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.     

磁流变液动态屈服行为的随机多尺度建模

根据能量保守原理,将微观粒子运动的动能等效成宏观动态屈服的应变能,建立内秉悬浮粒子运动涨落的磁流变液剪切应力的随机多尺度模型.分析表明,悬浮粒子初始随机条件和Brownian运动,以及剪切应变加载过程中,链簇反复断裂、重组的先后次序和数目不均匀,导致系统宏观屈服性态的非线性涨落和随机涨落;同时,微观运动涨落在体积平均过程中被严重弱化,宏观随机涨落相对不明显.拟合Bingham剪变率本构模型则进一步表明,外加场强对宏观屈服性态的变异性有一定程度的影响,磁流变液装置设计中应该考虑物理参数的随机性.     

Fundamental role of crystal structure curvature in plasticity and strength of solids

In the paper, we use the nonlinear multiscale approach of physical mesomechanics to demonstrate that the scales of local crystal structure curvature in solids play a fundamental role in the generation of strain-induced defects and cracks. It is shown that strain-induced defects arise at the interfaces of 2D planar and 3D crystal subsystems by the mechanism of “laser pumping” and cracks nucleate as structural phase decay in the zones of crystal structure curvature where the nonequilibrium thermodynamic potential or so-called Gibbs energy is higher than zero. Nonlinear fracture mechanics eliminates the problem of singularity 1/r in equations of crack growth but requires accounting for local lattice curvature at the crack tip.     

Physical meaning of nonholonomic strain measure

The paper overviews the main approaches to the introduction of strain measures. It has been concluded that the physical meaning of certain measures is insufficiently clear. Problems concerning the definition of the physical meaning of the nonholonomic asymmetric strain measure introduced in the framework of a multiscale model, which is based on the physical theory of plasticity, are discussed. This measure is calculated using the corotational integration of the asymmetric and frame-independent strain rate measure equal to the relative velocity gradient. The integration is carried in terms of the corotational coordinate system whose instantaneous motion is determined by averaging the spins of mesoscale elements. It is shown that if elastic distortions are neglected, the introduced mesoscale strain measure is equal to the sum (over all slip systems of the crystallite) of products of accumulated shear multiplied by the basis dyads of the slip systems. The averaging reveals that additional contribution to the value of the macroscale strain measure is attributed, along with elastic distortions, to corotational terms that appear due to different rotation rates of the introduced macroscale corotational frame and crystallite lattices. In view of the absence of analytical expressions for the meso- and macroscale spins, the physical meaning of the macroscale nonholonomic measure is defined in numerical experiments for several strain paths. Calculations have shown that contributions of the elastic and corotational components to the macroscale nonholonomic strain measure are negligible for strain paths of different complexity.     

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.     

Influence of multiscale localized plastic flow on stress-strain patterns

The paper considers the influence of multiscale plastic flow localization on rotational deformation modes and σ-? curves by analyzing the entropy production and equation of state of a deformed solid. It is shown that if the rotational deformation modes are fully self-consistent, the σ-? curve changes monotonically. If not, the curve reveals jerks or serrations due to nonlinear wave relaxation of stresses associated with macroscale non-compensated material rotations. At high loading rates, the rotational deformation modes attain self-consistency by the mechanism of dynamic rotations.     

Nonlinear wave processes in a deformable solid as a hierarchically organized system

Theoretical predictions and experiments demonstrate that solid state mechanics should consider, along with a structurally equilibrium 3D crystalline subsystem, a structurally nonequilibrium planar subsystem as a complex of all surface layers and internal interfaces with broken translation invariance. Primary plastic flow of a loaded solid develops in its structurally nonequilibrium planar subsystem as channeled nonlinear waves of local structural transformations that determine the self-organization law of multiscale plastic flow. These waves initiate mesoscale rotational deformation modes, giving rise to all types of microscale strain-induced defects in the planar subsystem. The strain-induced defects are emitted into the crystalline subsystem as an inhibitor of nonlinear waves of plastic flow in the planar subsystem. Plastic deformation of solids, whatever the loading type, evolves in the field of rotational couple forces. Loss of hierarchical self-consistency by rotational deformation modes culminates in fracture of material as an uncompensated rotational deformation mode on the macroscale.     

Multiscale combustion and turbulence

Multiscale physics is the interaction of different physical processes occurring at largely separated scales. In combustion, many elementary reactions combine to only a few, but still have separated time scales. In flames, owing to the presence of diffusion, time scales manifest themselves as length scales, i.e. thicknesses of reaction layers embedded within each other. For premixed flames there results a single velocity scale, the laminar burning velocity, which in turn defines a flame thickness and a flame time as global length and time scales, respectively. The laminar burning velocity represents the simplest microscale model to be used at a premixed combustion interface.While combustion is a multiscale process, this is not so evident for turbulence. Based on the picture of a cascade process traditional turbulent closure approximations treat turbulence as a single-scale problem. Attempts to model turbulent combustion in the same way by using methods developed for non-reacting turbulent flows therefore must fail, because they ignore the multiscale nature of combustion.There is, however, a long tradition and much progress in multiscale modeling of combustion, both on the macroscale as well as on the microscale level. Unfortunately much of that work is conceived only in its particular context, not as part of a multiscale approach. For instance, papers in the TURBULENT FLAMES Colloquium and the FIRE RESEARCH Colloquium at this and at previous Combustion Symposia often take the viewpoint of macroscale modeling only, while REACTION KINETICS and LAMINAR FLAMES concentrate on microscale aspects. What seems to be needed is a more explicit reference to the needs of models developed in the other parts of the community. Furthermore, research is needed to develop suitable definitions of the interface between macroscale and microscale models.     

Multiscaling of lattice curvature on friction surfaces of metallic materials as a basis of their wear mechanism

A comprehensive structural study has been performed to explore deformation and wear debris formation on friction surfaces of metallic materials. A hierarchy of structural scales of plastic deformation and failure during wear has been established. The nanoscale plays the major role in the hierarchical self-organization of multiscale debris formation processes. On this scale, bifurcational interstitial states arise in zones of local lattice curvature, with plastic distortion and motion of nonequilibrium point defects which determine the nonlinear dynamics of structure formation and wear of surface layers. Nonequilibrium vacancies on lattice sites form microporosity through the coalescence mechanism under plastic distortion. The microporosity is a precursor of meso- and macroscale plastic shearing that defines wear debris formation.     

Opportunities with Synchrotron Radiation at the Mesoscale

What is mesoscale science? The modifier “meso” can mean different things to different communities. In many areas of science, “mesoscale” generally refers to a middle-ground domain of length, energy, or time where theories accurate at both lower and higher scales fail. In materials science, for example, mesoscale behavior often rises when quantum behavior begins to fade, collective effects become important, or statistical variation and defects appear, often at length scales larger than a few nm. However, for atmospheric scientists and ecologists, mesoscale means miles. For meterologists, mesoscale means hundreds to thousands of miles. The mesoscale arena for cosmologists is many light-years across.     

A multiscale coupling method for the modeling of dynamics of solids with application to brittle cracks

We present a multiscale model for numerical simulations of dynamics of crystalline solids. The method combines the continuum nonlinear elasto-dynamics model, which models the stress waves and physical loading conditions, and molecular dynamics model, which provides the nonlinear constitutive relation and resolves the atomic structures near local defects. The coupling of the two models is achieved based on a general framework for multiscale modeling – the heterogeneous multiscale method (HMM). We derive an explicit coupling condition at the atomistic/continuum interface. Application to the dynamics of brittle cracks under various loading conditions is presented as test examples.     

Vertically nested nonhydrostatic model for multiscale resolution of flows in the upper troposphere and lower stratosphere

Vertical nesting with refined gridding in coupled mesoscale weather research and forecasting (WRF)/microscale models are presented with a particular emphasis on improved vertical resolution in the upper troposphere and lower stratosphere (UTLS). The finest mesoscale nest is coupled with a sequence of microscale nests with finer resolution in both the horizontal and the vertical. The fully three-dimensional, compressible nonhydrostatic Navier–Stokes equations are solved using a time-split method with a refined grid in the vertical, and improved resolution in the UTLS region. For nesting, both lateral and vertical boundary conditions are treated via implicit relaxation in buffer zones where all fields are relaxed to those obtained from the finest mesoscale nest. Computational results are presented demonstrating the ability of microscale nests to resolve multiscale physics of strongly nonlinear interactions and laminated structures observed in the Terrain-induced rotor experiment (T-REX) campaign of field measurements. Very high resolution real case nested simulations are conducted. The microscale nests fully resolve localized shear layers and sharp gradients of vertical velocity and potential temperature near the tropopause and in the lower stratosphere.     

一类非线性相对转动系统的组合共振分岔与混沌

研究一类具有异宿轨道的非线性相对转动系统的分岔与混沌运动. 应用耗散系统的拉格朗日方程建立一类组合谐波激励作用下非线性相对转动系统的动力学方程. 利用多尺度法求解相对转动系统发生组合共振时满足的分岔响应方程并进行奇异性分析, 得到了系统稳态响应的转迁集. 根据相对转动系统异宿轨道参数方程, 求解了异宿轨道的Melnikov函数, 并给出了系统发生Smale马蹄变换意义下混沌的临界条件. 最后采用数值方法, 通过分岔图, 最大Lyapunov指数图, 相轨迹图和庞加莱截面图研究系统参数对混沌运动的影响.