Establishing experiments to find material functions in tensor nonlinear constitutive relations

The basic scheme of an establishing experiment to find two material functions of two invariants in the constitutive relations of a nonlinear incompressible tensor medium, is described. A combination of radial spreading and two one-dimensional shears in mutually perpendicular directions observed in a cylindrical layer is taken as the base flow of such a medium. Percolation is possible at the boundaries of cylinders, but the so-called tangential component of the medium coincides with the velocity of cylinder motion. The fundamental question of a viscous potential existing for each medium is posed.     

High speed imaging for material parameters calibration at high strain rate

To describe the material behaviour at high strain rates dynamic experimental tests are necessary, and appropriate constitutive models are to be calibrated accordingly. A way to achieve this is through an inverse procedure, based on the minimization of an error function calculated as the difference between experimental and numerical data coming from Finite Element analysis. This approach, widely used in the literature, has a heavy computational cost associated with the minimization process that requires, for each variation of the material model parameters, the execution of FE calculations. In this work, a faster but yet effective calibration procedure is studied Experimental tests were performed on an aluminium alloy AA6061-T6, by means of a direct tension-compression Split Hopkinson bar. A fast camera with a resolution of 192 × 128 pixels and capable of a sample rate of 100,000?fps captured images of the deformation process undergone by the samples during the tests. The profile of the sample obtained after the image binarization and processing, was postprocessed to derive the deformation history; afterwards it was possible to calculate the true stress and strain, and carry out the inverse calibration by analytical computations. The results of this method were compared with the ones coming from the Finite Element approach.     

Nonlinear constitutive law for ferroelectric/ferroelastic material and its finite element realization

The hysteresis phenomena of ferroelectric/ferroelastic material in polarization procedure are investigated. Some assumptions are presented based on the published experimental data. The electrical yielding criterion, mechanical yielding criterion and isotropic hardening model are established. The flow theory in incremental forms in polarization procedure is presented. The nonlinear constitutive law for electrical-mechanical coupling is proposed phenomenologically. Finally, the nonlinear constitutive law expressed in a form of matrices and vectors, which is immediately associated with finite element analysis, is formulated. In the example problem of a rectangular specimen subjected to a uniaxial electric field, the procedure from virgin state to fully polarized state is simulated. Afterward, a uniaxial compressive loading is applied to depolarizing the specimen. Results are in agreement with the experimental data.     

Comments on boundary problems and electromagnetic constitutive parameters

In [A. Lakhtakia, Boundary-value problems and the validity of the Post constraint in modern electromagnetism, Optik 117 (2006) 188-192; A. Lakhtakia, On boundary conditions and constitution of homogeneous materials, Microwave Opt. Technol. Lett. 48(1) (2006) 56-57], claims are made concerning such constitutive scalars that are absent in the fundamental differential equations for spatially homogeneous media in frequency-domain electromagnetism. These claims are essentially saying that such scalars on two sides of a material boundary cannot appear in the boundary conditions. This comment examines the problem of a linearly polarized plane wave hitting a boundary where one of such scalars, namely the Tellegen parameter (the non-reciprocity parameter of bi-isotropic materials) changes. We show that the discontinuity clearly has an effect on the boundary conditions and therefore on the reflection of the wave, thus invalidating the conclusions of [A. Lakhtakia, Boundary-value problems and the validity of the Post constraint in modern electromagnetism, Optik 117 (2006) 188-192; A. Lakhtakia, On boundary conditions and constitution of homogeneous materials, Microwave Opt. Technol. Lett. 48(1) (2006) 56-57].     

Effects of material strain on triboelectric charging: Influence of material properties

We address electrostatic charging of unstrained and strained latex rubber sheets contacted with a series of materials: polytetrafluoroethylene (PTFE), polyurethane (PU) and stainless steel (SS). For PTFE, strain causes a reversal in the direction of charge transfer. For PU, the direction of charge transfer is reversed after repeated contacts due to material transfer, and strain increases the number of contacts needed for this reversal. For SS, strain reduces the frequency of electrical discharges occurring. These effects may be explained by strain either changing material properties relevant to triboelectric charging, or changing the nature of contact between the surfaces.     

Equivalent constitutive model-based design of wave-absorbing material system and controller

A design methodology for wave-absorbing active material system is reported. The design enforces equivalence between an assumed material model having wave-absorbing behavior and a set of target feedback controllers for an array of microelectro-mechanical transducers which are integral part of the active material system. The proposed methodology is applicable to problems involving the control of acoustic waves in passive-active material system with complex constitutive behavior at different length-scales. A stress relaxation type one-dimensional constitutive model involving viscous damping mechanism is considered, which shows asymmetric wave dispersion characteristics about the half-line. The acoustic power flow and asymptotic stability of such material system are studied. A single sensor non-collocated linear feedback control system in a one-dimensional finite waveguide, which is a representative volume element in an active material system, is considered. Equivalence between the exact dynamic equilibrium of these two systems is imposed. It results in the solution space of the design variables, namely the equivalent damping coefficient, the wavelength(s) to be controlled and the location of the sensor. The characteristics of the controller transfer functions and their pole-placement problem are studied.     

Phenomenological relations for neutrino masses and mixing parameters

Phenomenological relations for masses, angles, and CP phases in the neutrino mixing matrix are proposed with allowance for available experimental data. For the case of CP violation in the lepton sector, an analysis of the possible structure of the neutrino mass matrix and a calculation of the neutrino mass features and the Dirac CP phase for the bimodal-neutrino model are performed. The values obtained in this way can be used to interpret and predict the results of various neutrino experiments.     

Approximately linear relations between two-nucleon and three-nucleon parameters

The correlation between the triton binding energyE _t and then-d scattering length² a and the zero energy singlet and triplet wound integral I_os and I_ot is investigated, with phaseequivalent separableNN interactions obeying all the important off-shell constraints. It is found that the correlation betweenE _t and² a is stronger than betweenE _t (² a) andI _os ,I _ot separately. A strong correlation is also found between the percentageD-state in the deuteronP _d andI _ot . Fixing all the other off-shell parameters but allowing variations ofI _os andI _ot leads to surprisingly accurate linear relations betweenE _t(² a) andI _os ,I _ot (P _d). These relations depend strongly on the other off-shell parameters.     

Flow stress/strain rate/grain size coupling for fcc nanopolycrystals

A Hall–Petch (H–P)-type dependence is demonstrated for reciprocal activation volume measurements for nanocrystalline and conventional grain size, strengthened Ni and Cu materials, consistent with predictions derived from the dislocation pile-up model. The observed H–P dependence indicates that the shear stress for cross-slip must be involved in the full grain size regime for transmission of plastic flow at the grain boundaries of fcc metals.     

Response to comments on boundary problems and electromagnetic constitutive parameters

The positive conclusion on the recognizable existence of the Tellegen parameter, which invalidates the Post constraint, arrived at in the Comment of Sihvola and Tretyakov through the solution of a boundary-value problem relies on a framework of macroscopic electromagnetism that lacks a microscopic basis. But the microscopic viewpoint underlying the framework of modern macroscopic electromagnetism invalidates the boundary conditions used therein, and instead validates the Post constraint.     

Crystallographic variant selection of martensite at high stress/strain

The phenomenological theory of martensitic transformation is well understood that the displacive phase transformations are mainly influenced by the externally applied stress. Martensitic transformation occurs with 24 possible Kurdjomov-Sachs (K-S) variants, where each variant shows a distinct lattice orientation. The elegant transformation texture model of Kundu and Bhadeshia for crystallographic variant selection of martensite in metastable austenite at various stress/strain levels has been assessed in this present research. The corresponding interaction energies have also been evaluated. Encouraging correlation between model prediction and experimental data generation for martensite pole figures at many deformed austenite grains has been observed at different stress/strain levels. It has been investigated that the mechanical driving force alone is able to explain the observed martensite microtextures at all stress/strain levels under uniaxial tensile deformation of metastable austenite under low temperature at a slow strain rate. The present investigation also proves that the Patel and Cohen’s classical theory can be utilized to predict the crystallographic variant selection, if it is correctly used along with the phenomenological theory of martensite crystallography.     

Dispersion relations of vector and scalar bosons in material media

Bulletin of the Lebedev Physics Institute - The dispersion relations of vector, scalar, and pseudo-scalar bosons of a dielectric medium are determined taking into account their resonant interaction...     

Residual stress/strain analysis in thin films by X-ray diffraction

Residual stresses are found in the majority of multilayer thin film structures used in modem technology. The measurement and modeling of such stress fields and the elucidation of their effects on structural reliability and device operation have been a “growth area” in the literature, with contributions from authors in various scientific and engineering disciplines.

In this article the measurement of the residual stresses in thin film structures with X-ray diffraction techniques is reviewed and the interpretation of such data and their relationship to mechanical reliability concerns are discussed.     

Finite element analysis of stress and strain distributions in InAs/GaAs quantum dots

In this paper, we perform systematic calculations of the stress and strain distributions in InAs/GaAs truncated pyramidal quantum dots (QDs) with different wetting layer (WL) thickness, using the finite element method (FEM). The stresses and strains are concentrated at the boundaries of the WL and QDs, are reduced gradually from the boundaries to the interior, and tend to a uniform state for the positions away from the boundaries. The maximal strain energy density occurs at the vicinity of the interface between the WL and the substrate. The stresses, strains and released strain energy are reduced gradually with increasing WL thickness. The above results show that a critical WL thickness may exist, and the stress and strain distributions can make the growth of QDs a growth of strained three-dimensional island when the WL thickness is above the critical value, and FEM can be applied to investigate such nanosystems, QDs, and the relevant results are supported by the experiments.     

Effective electromagnetic and chiral parameters of chiral composite material

The effective parameters of chiral composite are studied using a simple model, that is, randomly oriented non-interacting wire helices embedded in a nonchiral host medium. It is found that both the effective permittivity and permeability are independent on the handedness of the chiral objects while the effective chirality admittance is dependent. It is also found that when the ratio of the radius of the chiral helix to its pitch is about 0.23, maximum chirality admittance is achieved. The effective parameters of equichiral sample are also discussed.     

Finite strain stress fields near the tip of an interface crack between a soft incompressible elastic material and a rigid substrate

We present a numerical study of finite strain stress fields near the tip of an interface crack between a rigid substrate and an incompressible hyperelastic solid using the finite element method (FEM). The finite element (FE) simulations make use of a remeshing scheme to overcome mesh distortion. Analyses are carried out by assuming that the crack tip is either pinned, i.e., the elastic material is perfectly bonded (no slip) to the rigid substrate, or the crack lies on a frictionless interface. We focus on a material which hardens exponentially. To explore the effect of geometric constraint on the near tip stress fields, simulations are carried out under plane stress and plane strain conditions. For both the frictionless interface and the pinned crack under plane stress deformation, we found that the true stress field directly ahead of the crack tip is dominated by the normal opening stress and the crack face opens up smoothly. This is also true for an interface crack along a frictionless boundary in plane strain deformation. However, for a pinned interface crack under plane strain deformation, the true opening normal stress is found to be lower than the shear stress and the transverse normal stress. Also, the crack opening profile for a pinned crack under plane strain deformation is completely different from those seen in plane stress and in plane strain (frictionless interface). The crack face flips over and the tip angle is almost tangential to the interface. Our results suggest that interface friction can play a very important role in interfacial fracture of soft materials on hard substrates.     

An invariant theory of the constitutive parameters of a plasma and a ferrite

Under the influence of a constant magnetic field, the electric property of a plasma and the magnetic property of a ferrite are anisotropic. In this paper, the general coordinatefree invariant forms of the dielectric tensor of a plasma and the permeability tensor of a ferrite are obtained. The tensors are expressed explicitly as a sum of three tensors: a unit tensor, a symmetric tensor and an antisymmetric tensor, each of which is weighted by different constants. The symmetric and antisymmetric tensors are related to the unit vector of the constant magnetic field. The invariant forms in terms of the sum of the projectors of the tensors are also derived. When a Cartesian coordinate system is introduced, the invariant forms are easily reduced to the commonly used matrix representations. The invariant forms clearly show the effects of the constant magnetic field on the anisotropies of the media. Moreover, they effectuate and simplify the deduction of the general solutions of problems involving wave propagation and excitation in plasma and ferrite and thus facilitate interpretations of the final results.     

高导无氧铜的高压与高应变率本构模型研究

基于Y/G及G/B为常数的假设,构建了高导无氧铜的七种高压与高应变率本构模型.对于高导无氧铜进行了平面冲击波试验,采用纵向与横向锰铜应力计记录了试件中的纵向与横向应力,从而得到了屈服应力历史.用所构建的七种本构模型进行了数值模拟,并与高导无氧铜的平面冲击波试验结果进行比较.结果表明,平面冲击波载荷下高导无氧铜的屈服强度对于压力、密度、温度以及塑性应变的依赖性是本构描述的关键.而由Hopkinson试验取得的高导无氧铜高应变率本构模型,并不适合描述平面冲击波载荷下的本构特性. 关键词： 本构模型 高导无氧铜 平面冲击波试验 锰铜应力计