Anisotropic model for granulated sea ice dynamics

A continuum model describing sea ice as a layer of granulated thick ice, consisting of many rigid, brittle floes, intersected by long and narrow regions of thinner ice, known as leads, is developed. We consider the evolution of mesoscale leads, formed under extension, whose lengths span many floes, so that the surrounding ice is treated as a granular plastic. The leads are sufficiently small with respect to basin scales of sea ice deformation that they may be modelled using a continuum approach. The model includes evolution equations for the orientational distribution of leads, their thickness and width expressed through second-rank tensors and terms requiring closures. The closing assumptions are constructed for the case of negligibly small lead ice thickness and the canonical deformation types of pure and simple shear, pure divergence and pure convergence. We present a new continuum-scale sea ice rheology that depends upon the isotropic, material rheology of sea ice, the orientational distribution of lead properties and the thick ice thickness. A new model of lead and thick ice interaction is presented that successfully describes a number of effects: (i) because of its brittle nature, thick ice does not thin under extension and (ii) the consideration of the thick sea ice as a granular material determines finite lead opening under pure shear, when granular dilation is unimportant.     

基于Voronoi切割算法的碎冰区构造及离散元分析

离散元方法广泛应用于海冰,特别是碎冰区的动力过程及其对海洋结构作用过程的数值模拟。为构造碎冰区中的冰块几何特性,基于二维Voronoi图方法对计算域进行随机切割以生成碎冰区中冰块的几何形态,并采用球体单元对每个碎冰块单元进行填充,从而确定碎冰区的初始分布场。在采用Voronoi图进行碎冰区构造时,可对冰块尺寸、几何形态和密集度等海冰参数进行设定。为确定冰块的不同几何规则度,综合采用排斥法和扰动法以定量地控制碎冰块几何形态从完全随机分布到规则分布的连续变换。为分析不同几何规则度下碎冰块的几何特性概率分布规律,对计算域内冰块的面积和边数等参数进行统计分析,从而可更合理地参数化控制初始冰场中碎冰块的几何特性。在此基础上,本文基于粘接-破碎的球体离散元方法对不同冰况下锥体结构的冰荷载进行了数值计算,讨论分析了碎冰区的海冰密集度、冰块面积和几何规则度对冰载荷的影响。     

Modeling ocean wave propagation under sea ice covers

Operational ocean wave models need to work globally, yet current ocean wave models can only treat ice covered regions crudely. The purpose of this paper is to provide a brief overview of ice effects on wave propagation and different research methodology used in studying these effects. Based on its proximity to land or sea, sea ice can be classified as: landfast ice zone, shear zone, and the marginal ice zone. All ice covers attenuate wave energy. Only long swells can penetrate deep into an ice cover. Being closest to open water, wave propagation in the marginal ice zone is the most complex to model. The physical appearance of sea ice in the marginal ice zone varies. Grease ice, pancake ice,brash ice, floe aggregates, and continuous ice sheet may be found in this zone at different times and locations. These types of ice are formed under different thermal-mechanical forcing. There are three classic models that describe wave propagation through an idealized ice cover: mass loading,thin elastic plate, and viscous layer models. From physical arguments we may conjecture that mass loading model is suitable for disjoint aggregates of ice floes much smaller than the wavelength, thin elastic plate model is suitable for a continuous ice sheet, and the viscous layer model is suitable for grease ice. For different sea ice types we may need different wave ice interaction models. A recently proposed viscoelastic model is able to synthesize all three classic models into one. Under suitable limiting conditions it converges to the three previous models. The complete theoretical framework for evaluating wave propagation through various ice covers need to be implemented in the operational ocean wave models. In this review, we introduce the sea ice types, previous wave ice interaction models, wave attenuation mechanisms,the methods to calculate wave reflection and transmission between different ice covers, and the effect of ice floe breaking on shaping the sea ice morphology. Laboratory experiments,field measurements and numerical simulations supporting the fundamental research in wave-ice interaction models are discussed. We conclude with some outlook of future research needs in this field.     

ANALYSIS OF SHIP MANEUVERING PERFORMANCES AND ICE LOADS ON SHIP HULL WITH DISCRETE ELEMENT MODEL IN BROKEN-ICE FIELDS

采用离散元模型对碎冰区浮冰与船舶结构的相互作用进行了数值研究。碎冰由三维圆盘单元构成,并考虑其在海流作用下的浮力、拖曳力和附加质量。船体结构由一系列三角形单元组合构造。通过海冰与船体单元间的接触判断和接触力计算,确定海冰与船体结构之间的相互作用。采用以上离散单元模型对不同冰况（冰速、冰厚、冰块尺寸和密集度）以及航速条件下,海冰对船体的动力作用过程进行了数值分析,对比分析了以上因素对船体冰载荷的影响,可为冰区船舶的安全运行和结构设计提供一定的借鉴作用。     

海冰动力学数值模拟中改进的PIC方法

为了准确地模拟海冰的动力过程,需要建立精确有效的数值方法。本文结合质点网格法(PIC)和光滑质点流体动力学方法(SPH)发展了一种改进的PIC方法。该方法在欧拉坐标下对海冰动量方程进行差分计算,在拉格朗日坐标下进行海冰质点位移、厚度和密集度计算,并采用Gauss函数进行欧拉网格点与拉格朗日质点间海冰参数的交互插值。采用改进的PIC方法对规则区域内的海冰堆积过程进行了数值试验,对渤海海冰的动力过程进行了72小时数值模拟。计算结果均表明改进的PIC方法具有计算量小,计算结果平稳精确的优点,可很好地适用于海冰动力作用过程的数值模拟。     

Numerical modelling of ice jam resistance to main channel flow

In northern countries, subfreezing temperatures during the winter season result in the formation of ice covers on most rivers. Towards the end of the winter season, during the spring break-up period, stationary ice covers become weak in strength and break up. The resulting broken ice pieces or ice floes are significantly larger in thickness and have a rougher undersurface relative to sheet ice and impose higher hydraulic resistance. The downstream movement of the ice floes may be arrested under conditions such as an intact ice cover, bridge piers or channel constrictions, among others, thereby initiating a break-up ice jam. These ice jams most often have been observed to cause very high water stages. Detrimental effects caused by these high water levels encompass those of operational and design-related problems such as the flooding of communities due to ice-jam-induced backwater, flood risk assessments, altering of the open water flow regime, bed scour and flooding of bridges. The ability to predict the influence of an ice jam on the main flow is of considerable importance in river engineering and can be viewed upon by its effects on the variation in the water surface levels. All other information is dependent on the foregoing. The ice jam influence on the main flow can be regarded with respect to local and global standpoints. The primary objective of this study is to formulate the influence of the ice jam on the main channel flow. The formulation is then coupled with a two-dimensional numerical model for the simulation of the water flow regime. The data from different laboratory experiments on ice jams are reproduced numerically. Various simulations are then carried out to compute the water surface levels and velocities in channels under ice jam conditions. The numerical results are then compared with the laboratory data. Results show that the mathematical formulation developed to predict the water surface levels and velocities along the ice jam length as well as upstream and downstream of its leading and trailing edges respectively gives satisfactory predictions.     

Anisotropic yield and plastic flow of polycrystalline solids

Deformation induced anisotropy in polycrystalline solids results mainly from crystallographic slip due to dislocation motion at the grain level and texture development due to grain rotation at the aggregate level. To describe these characteristics, the so-called scale invariance approach is adopted which allows information and constitutive relations pertaining to single slip to be cast in a form of macroscopic constitutive equations. An orientation distribution function (ODF) and a texture tensor are introduced into the earlier version (based on the hypotheses of single slip at the grain level and isotropic distribution of the crystallites at the aggregate level) of the scale invariance framework to describe texture effects in plastically deformed polycrystals. The texture tensor is calculated either directly through the solution of ODF, or indirectly through an appropriate set of evolution equations for the orientation tensors and the use of a closure approximation. Theoretical predictions for anisotropic yield and plastic flow behavior compare well with available experimental data.     

基于扩展多面体的离散单元法及其作用于圆桩的冰载荷计算

对于具有复杂几何形态的多面体单元,线性接触模型不能准确地计算不同接触模式下的作用力,且接触变形和作用力方向也不易判断.基于闵可夫斯基和(Minkowski sum)方法的扩展多面体单元能够准确描述非规则颗粒单元的几何形态,并可精确计算单元间的接触碰撞作用.该方法具有接触判断简单、计算效率高的特点.它将基本多面体和扩展球体相叠加以形成具有光滑棱边和角点的扩展多面体单元.考虑扩展多面体单元相互作用过程中角点、棱边和平面之间的不同接触模式,发展了相应的非线性黏弹性接触模型. 该接触模型将不同接触模型下的法向刚度统一表述为单元接触中接触点处等效曲率半径的函数;黏滞力和切向弹性力接触模型则借鉴球体单元非线性接触模型的处理方法. 为检验扩展多面体的可靠性,对碎冰区冰块对圆桩结构的冰载荷进行了离散元分析. 采用沃洛诺伊(Voronoi)切割算法获得了碎冰的初始随机分布状态,并考虑了海冰在运动过程中的海水浮力和拖曳力.计算表明该扩展多面体单元可描述海冰在海流拖曳下的运动过程以及圆桩结构的动冰力特性.在此基础上进一步分析了冰速和冰块尺寸对圆桩冰力的影响,并确定了冰力在圆桩上的分布规律. 最后,讨论了目前扩展多面体单元在计算冰载荷方面的局限性和改进方法.      

The evolution of Hooke's law due to texture development in FCC polycrystals

Initially isotropic aggregates of crystalline grains show a texture-induced anisotropy of both their inelastic and elastic behavior when submitted to large inelastic deformations. The latter, however, is normally neglected, although experiments as well as numerical simulations clearly show a strong alteration of the elastic properties for certain materials. The main purpose of the work is to formulate a phenomenological model for the evolution of the elastic properties of cubic crystal aggregates. The effective elastic properties are determined by orientation averages of the local elasticity tensors. Arithmetic, geometric, and harmonic averages are compared. It can be shown that for cubic crystal aggregates all of these averages depend on the same irreducible fourth-order tensor, which represents the purely anisotropic portion of the effective elasticity tensor. Coupled equations for the flow rule and the evolution of the anisotropic part of the elasticity tensor are formulated. The flow rule is based on an anisotropic norm of the stress deviator defined by means of the elastic anisotropy. In the evolution equation for the anisotropic part of the elasticity tensor the direction of the rate of change depends only on the inelastic rate of deformation. The evolution equation is derived according to the theory of isotropic tensor functions. The transition from an elastically isotropic initial state to a (path-dependent) final anisotropic state is discussed for polycrystalline copper. The predictions of the model are compared with micro–macro simulations based on the Taylor–Lin model and experimental data.     

考虑晶体滑移面分解正应力的细观损伤模型

材料内部的解理、滑移面剥离等细观损伤是引起宏观失效的根源, 从细观尺度研究损伤的发生和发展有助于深入认识材料的变形和失效过程. 本文基于晶体塑性理论, 从滑移系的受力和变形出发研究材料的细观损伤, 建立了考虑滑移面分解正应力的细观损伤模型, 为晶体材料解理断裂的分析提供了新方法. 首先, 在晶体弹塑性变形构型的基础上引入损伤变形梯度张量的概念, 从变形运动学着手建立了考虑损伤能量耗散的本构方程, 并推导了塑性流动方程与损伤演化方程; 然后, 建立了相应的数值计算方法, 给出了应力与状态变量的更新算法, 推导了Jacobian矩阵的表达式; 接着, 以$[100]$取向的单晶铜材料为例, 通过有限元计算与试验结果的对比, 并采用粒子群优化算法标定了11个材料细观参数; 最后, 将所提细观损伤模型应用于RVE单轴拉伸过程的模拟, 得到了考虑损伤影响的应力应变曲线, 并分析了材料的塑性流动与损伤演化过程. 结果表明, 本文所提模型能够计算材料在受载过程中的损伤累积效应, 合理反映晶体材料的细观损伤机理.      

Anisotropic damage mechanics for viscoelastic ice

We present a formulation of continuum damage in glacier ice that incorporates the induced anisotropy of the damage effects but restricts these formally to orthotropy. Damage is modeled by a symmetric second rank tensor that structurally plays the role of an internal variable. It may be interpreted as a texture measure that quantifies the effective specific areas over which internal stresses can be transmitted. The evolution equation for the damage tensor is motivated in the reference configuration and pushed forward to the present configuration. A spatially objective constitutive form of the evolution equation for the damage tensor is obtained. The rheology of the damaged ice presumes no volume conservation. Its constitutive relations are derived from the free enthalpy and a dissipation potential, and extends the classical isotropic power law by elastic and damage tensor dependent terms. All constitutive relations are in conformity with the second law of thermodynamics.PACS 83.60.Df, 62.20.Mk     

Robustness of pulsating jet-like layers in sheared nano-rod dispersions

Nano-rod dispersions in steady shear exhibit persistent transient responses both in experiments and simulations. The rotational contribution from shear flow couples with orientational diffusion, excluded-volume interactions, and distortional elasticity to yield complex dynamics and gradient morphology of the rod ensemble. The classification of sheared responses has mostly focused on “nematodynamics” of the collective particle response known as tumbling, wagging and kayaking; in heterogeneous simulations, one monitors the variability in nematodynamics across the domain. In this paper, we focus on flow coupling and non-Newtonian feedback in transient heterogeneous simulations, and in particular on a remarkable effect: the formation of localized, pulsating jet layers in the shear gap. We solve the Navier–Stokes momentum equations coupled through an orientation-dependent stress to three different orientational models (a kinetic Smoluchowski equation and two tensor models, one from kinetic closure and another from irreversible thermodynamics). A similar spurt phenomenon was reported in 1D simulations of a model for planar nematic liquids by Kupferman et al. [R. Kupferman, M. Kawaguchi, M.M. Denn, Emergence of structure in models of liquid crystalline polymers with elasticity, J. Non-Newt. Fluid Mech. 91 (2000) 255–271], which we extend to full orientational configuration space. We show: the pulsating jet layers correlate, in space and time, with the formation of a non-topological “oblate defect phase” in which the principal axis of orientation spreads from a unique direction to a circle; the jet-defect layers form where the local nematodynamics transitions from finite oscillation (wagging) to continuous rotation (tumbling), and when neighboring directors lose phase coherence; and, a negative first normal stress difference develops in the pulsating jet-defect layers. Finally, we extend one model algorithm to two space dimensions and show numerical stability of the jet-defect phenomenon to 2D perturbations.     

Self-similar regimes of liquid-layer spreading along a superhydrophobic surface

Within the Stokes film approximation, unsteady spreading of a thin layer of a heavy viscous fluid along a horizontal superhydrophobic surface is studied in the presence of a given localized mass supply in the film. The forced (induced by the mass supply) spreading regimes are considered, for which the surface tension effects are insignificant. Plane and axisymmetric flows along the principal direction of the slip tensor of the superhydrophobic surface are studied, when the corresponding slip tensor component is either a constant or a power function of the spatial coordinate, measured in the direction of spreading. An evolution equation for the film thickness is derived. It is shown that this equation has self-similar solutions of a source type. The examples of self-similar solutions are constructed for power and exponential time dependences of mass supply. In the final part of the paper, some of the solutions constructed are generalized to the case of a weak dependence of the flow on the second spatial coordinate, caused by a slight variability of the slip coefficient in the direction normal to that of spreading. The constructed self-similar solutions can be used for experimental determination of the parameters important for hydrodynamics, e.g. the slip tensor components of commercial superhydrophobic surfaces.     

Nonlocal continuum crystal plasticity with internal residual stresses

We derive a three-dimensional constitutive theory accounting for length-scale dependent internal residual stresses in crystalline materials that develop due to a non-homogeneous spatial distribution of the excess dislocation (edge and screw) density. The second-order internal stress tensor is derived using the Beltrami stress function tensor φ that is related to the Nye dislocation density tensor. The formulation is derived explicitly in a three-dimensional continuum setting for elastically isotropic materials. The internal stresses appear as additional resolved shear stresses in the crystallographic visco-plastic constitutive law for individual slip systems. Using this formulation, we investigate two boundary value problems involving single crystals under symmetric double slip. In the first problem, the response of a geometrically imperfect specimen subjected to monotonic and cyclic loading is investigated. The internal stresses affect the overall strengthening and hardening under monotonic loading, which is mediated by the severity of initial imperfections. Such imperfections are common in miniaturized specimens in the form of tapered surfaces, fillets, fabrication induced damage, etc., which may produce strong gradients in an otherwise nominally homogeneous loading condition. Under cyclic loading the asymmetry in the tensile and compressive strengths due to this internal stress is also strongly influenced by the degree of imperfection. In the second example, we consider simple shear of a single crystalline lamella from a layered specimen. The lamella exhibits strengthening with decreasing thickness and increasing lattice incompatibility with shearing direction. However, as the thickness to internal length-scale ratio becomes small the strengthening saturates due to the saturation of the internal stress.Finally, we present the extension of this approach for crystalline materials exhibiting elastic anisotropy, which essentially depends on the appropriate Green function within φ.     

On the Torsion of a Class of Nonlinear Fiber Composite Cylinders

This paper presents an analysis of the torsion of a solid or annular circular cylinder consisting of nonlinear material in the form of an elastic matrix with embedded unidirectional elastic fibers parallel to the cylinder axis. The specific class of composite considered is one for which nonlinear fiber-matrix interface slip is captured by uniform cohesive zones of vanishing thickness. Previous work on the effective antiplane shear response of this material leads to a stress–strain relation depending on the interface slip together with an integral equation governing its evolution. Here, we obtain an approximate single mode solution to the integral equation and utilize it to solve the torsion problem. Equations governing the radial distributions of shear stress and interface slip are obtained and formulae for torque–twist rate are presented. The existence of singular surfaces, i.e., surfaces across which the slip and the shear stress experience jump discontinuities are analyzed in detail. Specific results are presented for an interface force law that allows for interface failure in shear.     

A novel internal dissipation inequality by isotropy and its implication for inelastic constitutive characterization

In the present work a novel inelastic deformation caused internal dissipation inequality by isotropy is revealed. This inequality has the most concise form among a variety of internal dissipation inequalities, including the one widely used in constitutive characterization of isotropic finite strain elastoplasticity and viscoelasticiy. Further, the evolution term describing the difference between the rate of deformation tensor and the “principal rate” of the elastic logarithmic strain tensor is set, according to the standard practice by isotropy, to equal a rank-two isotropic tensor function of the corresponding branch stress, with the tensor function having an eigenspace identical to the eigenspace of the branch stress tensor. Through that a general form of evolution equation for the elastic logarithmic strain is formulated and some interesting and important results are derived. Namely, by isotropy the evolution of the elastic logarithmic strain tensor is embodied separately by the evolutions of its eigenvalues and eigenprojections, with the evolution of the eigenprojections driven by the rate of deformation tensor and the evolution of the eigenvalues connected to specific material behavior. It can be proved that by isotropy the evolution term in the present dissipation inequality stands for the essential form of the evolution term in the extensively applied dissipation inequality.     

桥墩-冰塞-局部冲刷相关问题研究进展

桥梁建设改变了河流的边界条件、水流条件和河床泥沙的运动状态,冬季河流中有冰塞出现时则产生相互影响作用.近年来,基于冰塞稳定性力学分析,开展了桥墩影响下冰塞稳定性研究,所得桥墩影响下冰塞稳定性判别公式计算结果和实测资料能够较好得吻合;研究了桥墩对河道卡封以及临界流凌密度的影响,计算得到的临界流凌密度与实验值较为接近;介绍...     

水位变化对正倒锥体冰载荷影响的离散元分析

在海冰与锥体海洋结构的相互作用过程中,潮汐水位变化时海冰作用于锥体结构的位置改变对冰载荷具有显著影响.本文采用具有粘结破碎功能的离散元方法计算海冰与锥体作用的破坏过程.同时考虑海冰上下表面温度差异对海冰强度的影响,将离散元计算冰载荷及海冰破坏模式与渤海现场实测数据进行对比验证.离散元结果表明,海冰与正锥和倒锥碰撞时均发生弯曲破坏,且冰载荷均随水线处锥径的增大而增大.在水线处锥径相同的情况下,正锥冰载荷大于倒锥冰载荷,而正锥作用下海冰的断裂长度则较小.基于离散元计算结果和渤海现场观测资料分析了海冰与正锥、倒锥作用时冰载荷和断裂长度差异的主要原因.海冰与正倒锥交界线处作用时,一般发生弯曲破坏.当冰层中心高度与正倒锥交界线的高度相同时,海冰才会发生局部挤压破碎,但冰荷载并没有明显升高.由此可见,倒锥体结构可有效降低冰载荷从而具有较好的抗冰性能.以上研究表明离散元方法可确定海冰与锥体结构作用时的海冰破碎规律和冰载荷特性,为海洋工程结构的抗冰设计提供参考依据.      

含微裂纹材料的损伤理论

本文从含微裂纹材料的变形能出发引出了裂纹的方位张量。在考虑裂纹受压闭合与滑动摩擦的基础上,给出了损伤张量、损伤应变及有效弹性常数。文中给出了损伤机构离散化的方法,并对方位密度给出了演化方程。最后给出一个单向拉压的应力应变关系例子,并揭示了裂纹扩展时的应力突跌现象。