PO Solution for Scattering by the Complex Object Coated with Anisotropic Materials

The physical optics solution is presented for the calculation of scattering by the complex conducting bodies coated with anisotropic materials, which is based on the tangential plane approximation and the equivalent currents on an anisotropic material backed by an infinite metal surface illuminated by the plane wave given in our previous work. The analytical scheme is proposed to realize fast computation of the solution. Numerical results for several coated bodies such as dihedral corner reflector and cone-cylinder geometry are given and discussed.

Equivalent strain hardening exponent of anisotropic materials based on spherical indentation response

Uniaxial strain hardening exponent is not suitable for describing the strain hardening behaviors of the anisotropic materials, especially when material deforms in the multi-axial stress states. In this work, a novel method was proposed to estimate the equivalent strain hardening exponent of anisotropic materials based on an equivalent energy method. By performing extensive finite element (FE) simulations of the spherical indentation on anisotropic materials, dimensionless function was proposed to correlate the strain hardening exponent of anisotropic materials with the indentation imprint parameters. And then, a mathematic expression on the strain hardening exponent of anisotropic materials with the indentation imprint was established to estimate the equivalent strain hardening exponent of anisotropic materials by directly solving this dimensionless function. Additionally, Meyer equation was modified to determine the yield stress of anisotropic materials. The effectiveness and reliability of the new method were verified by the numerical examples and by its application on the TC1M engineering material.

ANTIPLANE PROBLEMS OF PERIODICAL RIGID LINE INCLUSIONS BETWEEN DISSIMILAR ANISOTROPIC MATERIALS

The antiplane shear problems of periodical rigid line inclusions between dissimilar anisotropic materials are dealt with. By using the complex variable method, the closed form solutions are obtained. The stress distribution in the immediate vicinity of the rigid line is examined. The corresponding formulation between dissimilar isotropic materials and in homogeneous anisotropic medium can be derived from the special cases of those in the present paper, and the limit conditions are in agreement with the previously known results.

General Expression of Elastic Tensor for Anisotropic Materials

In order to formulate a general expression of elastic tensor for anisotropic materials, a method of tensor derivative is used for determining relationship between fourth-order elastic tensor and second-order structure tensor that has satisfied material symmetrical conditions. From this general expression of elastic tensor, specific expressions of elastic tensor for different anisotropic materials, such as isotropic materials, transverse isotropic materials and orthogonal-anisotropic materials, can be deduced. This expression underlies the scalar description of anisotropic factors, which are used for classifying and analyzing anisotropic materials. Cubic crystals are analyzed macroscopically by means of the general expression and anisotropic factor.

Unveiling the in-plane anisotropic dielectric waveguide modes in α-MoO_(3) flakes

The unique in-plane and out-of-plane anisotropy of α-MoO_(3) has attracted considerable interest with regard to potential optoelectronic applications. However, most research has focused on the mid-infrared spectrum, leaving its properties and applications in the visible and near-infrared light spectrum less explored. This study advances the understanding of waveguiding properties of α-MoO_(3) by near-field imaging of the waveguide modes along the [100] and [001] directions of α-MoO_(3) flakes at 633 nm and 785 nm. We investigate the effects of flake thickness and documented the modes' dispersion relationships, which is crucial for tailoring the optical responses of α-MoO_(3) in device applications. Our findings enhance the field of research into α-MoO_(3), highlighting its utility in fabricating next-generation optoelectronic devices due to its unique optically anisotropic waveguide.

Shape-free finite element method:The plane hybrid stress-function (HS-F) element method for anisotropic materials

The sensitivity problem to mesh distortion and the low accuracy problem of the stress solutions are two inherent difficulties in the finite element method.By applying the fundamental analytical solutions (in global Cartesian coordinates) to the Airy stress function of the anisotropic materials,8-and 12-node plane quadrilateral hybrid stress-function (HS-F) elements are successfully developed based on the principle of the minimum complementary energy.Numerical results show that the present new elements exhibit much better and more robust performance in both displacement and stress solutions than those obtained from other models.They can still perform very well even when the element shapes degenerate into a triangle and a concave quadrangle.It is also demonstrated that the proposed construction procedure is an effective way for developing shape-free finite element models which can completely overcome the sensitivity problem to mesh distortion and can produce highly accurate stress solutions.

Local grid refinement in multigrid method for point contact problems of polycrystalline anisotropic material under dry and lubricated conditions

Predicting rolling bearing fatigue life requires knowledge of the three-dimensional(3D)stress fields in the roller and raceway near the lubricated contact.Owing to the increasingly severe operating conditions,the effect of localized features such as surface roughness,subsurface inclusions,and even the crystallographic structure of the material becomes important.Achieving such detail requires(locally)extremely dense gridding in simulations,which in 3D is a major challenge.Multigrid techniques have been demonstrated to be capable of solving such problems.In this study,multigrid techniques are shown to further increase the efficiency of the solution by exploiting local grid refinement while maintaining the simplicity of a uniform discretization.This is achieved by employing increasingly finer grids only locally,where the highest resolution is required.Results are presented for dry contact and elastohydrodynamically lubricated contact cases,circular as well as elliptic,with varying crystallographic structure,and with surface roughness.The results show that the developed algorithm is very well suited for detailed analysis,with also excellent prospects for computational diagnostics involving actual material crystallographic structure from electron backscatter diffraction measurements.

Stress singularity analysis of anisotropic multi-material wedges under antiplane shear deformation using the symplectic approach

Symplectic approach has emerged a popular tool in dealing with elasticity problems especially for those with stress singularities. However, anisotropic material problem under polar coordinate system is still a bottleneck. This paper presents a subfield method coupled with the symplectic approach to study the anisotropic material under antiplane shear deformation. Anisotropic material around wedge tip is considered to be consisted of many subfields with constant material properties which can be handled by the symplectic approach individually. In this way, approximate solutions of the stress and displacement can be obtained. Numerical examples show that the present method is very accurate and efficient for such wedge problems. Besides, this paper has extended the application of the symplectic approach and provides a new idea for wedge problems of anisotropic material.

Inverse design for material anisotropy and its application for a compact X-cut TFLN on-chip wavelength demultiplexer

Inverse design focuses on identifying photonic structures to optimize the performance of photonic devices.Conventional scalar-based inverse design approaches are insufficient to design photonic devices of anisotropic materials such as lithium niobate(LN).To the best of our knowledge,this work proposes for the first time the inverse design method for anisotropic materials to optimize the structure of anisotropic-material based photonics devices.Specifically,the orientation dependent properties of anisotropic materials are included in the adjoint method,which provides a more precise prediction of light propagation within such materials.The proposed method is used to design ultra-compact wavelength division demultiplexers in the X-cut thin-film lithium niobate(TFLN)platform.By benchmarking the device performances of our method with those of classical scalar-based inverse design,we demonstrate that this method properly addresses the critical issue of material anisotropy in the X-cut TFLN platform.This proposed method fills the gap of inverse design of anisotropic materials based photonic devices,which finds prominent applications in TFLN platforms and other anisotropicmaterial based photonic integration platforms.

Static Analysis of Anisotropic Doubly-Curved Shell Subjected to Concentrated Loads Employing Higher Order Layer-Wise Theories

In the presentmanuscript,a Layer-Wise(LW)generalizedmodel is proposed for the linear static analysis of doublycurved shells constrained with general boundary conditions under the influence of concentrated and surface loads.The unknown field variable is modelled employing polynomials of various orders,each of them defined within each layer of the structure.As a particular case of the LW model,an Equivalent Single Layer(ESL)formulation is derived too.Different approaches are outlined for the assessment of external forces,as well as for non-conventional constraints.The doubly-curved shell is composed by superimposed generally anisotropic laminae,each of them characterized by an arbitrary orientation.The fundamental governing equations are derived starting from an orthogonal set of principal coordinates.Furthermore,generalized blending functions account for the distortion of the physical domain.The implementation of the fundamental governing equations is performed bymeans of the Generalized Differential Quadrature(GDQ)method,whereas the numerical integrations are computed employing theGeneralized IntegralQuadrature(GIQ)method.In the post-processing phase,an effective procedure is adopted for the reconstruction of stress and strain through-the-thickness distributions based on the exact fulfillment of three-dimensional equilibrium equations.A series of systematic investigations are performed in which the static response of structures with various curvatures and lamination schemes,calculated by the present methodology,have been successfully compared to those ones obtained fromrefined finite element three-dimensional simulations.Even though the present LW approach accounts for a two-dimensional assessment of the structural problem,it is capable of well predicting the three-dimensional response of structures with different characteristics,taking into account a reduced computational cost and pretending to be a valid alternative to widespread numerical implementations.

Cavitation for Incompressible Anisotropic Hyper-Elastic Materials

The cavitation problem in a solid sphere composed of an incompressible anisotropic hyper elastic material under a uniform radial tensile dead load was examined. A new analytical solution was obtained. The stress contributions were given and the jumping and concentration of stresses were discussed. The stability of solutions and the effect of the degree of anisotropy of the material were analyzed.

Characteristics of surface waves in anisotropic left-handed materials

We report the coexistence of TE and TM surface modes in certain same frequency domain at the interface between one isotropic regular medium and another biaxially anistotropic left-handed medium. The conditions for the existence of TE and TM polarized surface waves in biaxially anisotropic left-handed materials are identified, respectively. The Poynting vector and the energy density associated with surface modes are calculated. Depending on the system parameters, either TE or TM surface modes can have the time averaged Poynting vector directed to or opposite to the mode phase velocity. It is seen that the characteristics of surface waves in biaxially anisotropic left-handed media are significantly different from that in isotropic left-handed media.

Elasto-plastic analysis of masonry with anisotropic plastic material model

This paper establishes an anisotropic plastic material model to analyze the elasto-plastic behavior of masonry in plane stress state.Being an anisotropic material,masonry has different constitutive relation and fracture energies along each orthotropic axes.Considering the unique material properties of masonry,a new yield criterion for masonry is proposed combining the Hill's yield criterion and the Rankine's yield criterion.The new yield criterion not only introduces compression friction coefficient of shear but also considers yield functions for independent stress state along two material axes of tension.To solve the involved nonlinear equations in numerical analysis,several nonlinear methods are implemented,including Newton-Raphson method for nonlinear equations and Implicit Euler backward mapping algorithm to update stresses.To verify the proposed material model of masonry,a series of tests are operated.The simulation results show that the new developed material model implements successfully.Compared with isotropic material model,the proposed model performs better in elasto-plastic analysis of masonry in plane stress state.The proposed anisotropic model is capable of simulating elasto-plastic behavior of masonry and can be used in related applications.

Anisotropic Transport and Magnetic Properties of Charge-Density-Wave Materials RSeTe2（R=La,Ce,Pr,Nd）

Single crystals of RSeTe2 （R =La, Ce, Pr, Nd） are synthesized using LiC1/RbCI flux. Transport and magnetic properties in the directions parallel and perpendicular to the a-c plane are investigated. We find that the resistivity anisotropy P⊥/P∥ lies in the range 486-615 for different compounds at 2K, indicating the highly two-dimensional character. In both the orientations, the charge-density-wave transitions start near Tcow = 284（3）K, 316（3）K, 359（3）K for NdSeTe2, PrSeTe2, CeSeTe2, respectively, with a considerable increase in dc resistivity. While for LaSeTe2, no obvious resistivity anomaly is observed up to 380K. The value of TCDW increases monotonically with the increasing lattice parameters. Below TCDW, slight anomalies can be observed in NdSeTe2, PrSeTe2 and CeSeTe2 with onset temperature at 193（3）K, 161（3）K, 108（3）K, respectively, decreasing as lattice parameters increase. Magnetic susceptibility measurements show that the valence state of rare earth ions are trivalenee in these compounds. Antiferromagnetie-type magnetic order is formed in CeSeTe2 at 2.1 K, while no magnetic transition is observed in PrSeTe2 and NdSeTe2 down to 1.8 K.

CONSTITUTIVE EQUATION OF CO-ROTATIONAL DERIVATIVE TYPE FOR ANISOTROPIC-VISCOELASTIC FLUID

A constitutive equation theory of Oldroyd fluid B type,i.e.the co-rotational derivative type,is developed for the anisotropic-viscoelastic fluid of liquid crystalline(LC)polymer.Analyzing the influence of the orientational motion on the material behavior and neglecting the influence,the constitutive equation is applied to a simple case for the hydrodynamic motion when the orientational contribution is neglected in it and the anisotropic relaxation,retardation times and anisotropic viscosi- ties are introduced to describe the macroscopic behavior of the anisotropic LC polymer fluid.Using the equation for the shear flow of LC polymer fluid,the analytical expressions of the apparent viscosity and the normal stress differences are given which are in a good agreement with the experimental results of Baek et al.For the fiber spinning flow of the fluid,the analytical expression of the extensional viscosity is given.

Elliptical inclusion in an anisotropic plane:non-uniform interface effects

We study the plane deformation of an elastic composite system made up of an anisotropic elliptical inclusion and an anisotropic foreign matrix surrounding the inclusion.In order to capture the influence of interface energy on the local elastic field as the size of the inclusion approaches the nanoscale,we refer to the Gurtin-Murdoch model of interface elasticity to describe the inclusion-matrix interface as an imaginary and extremely stiff but zero-thickness layer of a finite stretching modulus.As opposed to isotropic cases in which the effects of interface elasticity are usually assumed to be uniform(described by a constant interface stretching modulus for the entire interface),the anisotropic case considered here necessitates non-uniform effects of interface elasticity(described by a non-constant interface stretching modulus),because the bulk surrounding the interface is anisotropic.To this end,we treat the interface stretching modulus of the anisotropic composite system as a variable on the interface curve depending on the specific tangential direction of the interface.We then devise a unified analytic procedure to determine the full stress field in the inclusion and matrix,which is applicable to the arbitrary orientation and aspect ratio of the inclusion,an arbitrarily variable interface modulus,and an arbitrary uniform external loading applied remotely.The non-uniform interface effects on the external loading-induced stress distribution near the interface are explored via a group of numerical examples.It is demonstrated that whether the nonuniformity of the interface effects has a significant effect on the stress field around the inclusion mainly depends on the direction of the external loading and the aspect ratio of the inclusion.

Optimal thermal design of anisotropic plates with arbitrary cutouts using genetic algorithm

Anisotropic plates in different applications may have geometric defects such as openings and cracks.The presence of the opening disturbs the heat flow,which creates significant thermal stress around the opening.When the heat flux is high enough,these extreme stresses can lead to structural failure.This article aims to obtain the optimal parameters for achieving the minimum value of the normalized stress near the cutout’s boundary in perforated anisotropic plates utilizing the genetic algorithm.Optimization parameters include the curvature of opening’s corners,orientation angle of opening,fibers angle,heat flux angle,and opening’s elongation.The plate is under heat flux,and the opening’s border is thermally insulated.The stress distribution around the opening is calculated using Lekhnitskii’s complex variable method and complex potential functions.The genetic algorithm is then implemented to find the optimal values for design parameters.The results show that by selecting the optimal parameters related to the anisotropic material and the opening’s geometry,the stress intensity factor of the perforated anisotropic plates is remarkably reduced.Furthermore,this optimization algorithm can be extended to find the optimized parameters and achieve the optimal designs in anisotropic and isotropic perforated plates under thermal loadings.

Static Analysis of Doubly-Curved Shell Structures of Smart Materials and Arbitrary Shape Subjected to General Loads Employing Higher Order Theories and Generalized Differential Quadrature Method

The article proposes an Equivalent Single Layer(ESL)formulation for the linear static analysis of arbitrarily-shaped shell structures subjected to general surface loads and boundary conditions.A parametrization of the physical domain is provided by employing a set of curvilinear principal coordinates.The generalized blendingmethodology accounts for a distortion of the structure so that disparate geometries can be considered.Each layer of the stacking sequence has an arbitrary orientation and is modelled as a generally anisotropic continuum.In addition,re-entrant auxetic three-dimensional honeycomb cells with soft-core behaviour are considered in the model.The unknown variables are described employing a generalized displacement field and pre-determined through-the-thickness functions assessed in a unified formulation.Then,a weak assessment of the structural problem accounts for shape functions defined with an isogeometric approach starting fromthe computational grid.Ageneralizedmethodology has been proposed to define two-dimensional distributions of static surface loads.In the same way,boundary conditions with three-dimensional features are implemented along the shell edges employing linear springs.The fundamental relations are obtained from the stationary configuration of the total potential energy,and they are numerically tackled by employing the Generalized Differential Quadrature(GDQ)method,accounting for nonuniform computational grids.In the post-processing stage,an equilibrium-based recovery procedure allows the determination of the three-dimensional dispersion of the kinematic and static quantities.Some case studies have been presented,and a successful benchmark of different structural responses has been performed with respect to various refined theories.

HYPERSINGULAR INTEGRAL EQUATIONS FOR PERIODIC ARRAYS OF PLANAR CRACKS IN A PERIODICALLY-LAYERED ANISOTROPIC ELASTIC SPACE UNDER ANTIPLANE SHEAR STRESS

Hypersingular integral equations are derived for the problem of determining the antiplane shear stress around periodic arrays of planar cracks in a periodically-layered anisotropic elastic space. The unknown functions are directly related to the jump in the displacements across opposite crack faces. Once the integral equations are solved, crack parameters of interest, such as the clack tip stress intensity factors, may be readily computed.For some specific examples of the problem, the integral equations are solved numerically by using a collocation technique, in order to compute the relevant stress intensity factors.