Tunable three-dimensional nonreciprocal transmission in a layered nonlinear elastic wave metamaterial by initial stresses

In this work,the three-dimensional(3 D)propagation behaviors in the nonlinear phononic crystal and elastic wave metamaterial with initial stresses are investigated.The analytical solutions of the fundamental wave and second harmonic with the quasilongitudinal(qP)and quasi-shear(qS_(1) and qS_(2))modes are derived.Based on the transfer and stiffness matrices,band gaps with initial stresses are obtained by the Bloch theorem.The transmission coefficients are calculated to support the band gap property,and the tunability of the nonreciprocal transmission by the initial stress is discussed.This work is expected to provide a way to tune the nonreciprocal transmission with vector characteristics.

Three-dimensional admittance analysis of lithospheric elastic thickness over the Louisville Ridge

Using bathymetry and altimetric gravity anomalies, a 1°×9 1° lithospheric effective elastic thickness（Te） model over the Louisville Ridge and its adjacent regions is calculated using the moving window admittance technique. For comparison, three bathymetry models are used： general bathymetric charts of the oceans, SIO V15.1,and BAT_VGG. The results show that BAT_VGG is more suitable for calculating T e than the other two models. T e along the Louisville Ridge was re-evaluated. The southeast of the ridge has a medium Te of 10–20 km, while Te increases dramatically seaward of the Tonga-Kermadec trench as a result of the collision of the Pacific and IndoAustralian plates.

MESHLESS ANALYSIS FOR THREE-DIMENSIONAL ELASTICITY WITH SINGULAR HYBRID BOUNDARY NODE METHOD

The singular hybrid boundary node method （SHBNM） is proposed for solving three-dimensional problems in linear elasticity. The SHBNM represents a coupling between the hybrid displacement variational formulations and moving least squares （MLS） approximation. The main idea is to reduce the dimensionality of the former and keep the meshless advantage of the later. The rigid movement method was employed to solve the hyper-singular integrations. The ＇boundary layer effect＇, which is the main drawback of the original Hybrid BNM, was overcome by an adaptive integration scheme. The source points of the fundamental solution were arranged directly on the boundary. Thus the uncertain scale factor taken in the regular hybrid boundary node method （RHBNM） can be avoided. Numerical examples for some 3D elastic problems were given to show the characteristics. The computation results obtained by the present method are in excellent agreement with the analytical solution. The parameters that influence the performance of this method were studied through the numerical examples.

Three-Dimensional Static Analysis of Nanoplates and Graphene Sheets by Using Eringen’s Nonlocal Elasticity Theory and the Perturbation Method

A three-dimensional(3D)asymptotic theory is reformulated for the static analysis of simply-supported,isotropic and orthotropic single-layered nanoplates and graphene sheets(GSs),in which Eringen’s nonlocal elasticity theory is used to capture the small length scale effect on the static behaviors of these.The perturbation method is used to expand the 3D nonlocal elasticity problems as a series of two-dimensional(2D)nonlocal plate problems,the governing equations of which for various order problems retain the same differential operators as those of the nonlocal classical plate theory(CST),although with different nonhomogeneous terms.Expanding the primary field variables of each order as the double Fourier series functions in the in-plane directions,we can obtain the Navier solutions of the leading-order problem,and the higher-order modifications can then be determined in a hierarchic and consistent manner.Some benchmark solutions for the static analysis of isotropic and orthotropic nanoplates and GSs subjected to sinusoidally and uniformly distributed loads are given to demonstrate the performance of the 3D nonlocal asymptotic theory.

Prediction of three-dimensional elastic behavior of filament-wound composites based on the bridging model

This work provides a method to predict the three-dimensional equivalent elastic properties of the filament-wound composites based on the multi-scale homogenization principle.In the meso-scale,a representative volume element(RVE)is defined and the bridging model is adopted to establish a theoretical predictive model for its three-dimensional equivalent elastic constants.The results obtained through this method for the previous experimental model are compared with the ones gained respectively by experiments and classical laminate theory to verify the reliability of this model.In addition,the effects of some winding parameters,such as winding angle,on the equivalent elastic behavior of the filament-wound composites are analyzed.The rules gained can provide a theoretical reference for the optimum design of filament-wound composites.

Effects of fracture distribution and length scale on the equivalent continuum elastic compliance of fractured rock masses

Fracture systems have strong influence on the overall mechanical behavior of fractured rock masses dueto their relatively lower stiffness and shear strength than those of the rock matrix. Understanding theeffects of fracture geometrical distribution, such as length, spacing, persistence and orientation, isimportant for quantifying the mechanical behavior of fractured rock masses. The relation betweenfracture geometry and the mechanical characteristics of the fractured rock mass is complicated due tothe fact that the fracture geometry and mechanical behaviors of fractured rock mass are stronglydependent on the length scale. In this paper, a comprehensive study was conducted to determine theeffects of fracture distribution on the equivalent continuum elastic compliance of fractured rock massesover a wide range of fracture lengths. To account for the stochastic nature of fracture distributions, threedifferent simulation techniques involving Oda＇s elastic compliance tensor, Monte Carlo simulation （MCS）,and suitable probability density functions （PDFs） were employed to represent the elastic compliance offractured rock masses. To yield geologically realistic results, parameters for defining fracture distributionswere obtained from different geological fields. The influence of the key fracture parameters andtheir relations to the overall elastic behavior of the fractured rock mass were studied and discussed. Adetailed study was also carried out to investigate the validity of the use of a representative elementvolume （REV） in the equivalent continuum representation of fractured rock masses. A criterion was alsoproposed to determine the appropriate REV given the fracture distribution of the rock mass.

THEORY OF NONLOCAL ASYMMETRIC ELASTIC SOLIDS

In this paper, a nonlinear theory of nonlocal asymmetric, elastic solids is developed on the basis of basic theories of nonlocal continuum field theory and nonlinear continuum mechanics. It perfects and expands the nonlocal elastic field theory developed by Eringen and others. The linear theory of nonlocal asymmetric elasticity developed in [1] expands to the finite deformation. We show that there is the nonlocal body moment in the nonlocal elastic solids. The nonlocal body moment causes the stress asymmetric and itself is caused by the covalent bond formed by the reaction between atoms. The theory developed in this paper is applied to explain reasonably that curves of dispersion relation of one-dimensional plane longitudinal waves are not similar with those of transverse waves.

ANALYSIS OF ELASTIC LAYERS WITH DILATIVE EIGENSTRAINS VARYING THROUGH THE THICKNESS

Elastic layers with varying dilative eigenstrains through the thickness were concerned. A general procedure was proposed for the analysis of such layers under arbitrary loads. The study is based on the state-space method and an asymptotic expansion technique. When the external loads are uniform, the expansion terminates after some leading terms, and an explicit representation for the mechanical field in a layer is obtained. This representation relies only on the displacement components of the mid-plane, which are governed by a set of two-dimensional differential equations similar to those in the classical plate theory. Consequently, obtaining the solution to the two-dimensional equations immediately gives the three-dimensional responses of the layer. As an illustrative example, a clamped elliptical layer under a uniformly distributed transverse load is analyzed in detail.

Elastic Behavior of Polymer Chains

The elastic behavior of the polymer chain was investigated in a three-dimensional off-lattice model. We sample more than 109 conformations of each kind of polymer chain by using a Monte Carlo algorithm, then analyze them with the non-Gaussian theory of rubberlike elasticity, and end with a statistical study. Through observing the effect of the chain flexibility and the stretching ratio on the mean-square end-to-end distance, the average energy, the average Helmholtz free energy, the elastic force, the contribution of energy to the elastic force, and the entropy contribution to elastic force of the polymer chain, we find that a rigid polymer chain is much easier to stretch than a flexible polymer chain. Also, a rigid polymer chain will become difficult to stretch only at a quite high stretching ratio because of the effect of the entropy contribution. These results of our simulation calculation may explain some of the macroscopic phenomena of polymer and biomacromolecular elasticity.

Investigation of long-wavelength elastic wave propagation through wet bentonite-filled rock joints

The saturation of the compacted bentonite buffer in the deep geological repository can cause bentonite swelling,intrusion into rock fractures,and erosion.Inevitably,erosion and subsequent bentonite mass loss due to groundwater inflow can aggravate the overall integrity of the engineered barrier system.Therefore,the coupled hydro-mechanical interaction between the buffer and rock during groundwater inflow and bentonite intrusion should be evaluated to guarantee the long-term safety of deep geological disposal.This study investigated the effect of bentonite erosion and intrusion on the elastic wave propagation characteristics in jointed rocks using a quasi-static resonant column test.Jointed rock specimens with different joint conditions(i.e.joint surface saturation and bentonite filling)were prepared using granite rock discs sampled from the Korea Underground Research Tunnel(KURT)and Gyeongju bentonite.The long-wavelength longitudinal and shear wave velocities were measured under different normal stress levels.A Hertzian-type power model was used to fit the wave velocities,and the relationship between the two fitted parameters provided the trend of joint conditions.Numerical simulations using three-dimensional distinct element code(3DEC)were conducted to better understand how the long-wavelength wave propagates through wet bentonite-filled rock joints.

Elastic scattering and total reaction cross sections of^(6)Li examined via a microscopic continuum discretized coupled-channels model

We present a systematic study of 6Li elastic scattering and total reaction cross sections at incident energies around the Coulomb barrier within the continuum discretized coupled-channels(CDCC)framework,where 6Li is treated in anα+d two-body model.Collisions with 27Al,64Zn,138Ba,and 208Pa are analyzed.The microscopic optical potentials(MOP)based on Skyrme nucleon-nucleon interaction forαand d are adopted in CDCC calculations and satisfactory agreement with the experimental data is obtained without any adjustment on MOPs.For comparison,αand d global phenomenological optical potentials(GOP)are also used in CDCC analysis and a reduction of no less than 50%on the surface imaginary part of deuteron GOP is required for describing the data.In all cases,the 6Li breakup effect is significant and provides repulsive correction to the folding model potential.The reduction on the surface imaginary part of GOP of deuteron reveals a strong suppression of the reaction probability of deuteron as a component of 6Li when compared with that of a free deuteron.Further investigation is performed by considering the d breakup process equivalently within the dynamic polarization potential approach,and the results show that d behaves in a manner similar to a tightly bound nucleus in 6Li induced reactions.

A review on the application of modified continuum models in modeling and simulation of nanostructures

Analysis of the mechanical behavior of nanos- tructures has been very challenging. Surface energy and non- local elasticity of materials have been incorporated into the traditional continuum analysis to create modified continuum mechanics models. This paper reviews recent advancements in the applications of such modified continuum models in nanostructures such as nanotubes, nanowires, nanobeams, graphenes, and nanoplates. A variety of models for these nanostructures under static and dynamic loadings are men- tioned and reviewed. Applications of surface energy and nonlocal elasticity in analysis of piezoelectric nanomateri- als are also mentioned. This paper provides a comprehensive introduction of the development of this area and inspires fur- ther applications of modified continuum models in modeling nanomaterials and nanostructures.

THREE-DIMENSIONAL ELASTIC ATMOSPHERIC NUMERICAL MODEL AND THE SIMULATION OF A SEVERE STORM CASE

A three-dimensional meso-γ,scale elastic atmospheric numerical model has been established and used to simulate a severe storm case.The important characteristics of the modeled storm are close to those of the observed case.

Three-dimensional elasticity solution of simple-supported rectangular plate on point supports, line supports and elastic foundation

This paper studies the bending of simple-supported rectangular plate on point supports, line supports and elastic foundation. On the basis of three-dimensional elasticity theory, the exact expressions of the displacement functions, which satisfy the governing differential equations and the simply supported boundary conditions at four edges of the plate, are analytically derived. The reaction forces of the in- termediate supports are regarded as the unknown external forces acting on the lower surface of the plate. The unknown coefficients are then determined by the boundary conditions on the upper and lower surfaces of the plate. Comparing the numerical results obtained from the proposed method to those obtained from Kirchhoff plate theory, Mindlin plate theory and those obtained from the commer- cial finite element software ANSYS, the high accuracy of the present method has been demonstrated.

A Modified Symmetric and Antisymmetric Decomposition-Based Three-Dimensional Numerical Manifold Method for Finite Elastic-Plastic Deformations

There are relatively few studies on large rotation or deformation by means of the three-dimensional(3D)numerical manifold method(NMM).A new modified symmetric and antisymmetric decomposition(MSAD)theory is developed and implemented into the 3D NMM,eliminating the false-volume expansion and false-rotation strain/stress problems.The Jaumann rate is used to measure the material rotation,and the geometric stiffness built on the Jaumann rate is deduced.The incremental formulas of the MSAD-based 3D NMM and a practical guide on the implementation of the MSAD theory are given in detail and exemplified.The new theory and formulas can be applied to analyze both large rotation and large deformation problems.Based on the hypoelasto-plasticity theory and the unified strength theory,the unified yield criterion with associated flow rule is implemented into the MSAD-based 3D NMM.Several typical examples are studied,showing the advantage and potential of the new MSAD theory and the MSAD-based 3D NMM.

A THREE-DIMENSIONAL ELASTICITY SOLUTION FOR TWO-DIRECTIONAL FGM ANNULAR PLATES WITH NON-UNIFORM ELASTIC FOUNDATIONS SUBJECTED TO NORMAL AND SHEAR TRACTIONS

In the present paper, bending and stress analyses of two-directional functionally graded （FG） annular plates resting on non-uniform two-parameter Winkler-Pasternak founda- tions and subjected to normal and in-plane-shear tractions is investigated using the exact three- dimensional theory of elasticity. Neither the in-plane shear loading nor the influence of the two- directional material heterogeneity has been investigated by the researchers before. The solution is obtained by employing the state space and differential quadrature methods. The material proper- ties are assumed to vary in both transverse and radial directions. Three different types of variations of the stiffness of the foundation are considered in the radial direction： linear, parabolic, and sinu- soidal. The convergence analysis and the comparative studies demonstrate the high accuracy and high convergence rate of the present approach. A parametric study consisting of evaluating effects of different parameters （e.g., exponents of the material properties laws, the thickness to radius ratio, trends of variations of the foundation stiffness, and different edge conditions） is carried out. The results are reported for the first time and are discussed in detail.

The Continuum Stored Energy for Constitutive Modeling Finite Deformations of Polymeric Materials

With symmetries measured by the Lie group and curvatures revealed by differential geometry, the continuum stored energy function possesses a translational deformation component, a rotational deformation component, and an ellipsoidal volumetric deformation component. The function, originally developed for elastomeric polymers, has been extended to model brittle and ductile polymers. The function fits uniaxial tension testing data for brittle, ductile, and elastomeric polymers, and elucidates deformation mechanisms. A clear distinction in damage modes between brittle and ductile deformations has been captured. The von Mises equivalent stress has been evaluated by the function and the newly discovered break-even stretch. Common practices of constitutive modeling, relevant features of existing models and testing methods, and a new perspective on the finite elasticity-plasticity theory have also been offered.

Derivation of Cylindrical Internal-Surface Acoustic Waves and Their Small Gravity Effect

The properties of Cylindrical Internal-Surface Acoustic Waves (CISAW) propagating on the inside surface of a high purity fused quartz tubular fiber are derived from basic principles using a variational method. The CISAW consist of Energy Momentum Packets (EMP) moving in a looping motion. The EMP have mass and are affected by gravity similar to a pendulum bob. The effect of gravity on CISAW is much larger than the effect of gravity in a light wave. Therefore, one can build much smaller CISAW Interferometer Gravity wave Observatories (CIGO) than the present km size Light Interferometer Gravity wave Observatories (LIGO). An array of CIGO can be used to detect gravity wave images. Since the wavelength of gravity waves is much larger than the expected spacing between CIGO array elements this would result in sub-wavelength images. It would be interesting to determine what new discoveries could be made using such an array.

The Elastic Continuum Limit of the Tight Binding Model

The authors consider the simplest quantum mechanics model of solids, the tight binding model, and prove that in the continuum limit, the energy of tight binding model converges to that of the continuum elasticity model obtained using Cauchy-Born rule. The technique in this paper is based mainly on spectral perturbation theory for large matrices.

循环加载条件下TiNi形状记忆合金超弹性变形特性分析与模拟

超弹性是形状记忆合金(SMA)重要的力学性能之一,本文在试验研究的基础上讨论了在不同试验温度和应变速率的循环加载条件下,TiNiSMA的超弹性变形特性。从唯象观点分析了循环变形期间相变应力和弹性模量的变化。通过引入三个内变量,即循环期间所累积的残余应力、残余应变和残余马氏体相,表征承受加载和卸载的TiNiSMA循环超弹性变形。在此基础上,提出了模拟TiNiSMA的超弹性变形方法。在部分加载的内循环情况下,采用相变应变函数的混合规则表达材料的弹性模量。