Motion decomposition,frame-indifferent derivatives,and constitutive relations at large displacement gradients from the viewpoint of multilevel modeling

Widespread approaches to generalizing geometrically linear constitutive relations to the case of large displacement gradients have been considered. These approaches are based on the replacement of the material derivatives of stress and strain tensors by frame-indifferent corotational or convective derivatives. The correctness of choosing the indifferent derivatives is analyzed from a more general viewpoint of motion decomposition into rigid and strain-induced motion. It is shown that the use of the Zaremba-Jaumann derivative in constitutive relations corresponds to motion decomposition by the Cauchy-Helmholtz theorem according to which instantaneous rigid rotation of a material particle with small neighborhood is described by the vorticity tensor. The relations derived with the use of the so-called "logarithmic spin" are analyzed. It is noted that the spin tensors entering into these relations are not associated with the material fibers (in particular with the symmetry axes of anisotropic materials) during the entire studied process of deformation. Hence these spins do not describe the rotation of the reference frame (crystallographic one for metals) in which the material property tensor is defined. A new method of motion decomposition is proposed on the basis of a two-level (macro and meso) approach for single and polycrystalline metals. The mesoscopic spin is determined by the rotation rate of the corotational coordinate system associated with the crystallographic direction and crystallographic plane. Mesoscopic constitutive relations are formulated using the proposed spin. The spin of a representative macrovolume is determined by averaging the spins of the crystallites contained in this volume. This spin is used to formulate rate-type elastic constitutive equations. Examples are given to illustrate the stress state determination for loading along closed strain paths and two-segment paths for isotropic and anisotropic (with cubic symmetry, hcp) elastic materials, and an elastoviscoplastic fcc crystallite. The determination is carried out by using the corotational derivatives in the constitutive relations which are obtained by different motion decomposition methods.     

Two-scale models of polycrystals: Evaluation of validity of Ilyushin’s isotropy postulate at large displacement gradients

This paper discusses multiscale models of inelastic deformation of single- and polycrystals, which are based on crystal plasticity theories, as applied to the verification and justification of Ilyushin’s isotropy postulate (in a special form) at large displacement gradients. Different approaches to motion decomposition on the macroscale into quasi-rigid (described by the motion of a corotational coordinate system) and strain-induced motion (a relatively moving coordinate system) are considered. The strain path is defined in terms of a moving coordinate system. Corresponding kinematic effects are defined in terms of a laboratory coordinate system. In this case, the loading process image is constructed and loading conditions are specified in terms of the moving coordinate system. Calculations are performed for two types of strain paths with different curvature by assuming two different hypotheses about quasi-rigid motion on the macroscale: (i) the spin of the moving coordinate system is equal to an averaged mesoscale spin, and (ii) the spin is equal to the macroscale vortex. It is shown that the isotropy postulate is more valid in the case of assuming the first hypothesis.     

A comparative analysis of the mesoscale stress-strain state in two- and three-dimensional polycrystalline specimens

A comparative analysis has been performed of mesoscale stress and strain distributions in sections of 3D polycrystalline specimens and in their 2D cousins under plane strain and plane stress conditions. For similar macroscale stress-strain curves, the mesoscale plastic strain localization patterns are shown to differ essentially both qualitatively and quantitatively in 2D and 3D models. In other words, the same effective mechanical response of the materials can be provided by different mesoscale stress and strain distributions depending on the loading technique used and geometric features of the specimens (thin plates, thick specimens, etc.).     

超细长弹性杆动力学的Gauss原理

研究基于Gauss 变分的超细长弹性杆动力学建模的分析力学方法.分别在弧坐标和时间的广义加速度空间定义虚位移,给出了非完整约束加在虚位移上的限制方程;建立了弹性杆动力学的Gauss原理,由此导出Kirchhoff方程、Lagrange方程、Nielsen方程以及Appell方程;对于受有非完整约束的弹性杆,导出了带乘子的Lagrange方程;建立了弹性杆截面动力学的Gauss最小拘束原理并说明其物理意义. 关键词： 超细长弹性杆动力学 分析力学 Gauss变分 最小拘束原理     

Dislocation field theory in 2D: Application to graphene

A two-dimensional (2D) dislocation continuum theory is being introduced. The present theory adds elastic rotation, dislocation density, and background stress to the classical energy density of elasticity. This theory contains four material moduli. Two characteristic length scales are defined in terms of the four material moduli. Non-singular solutions of the stresses and elastic distortions of an edge dislocation are calculated. It has been pointed out that the elastic strain agrees well with experimental data found recently for an edge dislocation in graphene.     

The Universe and the Quantum Computer

It is first pointed out that there is a common mathematical model for the universe and the quantum computer. The former is called the histories approach to quantum mechanics and the latter is called measurement-based quantum computation. Although a rigorous concrete model for the universe has not been completed, a quantum measure and integration theory has been developed which may be useful for future progress. In this work we show that the quantum integral is the unique functional satisfying certain basic physical and mathematical principles. Since the set of paths (or trajectories) for a quantum computer is finite, this theory is easier to treat and more developed. We observe that the sum of the quantum measures of the paths is unity and the total interference vanishes. Thus, constructive interference is always balanced by an equal amount of destructive interference. As an example we consider a simplified two-slit experiment.     

Experimental study of lattice distortion in ellipsoid-like nano-crystallites of copper

The elastic state of embedded inclusions is of considerable importance to the properties of materials. The non-uniform lattice distortion in the inclusions in which the interfaces are shaped with variable curvature cannot be measured by usual experimental methods. In this paper, the lattice distortions in an ellipsoid-like nano-crystallite of copper were measured by means of the peak finding method in the central part of the HRTEM image. The effects of contrast delocalization are studied by HRTEM image simulations, which show that the measured spacings of peaks in the middle part of the crystallite can be considered approximately equal to the true spacings of columns. With the HRTEM method, our measured results show that the nano-crystallite is expanded in the short axis direction and compressed in the long axis direction. The results calculated with the elasticity theory incorporating interface tension consist with the experimental results of HRTEM.     

Fundamentals of the nonholonomically covariant formulation of the general theory of relativity

The physical foundations of the nonholonomic formulation of general relativity are determined, and the role of the Fock-Ivanenko coefficients in setting up and developing the tetrad formalism in general relativity is discussed. The physical and geometrical meaning of the nonholonomic transformations used in general relativity is determined.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 55–60, December, 1974.     

Problems of the mesomechanics of strength and plasticity of nanostructured materials

The results of the investigations performed in collaboration with our co-workers are reviewed and used to formulate a conceptual framework of the physical mesomechanics of nanostructured materials. Low plasticity of materials of this kind is associated with suppression of the microscale deformation due to the motion of dislocations and with development of meso- and macroscale localized-deformation bands. For an optimum combination of strains at the micro- and mesoscale levels, formation of a nanocrystalline structure provides high strength and plastic properties of the materials. Strain localization at the macroscale level impairs the strength and plasticity of nanostructured materials.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 4–17, August, 2004.     

General theory of micropolar elastic thin shells

The paper formulates general hypotheses of micropolar elastic thin shells that are given asymptotic validation. Using these hypotheses and three-dimensional Cosserat (micropolar, asymmetric) theory of elasticity, general two-dimensional applied models of micropolar elastic thin shells with independent displacement and rotation fields, constrained rotation and low shear rigidity are constructed to suit dimensionless physical parameters of the shell material. The constructed micropolar shell models take into complete account transverse shear strain and related strain. Models of micropolar elastic thin plates and beams are particular cases of the constructed micropolar shell models. An axially symmetric stress-strain state problem of a hinged cylindrical micropolar shell is considered. Numerical analysis is used to demonstrate effective strength and rigidity characteristics of micropolar elastic shells.     

A theoretical approach to local attenuation measurements of shear waves by MRE. Preliminary experimental results

An essential highlight of the presented method is the employment of Magnetic Resonance Elastography (MRE) for local measurements of the attenuation of elastic shear waves introduced into a biological sample. Such a measurement can be accomplished by combining the MRE method with those methods, in which collective displacement of spins is induced by external physical factors, such as variable electric field, strong magnetic field gradient or longitudinal elastic wave. A theoretical basis of the method involving external factors and results of preliminary experiments have been presented in this paper.     

Heterogeneous crystallization of hard and soft spheres near flat and curved walls

Crystallization represents a long-standing problem in statistical physics and is of great relevance for many practical and industrial applications. It often occurs in the presence of container walls or impurities, which are usually unavoidable or might even be desirable to facilitate crystallization by exploiting heterogeneous nucleation. Heterogeneous nucleation relies on a seed. Here we discuss the role of the seed and concentrate on a very generic situation, namely crystallization of hard and soft colloidal spheres in the presence of flat or curved hard walls. Curvature serves as a simple means to introduce a tunable mismatch between the seed-induced crystal lattice and the thermodynamically-favoured lattice. The mismatch induces distortions and elastic stress, which accumulate while the crystallite grows. This has an important consequence: once the crystallite reaches a critical size, it detaches from the seed allowing it to relax. The relaxed crystal continues to grow in the bulk, but crystallization ceases before reaching the seed, which now represents an impurity. Therefore, while seeds favour nucleation, any mismatch, like the seed curvature or an incommensurate structure, induces unfavourable distortions and can lead to the detachment of the crystallite. An additional mechanism to relax distortions is available to soft spheres, which can exploit their interaction potential and possibly deform. The different multi-step processes have been investigated by confocal microscopy, which provides particle-level information, and compared to computer simulations and theoretical results.     

Mesoscale simulation of concrete spall failure

Although intensively studied, it is still being debated which physical mechanisms are responsible for the increase of dynamic strength and fracture energy of concrete observed at high loading rates, and to what extent structural inertia forces on different scales contribute to the observation. We present a new approach for the three dimensional mesoscale modelling of dynamic damage and cracking in concrete. Concrete is approximated as a composite of spherical elastic aggregates of mm to cm size embedded in an elastic cement stone matrix. Cracking within the matrix and at aggregate interfaces in the μm range are modelled with adaptively inserted—initially rigid—cohesive interface elements. The model is applied to analyse the dynamic tensile failure observed in Hopkinson-Bar spallation experiments with strain rates up to 100/s. The influence of the key mesoscale failure parameters of strength, fracture energy and relative weakening of the ITZ on macromechanic strength, momentum and energy conservation is numerically investigated.     

格子Boltzmann方法模拟微尺度流动和传热

本文采用格子Boltzmann方法(LBM)对微尺度Couette流的流动及传热进行了模拟.为了获得壁面边界的速度滑移和温度阶跃,在含有粘性热耗散的热格子模型的基础上,提出了一种新的直接基于宏观量的边界处理格式.模拟得到的速度场和温度分布与解析解吻合得相当好,充分说明了本文采用的模型和边界处理的合理性同时在模拟中还发现:对于不同的Kn数,均存在使得其上壁面的温度阶跃为零的临界Ec数,并且其临界值均在3.0附近.     

Characteristics of plastic flow localization autowaves

The dispersion relations for localized plastic strain autowaves are considered for some metals at the stages of easy slip and linear strain hardening. The quadratic form of this relation, the type of the dependences of the phase and group velocities of such autowaves on the wavenumber, and the quantitative relation between the characteristics of plastic flow localization wave processes and elastic wave parameters in solids being deformed are established and explained. An invariant for strain effects at micro- and macroscopic levels is introduced.     

Nanodipoles of partial disclinations in the region of localized elastic distortions

Strain localization in the region of elastic distortions is revealed in nickel dynamic recrystallization grains during torsion in Bridgman anvils, which leads to the formation of reorientation nanobands with the elastic lattice curvature equal to hundreds of degrees per micron. It is shown that the nanobands are formed by the motion of partial disclination nanodipoles, i.e., zones of constrained elastic shear and rotations distinguished by extremely high local internal stress gradients.     

Fission barriers for even-even actinide nuclei

Fission barriers for even-even nuclei in the region (Th ... Ku) are calculated in the framework of the Strutinsky method and using the concept of dynamic fission paths. The single particle states are calculated in a deformed Woods-Saxon potential including axial asymmetry at the inner barrier and deviation from reflection symmetry at the outer barrier. It is shown that in the present model also the mass symmetric outer barrier is unstable against axially asymmetric (γ) distortions.