Effect of radiation scattering on the melting and solidification of a flat layer of a translucent medium

The paper considers the effect of isotropic and anisotropic scattering of radiation on the melting (solidification) of a flat layer of a semitransparent medium between opaque surfaces. The mathematical model of the phase transition is the classical formulation of the Stefan problem. From results of numerical calculations it follows that radiation scattering has a significant effect on the rate of propagation of the phase transition front and formation of a temperature profile during melting (solidification) of a semitransparent medium.     

温度对冲击相变波传播的影响

冲击加载下,相界面的传播是一热力耦合过程。相变波阵面不仅是力学和物质间断面,也是温度界面。为考虑温度对相变波传播的影响,本文首先建立了相界面上的热传导方程和热力耦合的相变本构方程,然后采用一维特征线理论和有限差分数值计算相结合的方法,分析了温度界面和相变波的基本相互作用规律,进而给出了连续温度梯度下和绝热冲击下相变波传播规律。结果表明,温度对相变波传播的作用主要体现在两个方面,一方面是作为温度界面将与各类间断面相互作用,另一方面冲击相变波阵面后区域热力学状态变化影响卸载波结构。其原因在于相变方式（可逆、不可逆）和相变阈值应力具有强烈的温度相关性。     

The Effect of a Fluid in the Contact Gap on the Stress State of Conjugate Bodies

The contact interaction of two elastic isotropic half-spaces is analyzed. One of the half-spaces has a smooth shallow depression, resulting in an imperfect contact of the surfaces. The contact gap is assumed filled with a real gas. Gas–liquid transition due to variation in the external load and temperature is considered. The plane problem formulated is solved by the method of contact-gap functions. The effect of the filler and its phase transition on the width and depth of the gap and the contact pressure is studied     

Nb3Sn单晶超导相转变时的弹性性能变化

Nb3Sn超导体失超，是超导磁体装备运行过程中的重要现象。失超，即超导体从超导相转变为正常相的过程；在强磁场超导磁体工程中，由于超高的储能密度，失超伴随着力/热/电等物理参量在瞬时的剧烈变化。失超瞬时，超导相转变的同时伴随着弹性力学性能的突变，研究超导相转变时弹性性能的变化是失超诱发应力跨尺度分析的关键。本文首先采用第一性原理方法计算了弹性常数随温度的变化规律，结果表明由于未考虑A15结构的超导材料在环境温度变化的情况下产生的特殊电子能带结构，基于准静态近似方法的材料弹性常数计算从0K外推至有限温度时，会导致模拟结果与实验观测结果出现定性上的差异；之后，基于晶格自由能函数，给出了描述立方相Nb3Sn单晶弹性性能随温度变化的解析模型，模型预测结果与实验观测结果定性吻合，初步实现了对Nb3Sn单晶超导相转变时弹性性能变化的理论描述和预测。研究结果对于超导体失超应力的跨尺度模拟及超导磁体的安全分析具有一定的理论参考价值。     

相变柱壳的径向冲击特性

采用改进的SHPB (split Hopkinson pressure bar)装置和高速CCD (charge-coupled device)相机对TiNi合金圆柱壳进行了径向冲击实验研究,得到了动态载荷-位移曲线,并采用数字边界提取技术和纯弯曲假定对结构的动态全场变形过程进行了定量分析。结果表明,相变柱壳经受动态冲击后可以恢复,其加、卸载非线性行为与相变状态和相变铰的演化相关。同时,该结构具有良好的横向抗冲效应,对冲击加速度和冲击载荷的衰减量达到95%以上,耗能率为42.4%,可望在可重复使用的抗冲装置中得到应用。     

Temperature evolution associated with phase transition from quasi static to dynamic loading

Thermo-mechanical coupling is an intrinsic property of first order martensitic transformation. In this paper, we study the temperature evolution during phase transition at a wider strain rates from quasi static to impact loading to reveal the thermodynamic nature of the strain rate effect of phase transition materials. Based on the laws of thermodynamics and the principle of maximum dissipated energy, a thermal-mechanically coupled model was proposed. The model shows that, in the quasi static case, the temperature profile grades around the moving phase boundary, while for the dynamic case, thermal response of the specimen can be reached homogeneously due to random nucleation. The predicted results of the model are in good agreement with the experimental results, suggesting that the interaction between the self-heating effect and the temperature dependence of phase transition behavior plays a leading role in the process of the transformation deformation mechanism associated with the loading rate.

     

Combustion of a liquid fuel droplet in the process of non-equilibrium surface evaporation

As a rule, mathematical combustion and evaporation models are proposed for a single droplet under the assumption that the phase transition is in equilibrium. From theoretical and experimental results it follows that this assumption is valid in the case of large droplets and flat surfaces, but leads to essential errors in the case of small droplets. The aim of this paper is to develop a mathematical model for the droplet combustion with consideration of non-equilibrium evaporation and to evaluate the effect of the non-equilibrium condition imposed on the phase transition at the interface.     

子弹冲击下TiNi固支梁的结构动态响应特性研究

采用改装的霍普金森压杆装置结合数值模拟对伪弹性TiNi合金固支梁的结构动态响应特性进行了研究。结果表明,在子弹冲击下,撞击点和固定端附近首先发生相变,并随着载荷增加,进一步产生相变铰,梁演变为二杆铰接机构。由于轴力作用,此处相变铰为拉伸侧的单边铰。与传统塑性铰不同,卸载后相变铰完全消失,梁回复原状没有残余变形。此外,对固支边界条件的实现及其对实验结果的影响进行了专门研究。     

Effect of Radiation Scattering on the Dynamics of the Transitional Zone During Solidification of a Semitransparent Material

The effect of isotropic scattering in a two-phase zone on the velocity of boundaries, thickness of the transitional zone, and distribution of the solid phase over the two-phase zone thickness in the course of solidification of a semitransparent material is considered. A generalized model of phase transition in a semitransparent medium is used. The results of numerical calculations show that radiation scattering can exert a significant effect on the structure and size of the two-phase zone and also on heat transfer (temperature gradient) in the crystal being formed.     

Analysis of coupled thermo-hydro-mechanical behavior of unsaturated soils based on theory of mixtures I

This paper analyzes a coupled thermo-hydro-mechanical behavior of unsaturated soils based on the theory of mixtures. Unsaturated soil is considered as a mixture composed of soil skeleton, liquid water, vapor, dry air, and dissolved air. In addition to the mass and momentum conservation equations of each component and the energy conservation equation of the mixture, the system is closed using other 37 constitutive （or restriction） equations. As the change in water chemical potential is identical to the change in vapor chemical potential, a thermodynamic restriction relationship for the phase transition between pore water and pore vapor is formulated, in which the impact of the change in gas pressure on the phase transition is taken into account. Six final govern- ing equations are given in incremental form in terms of six primary variables, i.e., three displacement components of soil skeleton, water pressure, gas pressure, and temperature. The processes involved in the coupled model include thermal expansions of soil skeleton and soil particle, Soret effect, phase transition between water and vapor, air dissolution in pore water, and deformation of soil skeleton.     

A preparation method of functionally graded materials with phase transition under shock loading

The propagation of phase boundary in a material undergoing shock induced irreversible phase transition is studied theoretically using a model based on simple-mixture rule. It is found that along with the decay of the phase boundary, a functionally graded material (FGM) forms in the mixed-phase region. Such FGMs are composed of parent phase and product phase, and the composition and physical properties are changing continuously without apparent macro-interfaces. The effect of stress boundary conditions on formation of the FGM is investigated in detail with a numerical method. The possibility of producing FGMs with impact method is proposed and the limit of this method is discussed.     

Simulation of bacterial flagellar phase transition by non-convex and non-local continuum modeling

Bacterial flagellar filament can undergo a stress-induced polymorphic phase transition in both vitro and vivo environments. The filament has 12 different helical forms (phases) characterized by different pitch lengths and helix radii. When subjected to the frictional force of flowing fluid, the filament changes between a left-handed normal phase and a right-handed semi-coiled phase via phase nucleation and growth. This paper develops non-local finite element method (FEM) to simulate the phase transition under a displacement-controlled loading condition (controlled helix-twist). The FEM formulation is based on the Ginzburg-Landau theory using a one-dimensional non-convex and non-local continuum model. To describe the processes of the phase nucleation and growth, viscosity-type kinetics is also used. The non-local FEM simulation captures the main features of the phase transition: two-phase coexistence with an interface of finite thickness, phase nucleation and phase growth with interface propagation. The non-local FEM model provides a tool to study the effects of the interfacial energy/thickness and loading conditions on the phase transition.     

基于分子动力学模拟的单晶硅冲击压缩相变研究

晶体硅具有复杂的相变机制,在相图研究中受到广泛关注,其在动载荷下的变形机制是当前研究热点。为揭示晶体硅在强动加载下的变形和相变行为特征,基于分子动力学方法,采用平板冲击加载方式,模拟研究了单晶硅在初始环境温度为300 K时分别沿[001]、[110]和[111]晶向的不同强度下的冲击压缩行为,冲击粒子速度为0.3～3.2 km/s。研究发现,随着冲击粒子速度的增加,单晶硅剪切应力在逐渐增加后由于结构相变发生急剧下降,相变阈值和相变机制均呈现各向异性。其中,沿[001]晶向冲击压缩下观察到多种固-固相变以及固-液相变,并观察到与最新文献的实验高度一致的固-液共存现象。研究结果可为动加载下晶体硅的相变研究提供纳米尺度的结果支撑。     

Electromechanical phase transition of a dielectric elastomer tube under internal pressure of constant mass

The electromechanical phase transition for a dielectric elastomer(DE) tube has been demonstrated in recent experiments, where it is found that the unbulged phase gradually changed into bulged phase.Previous theoretical works only studied the transition process under pressure control condition, which is not consistent with the real experimental condition. This paper focuses on more complex features of the electromechanical phase transition under internal pressure of constant mass. We derive the equilibrium equations and the condition for coexistent states for a DE tube under an internal pressure, a voltage through the thickness and an axial force. We find that under mass control condition the voltage needed to maintain the phase transition increases as the process proceeds. We analyze the entire process of electromechanical phase transition and find that the evolution of configurations is also different from that for pressure control condition.     

铈γ→α相变的室温动态特性

通过试样组件尺寸匹配设计的被动围压SHPB实验,获得了99.8%纯铈在1.7GPa静水压内的、包含γ?α相变和逆相变过渡区的室温动态静水压-体应变连续曲线。研究显示:室温铈γ→α相变是具有明显滞后现象的一级相变,而非以往研究认为的体积跃变的一级相变;相变过渡区的静水压范围是0.8~1.3GPa。逆相变过渡区的静水压范围是0.6~1.1GPa;逆相变过渡区的静水压-体应变曲线滞后于相变过渡区的静水压-体应变曲线0.15GPa静水压;在相变和逆相变过渡区内,静水压-体应变曲线按照约4.2GPa体积模量的线性关系演化;演化机制为γ和α两相均匀混合、静水压驱动两相组份转化。基于该演化机制,构建了描述相变前后和相变过程的静水压-体应变响应的三段线性模型。     

The Cubic-to-Orthorhombic Phase Transition: Rigidity and Non-Rigidity Properties in the Linear Theory of Elasticity

In this paper we investigate the cubic-to-orthorhombic phase transition in the framework of linear elasticity. Using convex integration techniques, we prove that this phase transition represents one of the simplest three-dimensional examples in which already the linearised theory of elasticity displays non-rigidity properties. As a complementary result, we demonstrate that surface energy constraints rule out such highly oscillatory behaviour. We give a full characterization of all possibly emerging patterns for generic material parameters.     

Combined stress waves with phase transition in thin-walled tubes简

The incremental constitutive relation and governing equations with combined stresses for phase transition wave propagation in a thin-walled tube are established based on the phase transition criterion considering both the hydrostatic pressure and the deviatoric stress. It is found that the centers of the initial and subsequent phase transition ellipses are shifted along the σ-axis in the στ-plane due to the tension-compression asymmetry induced by the hydrostatic pressure. The wave solution offers the "fast" and "slow" phase transition waves under combined longitudinal and torsional stresses in the phase transition region. The results show some new stress paths and wave structures in a thin-walled tube with phase transition, differing from those of conventional elastic-plastic materials.     

Analyses of the driver’s anticipation effect in a new lattice hydrodynamic traffic flow model with passing

In this paper, we studied the effect of driver’s anticipation with passing in a new lattice model. The effect of driver’s anticipation is examined through linear stability analysis and shown that the anticipation term can significantly enlarge the stability region on the phase diagram. Using nonlinear stability analysis, we obtained the range of passing constant for which kink soliton solution of mKdV equation exist. For smaller values of passing constant, uniform flow and kink jam phase are present on the phase diagram and jamming transition occurs between them. When passing constant is greater than the critical value depending on the anticipation coefficient, jamming transitions occur from uniform traffic flow to kink-bando traffic wave through chaotic phase with decreasing sensitivity. The theoretical findings are verified using numerical simulation which confirm that traffic jam can be suppressed efficiently by considering the anticipation effect in the new lattice model.     

A new lattice hydrodynamic model for bidirectional pedestrian flow considering the visual field effect

In this paper, a new lattice hydrodynamic model for bidirectional pedestrian flow is proposed by considering the pedestrian’s visual field effect. The stability condition of this model is obtained by the linear stability analysis. The mKdV equation near the critical point is derived to describe the density wave of pedestrian jam by applying the reductive perturbation method. The phase diagram indicates that the phase transition occurs among the freely moving phase, the coexisting phase, and the uniformly congested phase below the critical point \(a_c\) . Furthermore, the analytical results show that the visual field effect plays an important role in jamming transition. To take into account the visual information about the motion of more pedestrian in front can improve efficiently the stability of pedestrian system. In addition, the numerical simulations are in accordance with the theoretical analysis.     

MECHANICAL MODELING OF THE BISTABLE BACTERIAL FLAGELLAR FILAMENT

We extend the 2D Landau phase transition theory to the bacterial flagellar filament which displays the phase transition between the left handed normal form and the right handed semi-coiled form. The bacterial flagellar filament is treated as an elastic thin rod based on the Kirchhoff’s thin rod theory. Mechanical analysis is performed on the periodical phase transition of the filament between the two helical structures of the opposite charity. The curvature and twist are chosen as the order parameters in constructing the phase transition model of the filament. The established model is applied to study the instability properties of the filament and to investigate the loading and deformation conditions of the phase transition. In addition, the curvature and twist gradient energy are considered to describe the interface properties of the two phases.