tension becomes a finite summation ofN+1 terms related directly to the local compressibility. When the inhomogeneous compressibility equation is considered, the theory provides a microscopic expression of the surface tension coefficient. A calculation for argon near the critical point is done; the agreement with experiment is satisfactory.     

Axiomatic renormalization of the stress tensor of a conformally invariant field in conformally flat spacetimes

Using only the general properties which the renormalized stress-energy tensor T_μν should satisfy—and not relying on any assumptions associated with specific renormalization techniques—we derive the expression for T_μν for conformally invariant fields in conformally flat spacetimes of two and four dimensions. In two dimensions, these arguments rederive the Davies-Fulling-Unruh expression for the stress tensor of a scalar field; in four dimensions the results agree with those of Brown and Cassidy, except that we exclude the local curvature term depending on fourth-order derivatives of the metric. The dynamics of a k = 0 Robertson-Walker universe filled with radiation of the conformally invariant field is investigated and it is found that the equations cease to admit a solution when the Planck density is reached.     

Internal structure of a classical spinning electron

A classical model of the spinning electron in general relativity consisting of a rotating charge distribution with Poincaré stresses is set up. It is made out of a continuous superposition of thin charged shells with differential rotation. Each elementary shell is maintained in stationary equilibrium in the gravitational field created by the others. A class of interior solutions of the Kerr-Newman field is thus obtained. The corresponding stress-energy tensor naturally splits into the sum of two terms. The first one is the Maxwell tensor associated to a rotating charge distribution, and the second one corresponds to a material source having zero energy density everywhere, no radial pressure, and an isotropic transverse stress. These negative pressures or tensions are identified with the cohesive forces introduced by Poincaré to stabilize the Lorentz electron model. They are shown to be the source of a negative gravitational mass density and thereby of the violation of the energy conditions inside the electron.     

The stress tensor of an atomistic system

We prove that the stress tensor conservation equation expressing the local equilibrium condition of a body results from the invariance of its partition function under canonical point transformations. From this result the expression of the stress tensor of a general atomistic system (with short range interactions) in terms of its microscopic degrees of freedom can be obtained. The derivation, which can be extended to encompass the quantum mechanical case, works in the canonical as well as the micro-canonical ensemble and is valid for systems endowed with arbitrary boundary conditions. As an interesting by-product of our general approach, we are able to positively answer the old question concerning the uniqueness of the stress tensor expression.     

Scaling laws for the response of nonlinear elastic media with implications for cell mechanics

We show how strain stiffening affects the elastic response to internal forces, caused either by material defects and inhomogeneities or by active forces that molecular motors generate in living cells. For a spherical force dipole in a material with a strongly nonlinear strain energy density, strains change sign with distance, indicating that, even around a contractile inclusion or molecular motor, there is radial compression; it is only at a long distance that one recovers the linear response in which the medium is radially stretched. Scaling laws with irrational exponents relate the far-field renormalized strain to the near-field strain applied by the inclusion or active force.     

Optical rectification effect due to surface plasmon polaritons at normal incidence in a nondiffraction regime

We carried out an experimental and numerical investigation of photoinduced voltage at normal incidence in the nondiffraction regime, which was not predicted to occur by the simple momentum conservation model. We prepared two samples: one having space inversion symmetry and the other without this feature. At normal incidence in the nondiffraction regime, we observed a finite signal only for the asymmetric structure. We found that surface plasmon polaritons (SPPs) are excited by the signal and are attributed to the origin of the voltage. We also evaluated the radiation force of light by using the Maxwell stress tensor and found that pressure of light and not shear force is mainly induced in the structure due to the asymmetric excitation of SPPs.     

Can the definition of mechanical stress tensor be applied to a dielectric fluid in an electrostatic or magnetostatic field?

Summary It is proved that, for an uncharged and linear dielectric fluid at rest and in local equilibrium in an electrostatic or magnetostatic field, the definition of stress tensor employed in continuum mechanics is inconsistent with the assumption that the stress tensor depends only on the local values of mass density, temperature, electric- or magnetic-field components and the derivatives of these quantities with respect to space and time.     

A material frame approach for evaluating continuum variables in atomistic simulations

We present a material frame formulation analogous to the spatial frame formulation developed by Hardy, whereby expressions for continuum mechanical variables such as stress and heat flux are derived from atomic-scale quantities intrinsic to molecular simulation. This formulation is ideally suited for developing an atomistic-to-continuum correspondence for solid mechanics problems. We derive expressions for the first Piola–Kirchhoff (P–K) stress tensor and the material frame heat flux vector directly from the momentum and energy balances using localization functions in a reference configuration. The resulting P–K stress tensor, unlike the Cauchy expression, has no explicit kinetic contribution. The referential heat flux vector likewise lacks the kinetic contribution appearing in its spatial frame counterpart. Using a proof for a special case and molecular dynamics simulations, we show that our P–K stress expression nonetheless represents a full measure of stress that is consistent with both the system virial and the Cauchy stress expression developed by Hardy. We also present an expanded formulation to define continuum variables from micromorphic continuum theory, which is suitable for the analysis of materials represented by directional bonding at the atomic scale.