Third order elastic constants of hexagonal boron nitride

Third order elastic constants of hexagonal Boron Nitride have been evaluated using the Lannard-Jones potential. The results obtained are presented and compared with the only available measurement ofC ₃₃₃ for this material.     

The influence of the third order elastic constants to the generalized Rayleigh wave dispersion in a pre-stressed stratified half-plane

Within the framework of the piecewise homogeneous body model with the use of the three-dimensional linearized theory of elasticity the influence of the third order elastic constants on the velocity of the generalized Rayleigh wave propagation in a pre-stressed stratified half-plane is investigated. Between the layer and half-plane the complete contact conditions are satisfied. The concrete numerical investigations are made on the various materials for which the values of the third order elastic constants are known. The initial stresses are determined within the framework of the classical linear theory of elasticity.     

Crystal structure and elastic constants of Dharwar cotton fibre using WAXS data

Wide-angle X-ray scattering (WAXS) recordings were carried out on raw Dharwar cotton fibres available in Karnataka. Using this data and employing linked atom least squares (LALS) method, we report here the molecular and crystal structure of these cotton fibres. Employing structural data, we have computed elastic moduli tensor components of these fibres. From these investigations, it turns out that the intrinsic strains present in the fibre arise due to hydrogen bonds and not covalent bonds, which is a significant result.     

First-principles calculations of elastic constants for epsilon-carbide and the consequences

ABSTRACT

The elastic constants of ?-carbide at 0?K and zero pressure have been calculated using first-principle methods. The iron to carbon ratio for the carbide is not established and may, in fact, vary between 3 and 2. As a consequence, the calculations have been conducted as a function of the chemical composition using the special quasi-random structures method. In all cases, the elastic constants obtained are consistent with ?-carbide being mechanically stable. The analysis indicates that in comparison with cementite, ?-carbide should be more brittle; that when present as a precipitate in steel, it would be less effective in participating in the overall plastic deformation, and that its coherency strain field in the surrounding matrix should be less extensive than cementite.     

Influence of spin orbit coupling and lanthanide contraction on the exchange interaction in rare earth garnets

The exchange constants observed in the rare earth iron garnets, obtained from fitting magnetization and paramagnetic susceptibility as a function of temperature have been analysed in terms of Anderson’s theory of superexchange. The transfer integrals and covalency parameters have been obtained for various rare earth ions overlapping with oxygen.     

提高碳纤维增强树脂基复合材料弹性常数超声表征精度的方法

为提高碳纤维增强树脂基复合材料（Carbon Fiber Reinforced Plastic,CFRP）单向板弹性常数的超声表征精度,基于超声液浸背反射法开展了实验测量和数值模拟。首先,搭建了角度旋转测试装置,并结合信号互相关处理技术实现了不同方向上的延时测量和声速计算;然后,通过模拟退火优化算法反演声速数据,得到了5个独立弹性常数;最后,利用理论计算和CIVA软件模拟仿真对实验测量结果进行了验证。结果表明:1-3平面内准纵波和准横波声速随入射角度而变化,与1-2平面内的表现出明显差异,由此显示材料为横观各向同性的;独立弹性常数分别为12.88、6.39、126.83、4.85、2.97 GPa;理论计算、CIVA软件模拟仿真及实验测量结果的声速偏差小于6.4 m/s,实验数据波动范围小于0.33%,对应的弹性常数误差均小于0.47%。相关方法同样适用于其他正交各向异性介质的弹性常数测试。      

Advanced resonant ultrasound spectroscopy for measuring anisotropic elastic constants of thin films

This paper presents an advanced resonant ultrasound spectroscopy (RUS) method to determine the elastic constants C_ij of thin films. Polycrystalline thin films often exhibit elastic anisotropy between the film growth direction and the in‐plane direction, and they macroscopically show five independent elastic constants. Because all of the C_ij of a deposited thin film affect the mechanical resonance frequencies of the film/substrate layer specimen, measuring resonance frequencies enables one to determine the C_ij of the film with known density, dimensions and the C_ij of the substrate. Resonance frequencies have to be measured accurately because of low sensitivity of the C_ij of films to them. We achieved this by a piezoelectric tripod. Mode identification has to be made unambiguously. We made this measuring displacement–amplitude distributions on the resonated specimen surface by laser Doppler interferometry. We applied our technique to copper thin film and diamond thin film. They show elastic anisotropy and the C_ij smaller than bulk values of C_ij. Micromechanics calculations indicate the presence of incohesive bonded regions.     

二维机织复合材料弹性常数的有限元法预测

为了预测二维机织复合材料的弹性性能,建立了有限元力学分析模型。基于二维机织复合材料的几何特征,建立了参数化的单胞模型;考虑了织物纤维束呈现出的各向异性材料特征,将有限元中材料主方向转化到纤维屈曲方向,建立其力学分析有限元模型;分析了单胞边界面保持平面假设的不足,提出了对于二维机织复合材料通用的周期边界条件,获得了更为准确的二维机织复合材料的工程弹性常数。结果表明:织物衬垫单胞边界面,在单向拉伸载荷和纯剪切载荷下,呈凹凸翘曲变形,即为周期边界;应用给出的织物参数化几何建模方法与有限元求解方法,可以精确地获得工程弹性常数,数值计算结果与实验值吻合较好。      

First-principles elastic constants and electronic structure of beryllium chalcogenides BeS, BeSe and BeTe

A theoretical study of structural, elastic and electronic properties of BeS, BeSe and BeTe is presented using the full-potential augmented plane-waves plus local orbitals (APW + lo) within density-functional theory (DFT). Results are obtained using both the local-density approximation (LDA) and the generalized gradient approximation (GGA) for the exchange-correlation potentials. The ground-state properties, like lattice constant, bulk modulus and its first derivative obtained from our calculations agree very well with experimental and other theoretical calculations. Band structures, and total valence charge densities including spin–orbit interaction are analyzed in great detail. The calculated values of the energy gaps, bandwidths, and spin–orbit splittings and the correct band degeneracies are compared to experimental and/or ab initio results. The calculated energy gap for the series of beryllium chalcogenides BeS, BeSe and BeTe is found to be indirect (Γ–X) and underestimated by about 40% for both LDA and PBE-GGA compared to experiment. We have also reported the elastic constants of these materials; the elastic constants have been derived by the stress–strain relation.     

Micromechanical modelling of size effects in failure of porous elastic solids using first order plane strain gradient elasticity

In this paper a first order porous strain gradient elasticity model is presented. The constitutive equations have been obtained by higher order homogenization and the model is used with a failure criterion in order to discuss size effects in failure of porous elastic solids. The model contains two microstructural parameters namely the void volume fraction and the half void spacing. After an extended numerical validation of the porous strain gradient elasticity model, the boundary value problem of a plate with a hole under bi- and uniaxial remote tension is investigated. The numerical simulations have been performed varying both microstructural parameters in order to study the influence of different microstructural dimensions on the onset of macroscopic failure. The numerical results show that the presented model is able to predict size effects and that size effects in failure do not only depend on the microstructural properties but also on the macroscopic geometry, loading conditions, and the failure mechanism.     

Analysis of intrinsic stability criteria for isotropic third-order Green elastic and compressible neo-Hookean solids

Internal stability of isotropic nonlinear elastic materials under homogeneous deformation is studied. Results provide new insight into various intrinsic stability measures, first proposed elsewhere, for generic nonlinear elastic solids. Three intrinsic stability criteria involving three different tangent elastic stiffness matrices are considered, corresponding to respective increments in strain measures conjugate to thermodynamic tension, first Piola–Kirchhoff stress, and Cauchy stress. Primary deformation paths of interest include spherical (i.e., isotropic) deformation, uniaxial strain, and simple shear; unstable modes are not constrained to remain along primary deformation paths. Effects of choices of second- and third-order elastic constants on intrinsic stability are systematically studied for physically realistic ranges of constants. For most cases investigated here, internal stability according to strain increments conjugate to Cauchy stress is found to be the most stringent criterion. When third-order constants vanish, internal stability under large compression tends to decrease as Poisson’s ratio increases. When third-order constants are nonzero, a negative (positive) pressure derivative of the shear modulus often promotes unstable modes in compression (tension). For large shear deformation, larger magnitudes of third-order constants tend to result in more unstable behavior, regardless of the sign of the pressure derivative of the shear modulus. A compressible neo-Hookean model is generally much more intrinsically stable than second- and third-order elastic models when Poisson’s ratio is non-negative.     

On the effective elastic properties of matrix composites: Combining the effective field method and numerical solutions for cell elements with multiple inhomogeneities

The work is devoted to calculation of effective elastic constants of homogeneous materials containing random or regular sets of isolated inclusions. Our approach combines the self-consistent effective field method with the numerical solution of the elasticity problem for a typical cell. The method also allows analysis of detailed elastic fields in the composites. By the numerical solution of the elasticity problem for a cell, integral equations for the stress field are used. Discretization of these equations is carried out by Gaussian approximating functions. For such functions, elements of the matrix of the discretized problem are calculated in explicit analytical forms. If the lattice of approximating nodes is regular, the matrix of the discretized problem proves to have the Toeplitz structure. The matrix-vector products with such matrices may be carried out by the Fast Fourier Transform technique. The latter strongly accelerates the process of iterative solution of the discretized problem. Results are given for 2D-media with regular and random sets of circular inclusions, and compared with existing exact solutions.     

Recent investigations on some cubic Laves phase compounds of rare earth and transition metals

Pseudobinary alloy, Tb_0·27Dy_0·73Fe_2−δ , belonging to C-15 cubic Laves phase having MgCu₂-type structure, possesses large magnetostriction and high magnetomechanical coupling coefficient. The advantages of this material over existing piezoelectric materials, particularly for SONAR applications, are highlighted. Recent results on the influence of cobalt (Co) on magnetic and magnetomechanical properties of Tb_0·27Dy_0·73Fe₂ are discussed.     

射影线束形成的二阶曲线及其退化形式

论文用图示法首次系统表达了在二射影平面场中,存在3种形式的射影对应线束。这些对应线束形成二阶曲线时有一定的变化规律。其中底都为非固有点的二线束形成双曲线;底为固有点和非固有点的二线束形成抛物线;底都为固有点的二线束,只要旋转其中之一就可以分别形成双曲线、抛物线和椭圆。这些结论为我们实现二阶曲线之间的转换奠定了理论基础。     

Large‐deformation and friction analysis of non‐linear elastic cable networks by second‐order cone programming

A new formulation is presented for equilibrium shape analysis of cable networks considering geometrical and material non‐linearities. Friction between cables and joint devices is also considered. The second‐order cone programming (SOCP) problem which has the same solution as that of minimization of total potential energy is solved to obtain the equilibrium configuration. The optimality conditions are derived to verify that the solution satisfies equilibrium conditions and friction laws. Since no assumption on stress state is needed in the proposed method, no process of trial and error is involved. No effort is required to develop any analysis software because SOCP can be solved by using the well‐developed software based on the interior‐point method. Copyright © 2002 John Wiley & Sons, Ltd.     

Application of a genetic algorithm: near optimal estimation of the rate and equilibrium constants of complex reaction mechanisms

In iterative non-linear least-squares fitting, the reliable estimation of initial parameters that lead to convergence to the global optimum can be difficult. Irrespective of the algorithm used, poor parameter estimates can lead to abortive divergence if initial guesses are far from the true values or in rare cases convergence to a local optimum. For determination of the parameters of complex reaction mechanisms, where often little is known about what value these parameters should take, the task of determining good initial estimates can be time consuming and unreliable. In this contribution, the methodology of applying a genetic algorithm (GA) to the task of determining initial parameter estimates that lie near the global optimum is explained. A generalised genetic algorithm was implemented according to the methodology and the results of its application are also given. The parameter estimates obtained were then used as the starting parameters for a gradient search method, which quickly converged to the global optimum. The genetic algorithm was successfully applied to both simulated kinetic measurements where the reaction mechanism contained one equilibrium constant and two rate constants to be fitted, and to kinetic measurements of the complexation of Cu²⁺ by 1,4,8,11-tetraazacyclotetradecane where two equilibrium and two rate constants were fitted. The implementation of the algorithm is such that it can be generally applied to any reaction mechanism that can be expressed by standard chemistry notation. The control parameters of the algorithm can be varied through a simple user interface to account for parameter range and the number of parameters involved.     

Limit analysis of plates using the EFG method and second‐order cone programming

The meshless element‐free Galerkin (EFG) method is extended to allow computation of the limit load of plates. A kinematic formulation that involves approximating the displacement field using the moving least‐squares technique is developed. Only one displacement variable is required for each EFG node, ensuring that the total number of variables in the resulting optimization problem is kept to a minimum, with far fewer variables being required compared with finite element formulations using compatible elements. A stabilized conforming nodal integration scheme is extended to plastic plate bending problems. The evaluation of integrals at nodal points using curvature smoothing stabilization both keeps the size of the optimization problem small and also results in stable and accurate solutions. Difficulties imposing essential boundary conditions are overcome by enforcing displacements at the nodes directly. The formulation can be expressed as the problem of minimizing a sum of Euclidean norms subject to a set of equality constraints. This non‐smooth minimization problem can be transformed into a form suitable for solution using second‐order cone programming. The procedure is applied to several benchmark beam and plate problems and is found in practice to generate good upper‐bound solutions for benchmark problems. Copyright © 2009 John Wiley & Sons, Ltd.     

Pseudo second order kinetics and pseudo isotherms for malachite green onto activated carbon: comparison of linear and non-linear regression methods

Pseudo second order kinetic expressions of Ho, Sobkowsk and Czerwinski, Blanachard et al. and Ritchie were fitted to the experimental kinetic data of malachite green onto activated carbon by non-linear and linear method. Non-linear method was found to be a better way of obtaining the parameters involved in the second order rate kinetic expressions. Both linear and non-linear regression showed that the Sobkowsk and Czerwinski and Ritchie's pseudo second order model were the same. Non-linear regression analysis showed that both Blanachard et al. and Ho have similar ideas on the pseudo second order model but with different assumptions. The best fit of experimental data in Ho's pseudo second order expression by linear and non-linear regression method showed that Ho pseudo second order model was a better kinetic expression when compared to other pseudo second order kinetic expressions. The amount of dye adsorbed at equilibrium, q(e), was predicted from Ho pseudo second order expression and were fitted to the Langmuir, Freundlich and Redlich Peterson expressions by both linear and non-linear method to obtain the pseudo isotherms. The best fitting pseudo isotherm was found to be the Langmuir and Redlich Peterson isotherm. Redlich Peterson is a special case of Langmuir when the constant g equals unity.