An evaluation of the computational error near the boundary withmagnetostatic field calculation by BEM

A 3-D magnetostatic field is calculated using the reduced scalar potential method for a two-region model: a current-free iron region with linear and isotropic property, and an air region including the source domain. An unstable computational error near the boundary is investigated from the viewpoints of numerical integration and discretization. Specifically it is shown that near the boundary elements, the calculated results of the magnetic flux density often contain an unstable error. The error is affected by the fineness of the discretization, the point number for Gaussian quadrature, and the distance from the boundary elements. It is found that close integration of the internal field calculation effectively removes the unstable computational error     

Inside Front Cover: Experimental Evidence for Superprism Effects in Three‐Dimensional Polymer Photonic Crystals (Adv. Mater. 2/2006)

The inside cover illustrates the highly dispersive propagation of light in a three‐dimensional polymer photonic crystal. White light is coupled into a woodpile structure and split into its wavelength components due to the frequency‐dependent dispersion properties of the structure. This superprism effect is orders of magnitudes higher than in a conventional glass prism and is caused by the strong anisotropy of the dispersion surface at frequencies slightly above the photonic bandgap. In work reported on p. 221, Serbin and Gu fabricated these woodpile structures operating in the near‐infrared wavelength range by means of two‐photon polymerization and give theoretical and experimental evidence for the superprism effect in these low‐index photonic‐crystal structures.     

Developments in a least squares asymptotic analysis of isochromatic data from stress concentration regions in plane problems

A complete separation of stresses throughout the entire stress concentration region near notches in plane, isotropic, linearly elastic plates is achieved using only isochromatic (difference of principal stresses) data. These data, which are obtained easily by conventional photoelastic techniques, are analysed by a non-linear least squares technique based upon previously derived equations describing the asymptotic character of the rapidly varying stress field near the root of the notch. This paper demonstrates that isochromatic data of typical experimental accuracy from relatively few, arbitrarily located data points within the highly stressed region is sufficient to accurately predict the entire stress field, including location and magnitude of critical stress(es).     

Study of hardening and cyclic plastic behaviour around the crack tip of C(T) specimen made by as‐received and annealed copper

The purpose of this research is determining experimentally the characteristics of tension and cyclic plastic behaviours of as‐received and annealed coppers and studying distribution of stress/strain field near the crack tip. Samples made by pure copper were annealed at 420°C for 40 minutes in electric furnace. To determine the properties of the cyclic plastic behaviour, proper tests with symmetric strain‐controlled conditions were performed on standard samples. Chaboche nonlinear hardening model was used to determine the cyclic plastic behaviour of both materials. According to results, annealing process creates isotropic hardening in the copper and also changes its initial kinematic hardening behaviour. Effects of the annealing and hardening on the variations of the stresses and strains around the crack tip were investigated. Also, ratcheting and mean stress relaxations versus number of cycles, inside the plastic region, were studied.     

Anomalous refractive properties of photonic crystals

We describe methods of investigating the behavior of photonic crystals. Our approach establishes a link between the dispersion relation of the Bloch modes for an infinite crystal (which describes the intrinsic properties of the photonic crystal in the absence of an incident field) and the diffraction problem of a grating (finite photonic crystal) illuminated by an incident field. We point out the relationship between the translation operator of the first problem and the transfer matrix of the second. The eigenvalues of the transfer matrix contain information about the dispersion relation. This approach enables us to answer questions such as When does ultrarefraction occur? Can the photonic crystal simulate a homogeneous and isotropic material with low effective index? This approach also enables us to determine suitable parameters to obtain ultrarefractive or negative refraction properties and to design optical devices such as highly dispersive microprisms and ultrarefractive microlenses. Rigorous computations add a quantitative aspect and demonstrate the relevance of our approach.     

裂纹稳态扩展下正交异性材料的动应力强度因子K_(Ⅲ)解答

研究了无限大正交异性材料中半无限长Ⅲ型裂纹的动态扩展问题。裂纹尖端附近的应力和位移被表达为解析复函数的形式,而复函数可以表达为幂级数的形式,幂级数的系数由研究问题的边界条件来确定。这样就给出了裂纹尖端附近的应力分量和位移分量的简单近似表达式,由推导出的动应力分量和动位移分量可以退化为其在各向同性材料静态断裂问题中的情况。最后,裂纹扩展特性由裂纹几何参数和裂纹扩展速度来反映出来,相同的几何参数情况下,裂纹扩展愈快,裂纹尖端附近的最大应力分量和最大位移分量愈大。     

On the application of Biot's theory to acoustic wave propagation in snow

A fluid-saturated, elastic, porous media model is used to describe acoustic wave propagation in snow. This model predicts the existence of two dilatational waves and a shear wave. In homogeneous, isotropic snow the two dilatational waves are uncoupled from one another but involve coupled motion between the interstitial air and ice skeleton. Dilatational waves of the first kind and shear waves are slightly dispersive and attenuated with distance. Dilatational waves of the second kind are strongly dispersive and highly attenuated. The model also predicts that the wave impedance for snow is close to that of air and that snow strongly absorbs acoustic wave energy.Available experimental phase velocity, impedance and attenuation data support the calculated results. Phase velocity measurements indicate three identifiable categories: fast dilatational waves (phase velocity ? 500 m/s), slow dilatational waves (phase velocity < 500 m/s) and shear waves. Wave impedance and attenuation measurements illustrate the low impedance, highly absorbing characteristics of snow. Additional impedance, attenuation and phase velocity data are required to further test and improve the model.     

Asymptotic fields near an interface corner in orthotropic bi-materials

Based on the existing asymptotic solutions of the displacement and singular stress fields in the vicinity of a singular point in 2D orthotropic elastic materials, the two simple eigenequations are explicitly given for the symmetric and anti-symmetric deformation modes to determine the orders of the stress singularity at the interface corner in orthotropic bi-materials, respectively. The related displacement and singular stress fields near the interface corner are also explicitly established. The relevant stress intensity factors are defined as in the case of crack problems. The theoretical results have been confirmed by numerical, finite-element-based results in a special bi-material case. The solution obtained in this paper may be applied to the interface corner in the orthotropic/orthotropic, orthotropic/isotropic, and isotropic/isotropic bi-materials, and it will be very useful to evaluate the strength of the bonded orthotropic bi-materials with interface corners.     

The role of a loading surface in viscoplasticity theory

Summary A multiaxial theory of viscoplasticity is further generalized to incorporate an isotropic loading surface and an anisotropic hardening rule for the unsymmetric cyclic distortion of the yield surface. The loading surface is defined as the smallest surface in stress space containing all the previous loading points; and the subsequent elastic region is assumed to be defined jointly by a yield surface and an isotropic surface which is contained by the loading surface and expands with a rate depending on the location of the loading point and the quasistatic loading point. The theory is applied to the modeling of stress-strain response and yield surface deformation of 1100-O aluminum subject to non-proportional loading in tension-torsion space.With 8 Figures     

Isotropic-BEM coupled with a local point interpolation method for the solution of 3D-anisotropic elasticity problems

This paper presents a solution procedure for the three-dimensional linear elastic problem with anisotropic properties. The approach uses the partition of the displacement field into complementary and particular parts. The former is the solution of a differential equation similar to that of an isotropic elastostatic and is obtained by the isotropic boundary element method. The particular integral is obtained by solving the corresponding strong form differential equations, using the local radial point interpolation method. This promising approach is simple to implement and leads to highly accurate solutions in some simple tested situations.     

Three-dimensional singularities in double lap joints

A 3-dimensional numerical analysis of a double lap joint specimen is presented. It is focused on the stress field on the interface plane where delamination would probably start. Combinations of isotropic and orthotropic layers are studied. It is shown that the most favorable point for delamination onset according to the linear fracture mechanics (LFM) approach lies near the 3-D corner, where all three modes of fracture are present, for all cases checked. The shear energy, which represents the tendency for yielding, is at the corner itself. The singular region for common combinations of adhesives-adherents is so small that regular continuum mechanics tools may be limited in failure predictions. The special features of the 3-D singularity at the comer point is discussed. Limitations of LFM for delamination onset prediction may lead to an extended type of failure criteria which is based on the shear energy state of the adhesive as well as the regular stress intensity factors. Two-dimensional solutions would show higher critical loads for the same problem.     

Modeling of 3D transversely piezoelectric and elastic bimaterials using the boundary element method

 This paper presents a numerical model for three-dimensional transversely isotropic bimaterials based on the boundary element formulation. The point force solutions expressed in a united-form for distinct eigenvalues are studied for transversely isotropic piezoelectricity and pure elasticity. A boundary integral formulation is implemented for the modeling of two-phase materials. In this study, the stress distributions are computed for a near interface flaw. The influences of the shape and location of the flaw on the the stress concentration are examined. The accuracy of the numerical procedures is validated through selected example problems and comparison studies. Received 3 October 2001 / Accepted 9 April 2002     

Anomalies of the specific heat in the vicinity of the phase transition from isotropic liquid to nematic liquid crystal

Precision measurements were made of the specific heat in the vicinity of the phase transition from nematic liquid crystal to isotropic liquid, an analysis of the results indicating that this transition occurs near the tricritical point.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 39, No. 6, pp. 1110–1107, December, 1980.     

Scattering of a point generated field by a multilayered spheroid

Summary The point source excitation acoustic scattering problem by a multilayer isotropic and homogeneous spheroidal body is presented. The multilayer spheroidal body is reached by an acoustic wave emanated by an external point source. The core spheroidal region is inpenetrable and rigid. The exterior interface and the interfaces separating the interior layers are penetrable. The scattered field is determined given the geometrical and physical characteristics of the spheroidal body, the location of the point source and the form of the incident field. The approach is not limited in a certain region of frequencies.     

On the dynamic behavior of honeycomb based composite solids

Summary The aim of this contribution is twofold. First, a dispersive model of periodic composite solids made of an isotropic matrix reinforced by a hexagonal system of slender fibres or by a honeycomb-like slender skeleton is formulated. Second, this model is applied to the analysis of vibration and wave propagation problems in the above honeycomb based composites. Contrary to the known homogenized models the main feature of the proposed model is that it describes the effect of cell size on the overall dynamic behavior of a composite solid. It is shown that on the macro-level the response of honeycomb based composites is isotropic. It is also proved that there exist dispersive dilatational-type and shear-type waves, which can propagate in these composites. Simple formulae for lower and higher free vibration frequencies are derived, and the existence of certain restrictons imposed on the physically allowable wave propagation speeds is shown.     

Interaction of screw dislocation and anisotropic (or isotropic) circular inclusion in isotropic (or anisotropic) matrix

Interaction of a screw dislocation (or an out-of-plane force) and anisotropic circular inclusion in isotropic matrix is studied. Similar problems for an anisotropic circular inclusion in an anisotropic matrix or the isotropic circular inclusion in the isotropic matrix have been solved, however, the anisotropic/isotropic problem (we will here after use this notation, meaning anisotropic circular inclusion in isotropic matrix) has not been solved yet. Recently, Choi et al.(2003) proposed a method based on ‘equivalence theorem’ to deal with a bimaterial interface (straight interface such as x₂ = 0) of anisotropic material bonded onto isotropic material. We apply this method to the stated problem.     

Using a Genetic Algorithm to Generate D‐optimal Designs for Mixture Experiments

We propose and develop a genetic algorithm (GA) for generating D‐optimal designs where the experimental region is an irregularly shaped polyhedral region. Our approach does not require selection of points from a user‐defined candidate set of mixtures and allows movement through a continuous region that includes highly constrained mixture regions. This approach is useful in situations where extreme vertices (EV) designs or conventional exchange algorithms fail to find a near‐optimal design. For illustration, examples with three and four components are presented with comparisons of our GA designs with those obtained using EV designs and exchange‐point algorithms over an irregularly shaped polyhedral region. The results show that the designs produced by the GA perform better than, if not as well as, the designs produced by the exchange‐point algorithms; however, the designs produced by the GA perform better than the designs produced by the EV. This suggests that GA is an alternative approach for constructing the D‐optimal designs in problems of mixture experiments when EV designs or exchange‐point algorithms are insufficient. Copyright © 2012 John Wiley & Sons, Ltd.     

Analysis of elliptical cracks perpendicular to the interface of two joined transversely isotropic solids

This paper presents a boundary element analysis of elliptical cracks in two joined transversely isotropic solids. The boundary element method is developed by incorporating the fundamental singular solution for a concentrated point load in a transversely isotropic bi-material solid of infinite space into the conventional displacement boundary integral equations. The multi-region method is used to analyze the crack problems. The traction-singular elements are employed to capture the singularity around the crack front. The values of stress intensity factors (SIFs) are obtained by using crack opening displacements. The results of the proposed method compare well with the existing exact solutions for an elliptical crack parallel to the isotropic plane of a transversely isotropic solid of infinite extent. Elliptical cracks perpendicular to the interface of transversely isotropic bi-material solids of either infinite extent or occupying a cubic region are further examined in detail. The crack surfaces are subject to the uniform normal tractions. The stress intensity factor values of the elliptical cracks of the two types are analyzed and compared. Numerical results have shown that the stress intensity factors are strongly affected by the anisotropy and the combination of the two joined solids.     

Least squares asymptotic analysis of photoelastic data from stress concentration regions in plane problems

A complete separation of stresses throughout the entire stress concentration region near notches in plane, isotropic, linearly elastic plates is achieved using only conventional, easily obtained photoelastic (difference and directions of principal stresses) data. These data are analysed by a special least squares technique based on previously derived equations which describe the asymptotic character of the rapidly varying stress field near the root of the notch. The paper demonstrates the ability of the technique to predict stress concentrations as well as individual stresses accurately using only a small amount of data of typical experimental accuracy from arbitrary data points within the stress concentration zone.     

Stress in an elastic wedge or notch loaded by a localized internal source

A study is presented of the stress inside a two-dimensional elastic solid which has a boundary surface angle and which is loaded by an internal point source of expansion. An exact analytic solution for the stress is obtained, for general surface angle and source position, and evaluated numerically for several representative cases of wedges and notches. The singular behaviour given by the leading terms near the angle vertex is found to be highly localized, and there is little or no stress enhancement near the source. For many combinations of boundary angle and source location, however, a local region of significant enhancement occurs on that part of the surface nearest the source. Implications of these results are discussed, with particular reference to surface steps.