Transition waves in bistable structures. II. Analytical solution: wave speed and energy dissipation

We consider dynamics of chains of rigid masses connected by links described by irreversible, piecewise linear constitutive relation: the force-elongation diagram consists of two stable branches with a jump discontinuity at the transition point. The transition from one stable state to the other propagates along the chain and excites a complex system of waves. In the first part of the paper (Cherkaev et al., 2004, Transition waves in bistable structures. I. Delocalization of damage), the branches could be separated by a gap where the tensile force is zero, the transition wave was treated as a wave of partial damage. Here we assume that there is no zero-force gap between the branches. This allows us to obtain steady-state analytical solutions for a general piecewise linear trimeric diagram with parallel and nonparallel branches and an arbitrary jump at the transition. We derive necessary conditions for the existence of the transition waves and compute the speed of the wave. We also determine the energy of dissipation which can be significantly increased in a structure characterized by a nonlinear discontinuous constitutive relation. The considered chain model reveals some phenomena typical for waves of failure or crushing in constructions and materials under collision, waves in a structure specially designed as a dynamic energy absorber and waves of phase transitions in artificial and natural passive and active systems.     

带变截面可更换耗能梁段的高强钢框架-偏心支撑有限元参数分析

提出了一种新型变截面可更换耗能梁,控制塑性变形集中在耗能区域中,通过扩大截面与框架梁采取翼缘和腹板螺栓拼接连接,易于实现螺栓弹性设计,减小螺栓滑移,完成耗能梁端在地震作用后的更换。利用变截面可更换耗能梁段中部区域耗能集中与塑性变形优越的特性,结合高强钢的较大弹性变形,在偏心支撑钢框架中设置变截面可更换耗能梁段,形成带变截面可更换耗能梁段的高强钢框架-偏心支撑结构体系,通过有限元软件模拟验证了已有端板连接可更换耗能梁段试验,对比破坏模式、承载能力与耗能特性,以此为基础,建立了带变截面可更换耗能梁段的高强钢框架-偏心支撑结构有限元模型,通过循环加载研究了结构的承载能力、刚度、受力特点、塑性转角和塑性分布等受力机理。考虑了中间耗能区域长度(e)、钢材牌号组合和变截面可更换耗能梁段长度(e'')三个参数变化对结构抗震性能的影响规律。     

(Adiabatic) phase boundaries in a bistable chain with twist and stretch

Mass–spring chains with only extensional degrees of freedom have provided insights into the behavior of crystalline solids, including those capable of phase transitions. Here we add rotational degrees of freedom to the masses in a chain and study the dynamics of phase boundaries across which both the twist and stretch can jump. We solve impact and Riemann problems in the chain by numerical integration of the equations of motion and show that the solutions are analogous to those in a phase transforming rod whose stored energy function depends on both twist and stretch. From the dynamics of phase boundaries in the chain we extract a kinetic relation whose form is familiar from earlier studies involving chains with only extensional degrees of freedom. However, for some combinations of parameters characterizing the energy landscape of our springs we find propagating phase boundaries for which the rate of dissipation, as calculated using isothermal expressions for the driving force, is negative. This suggests that we cannot neglect the energy stored in the oscillations of the masses in the interpretation of the dynamics of mass–spring chains. Keeping this in mind we define a local temperature of our chain and show that it jumps across phase boundaries, but not across sonic waves. Hence, impact problems in our mass–spring chains are analogous to those on continuum thermoelastic bars with Mie–Gruneisen type constitutive laws. At the end of the paper we use our chain to shed some light on experiments involving yarns that couple twist and stretch to perform useful work in response to various stimuli.     

基于能量耗散分析的混凝土随机疲劳损伤模型

基于微-细观随机断裂模型(MMSF)发展了一类混凝土随机疲劳损伤模型。该模型将MMSF中的微弹簧视为一能量耗散单元并考察了其跨尺度的能量耗散过程。在纳观尺度,引入速率过程理论描述裂纹的扩展速度,并基于裂纹层级模型和自相似假定完成从纳观尺度到微观尺度的过渡。由此建立了微弹簧在疲劳荷载作用下的多尺度耗能描述。此外,为了考虑疲劳加载中混凝土多条裂纹的相互影响,引入了包含损伤扩展效应和损伤愈合效应的疲劳损伤因子来修正耗能表达。通过与相关试验的对比,证明了该模型能反映疲劳荷载作用下混凝土的主要力学行为,如疲劳损伤三阶段特点、疲劳寿命的离散性和疲劳寿命随加载频率的变化趋势等。     

新型齿形链磨损机制及其温度和速度特性的实验研究

在给定的试验条件下，通过对比磨损试验研究了新型齿形链与普通外啮合齿形链的磨损机制，分析了销轴的磨损表面形貌，研究了不同油温和交变速度下新型齿形链的磨损特性．结果表明，新型齿形链的耐磨性能明显优于普通外啮合齿形链，新型齿形链在交变速度下的磨损伸长率大于非交变速度下的磨损伸长率；随着试验油温的升高，新型齿形链的磨损伸长率明显增大．     

A micromechanical damage and fracture model for polymers based on fractional strain-gradient elasticity

We formulate a simple one-parameter macroscopic model of distributed damage and fracture of polymers that is amenable to a straightforward and efficient numerical implementation. We show that the macroscopic model can be rigorously derived, in the sense of optimal scaling, from a micromechanical model of chain elasticity and failure regularized by means of fractional strain-gradient elasticity. In particular, we derive optimal scaling laws that supply a link between the single parameter of the macroscopic model, namely, the critical energy-release rate of the material, and micromechanical parameters pertaining to the elasticity and strength of the polymer chains and to the strain-gradient elasticity regularization. We show how the critical energy-release rate of specific materials can be determined from test data. Finally, we demonstrate the scope and fidelity of the model by means of an example of application, namely, Taylor-impact experiments of polyurea 1000 rods.     

Nonlinear supratransmission of multibreathers in discrete nonlinear Schrödinger equation with saturable nonlinearities

We show that the transport of vibrational energy in protein chains modeled by the Discrete Nonlinear Schrödinger equation (DNSE) with saturable nonlinearities can be done through the nonlinear supratransmission phenomenon: we find numerically and semi-analytically threshold amplitudes beyond which the wave propagation takes place within the molecular chains. Subsequently, it is shown that the saturable higher order nonlinearity parameter reduces the supratransmission threshold amplitude. We also prove that the discrete gap multibreathers can be transmitted or supratransmitted according to the frequency belonging to the lower forbidden band gap. More precisely, the discrete gap multibreathers are supratransmitted close to the edge of the lower forbidden band.     

微振激励下黏弹性阻尼器微观链结构力学模型

减小微振动对高精密仪器至关重要,利用黏弹性阻尼器进行微振动抑制是一个新兴而又具有挑战性的课题.本文采用分子链网络模型方法分析了黏弹性材料的微观分子链结构,综合考虑材料分子链结构中的网络链和自由链对黏弹性材料力学性能的影响,提出一种基于材料微观分子链结构的微振激励下黏弹性阻尼器力学模型.模型分别采用标准线性固体模型和Maxwell模型来描述网络链和自由链中单个链的力学性能,并分别采用8链网络模型和3链网络模型考虑两种类型分子链的综合效应,引入温频等效原理描述温度对微振激励下黏弹性阻尼器力学性能的影响.该模型能够描述温度和频率对黏弹性阻尼器动态力学性能的影响,并能够反映黏弹性材料的微观结构与材料力学性能的关系.为验证所提模型的有效性及考察黏弹性阻尼器在微振激励下的耗能能力和动态力学性能,在微振条件下对黏弹性阻尼器进行了动态力学性能试验.研究结果表明黏弹性阻尼器具有较好的微振耗能能力,其动态力学性能受温度和频率影响较大,所提的力学模型能够精确地描述微振激励下黏弹性阻尼器动态力学性能随温度和频率的变化关系.      

双稳态电磁式振动能量捕获器超谐波响应研究

超谐波响应是非线性振动系统在较大激励下表现的特性,在某种条件下双稳态振动能量捕获系统的超谐波响应可使系统产生优越的输出功率。本文将质量-非线性弹簧-阻尼系统与双稳态振动能量捕获器相结合,提出了附加非线性振子的双稳态电磁式振动能量捕获器,建立系统的力学模型及控制方程。采用两项式谐波平衡法,获得了双稳态系统在简谐激励下产生大幅运动的基谐波和超谐波响应的解析解,借助数值仿真分析了质量比和调频比对双稳态振动能量捕获器产生大幅运动的影响规律,获得了双稳态系统的结构参数的最佳配置范围,且当外部激励频率处于低频段时,系统发电主要表现为超谐波发电,随着激励频率的增大,振动发电系统主要呈现基谐波发电。上述研究,为双稳态能量捕获装置的理论研究提供了参考。     

Dissipative discrete breathers in a chain of Rayleigh oscillators

The dynamics of chains of interacting active particles with Rayleigh-type dissipation and coupled by a Morse potential were previously studied. In this work we introduce an on-site potential to transform this system into a chain of oscillators. We study the evolution of modes previously found in a chain of active particles as a consequence of the on-site force. Beside this, a new class of modes, dissipative discrete breathers, is found. These new modes appear due to the new time scales introduced by the on-site potential. Interaction of the dissipative discrete breathers is also investigated. We find different behaviors; for short chains dissipative discrete breathers can meet during the transitory formation reaching the stationary modes including the optical one, sufficiently long chains the dissipative discrete breathers reach its stationary state without interactions and for medium lengths, the dissipative discrete breathers interact by forming a standing wave in between.

     

Dynamics of branched chain solutions in adsorbing slit. A Monte Carlo study

A coarse-grained model of branched polymers confined in a slit formed by two parallel impenetrable surfaces that were attractive for polymer segments was developed and studied. The model chains were regular stars consisting of f?=?3 branches of equal length. The positions of chains were restricted to vertices of a simple cubic lattice. The chains were at good solvent conditions—the excluded volume was the only interaction between the segments of the chain. The properties of the model chains were determined by means of Monte Carlo simulations with a sampling algorithm based on chain’s local changes of conformation. The dependence of chain mobility on the width of the slit and the polymer concentration was studied. The conditions at which the strongly adsorbed chains could swap between both confining surfaces were studied. The mechanism of the chain motion was also discussed.     

Helmholtz and Gibbs ensembles,thermodynamic limit and bistability in polymer lattice models

Representing polymers by random walks on a lattice is a fruitful approach largely exploited to study configurational statistics of polymer chains and to develop efficient Monte Carlo algorithms. Nevertheless, the stretching and the folding/unfolding of polymer chains within the Gibbs (isotensional) and the Helmholtz (isometric) ensembles of the statistical mechanics have not been yet thoroughly analysed by means of the lattice methodology. This topic, motivated by the recent introduction of several single-molecule force spectroscopy techniques, is investigated in the present paper. In particular, we analyse the force–extension curves under the Gibbs and Helmholtz conditions and we give a proof of the ensembles equivalence in the thermodynamic limit for polymers represented by a standard random walk on a lattice. Then, we generalize these concepts for lattice polymers that can undergo conformational transitions or, equivalently, for chains composed of bistable or two-state elements (that can be either folded or unfolded). In this case, the isotensional condition leads to a plateau-like force–extension response, whereas the isometric condition causes a sawtooth-like force–extension curve, as predicted by numerous experiments. The equivalence of the ensembles is finally proved also for lattice polymer systems exhibiting conformational transitions.     

考虑损伤的内变量黏弹-黏塑性本构方程

基于Rice 不可逆内变量热力学框架,在约束构型空间中讨论材料的蠕变损伤问题. 通过给定具体的余能密度函数和内变量演化方程推导出考虑损伤的内变量黏弹-黏塑性本构方程. 通过模型相似材料单轴蠕变加卸载试验对一维情况下的本构方程进行参数辨识和模型验证,本构方程能很好地描述黏弹性变形和各蠕变阶段.不同的蠕变阶段具有不同的能量耗散特点. 受应力扰动后,不考虑损伤的材料系统能自发趋于热力学平衡态或稳定态. 在考虑损伤的整个蠕变过程中,材料系统先趋于平衡态再背离平衡态发展. 能量耗散率可作为材料系统热力学状态偏离平衡态的测度;能量耗散率的时间导数可用于表征系统的演化趋势;两者的域内积分值可作为结构长期稳定性的评价指标.      

新型空壳颗粒材料在人防工程中应用的实验研究

研发了一种内衬PVC壳体,外裹泡沫陶瓷壳体的新型空壳颗粒作为人防结构分配层。通过大比尺化爆实验,研究了爆炸载荷下新型空壳颗粒分配层人防结构和普通黄沙分配层人防结构的破坏情况和冲击波传播规律。实验证明:同样当量爆炸载荷下,相对黄沙分配层,新型空壳颗粒分配层可以降低应力峰值50%左右;相对常规空壳颗粒,新型空壳颗粒分配层受损情况显著减小。这表明:新型空壳颗粒作为人防工程的分配层兼具显著的削波耗能效果和抵抗二次爆炸的能力,因此可以提高人防工程的抗爆能力,具有广阔的军事应用前景。     

Large-deformation properties of wheat dough in uni- and biaxial extension. Part I. Flour dough

Rheological and fracture properties of optimally mixed flour doughs from three wheat cultivars which perform differently in cereal products were studied in uniaxial and biaxial extension. Doughs were also tested in small angle sinusoidal oscillation. In accordance with previously published results the linear region was found to be very small. The rheological properties at small deformations hardly depended on the cultivar. A higher water content of the dough resulted in a lower value for the storage modulus and a slightly higher value for tan . For both uniaxial and biaxial extension a more than proportional increase in stress was found with increasing strain, a phenomenon called strain hardening. In uniaxial extension (i) stresses at a certain strain were higher and (ii) the stress was less dependent on the strain rate than in biaxial extension. This indicates that in elongational flow orientational effects are of large importance for the mechanical properties of flour dough. This conclusion is consistent with published data on birefringence of stretched gluten. Fracture stress and strain increased with increasing deformation rate. The observed time-dependency of fracture properties can best be explained by inefficient transport of energy to the crack tip. Presumably, this is caused by energy dissipation due to inhomogeneous deformation because of friction between structural elements, e.g. between dispersed particles and the network. Differences in the rheological properties at large deformations between the cultivars were observed with respect to (i) stress, (ii) strain hardening, (iii) strain rate dependency of the stress, (iv) fracture properties and (v) the stress difference between uniaxial and biaxial extension.     

On the dissipation of energy in a chain of coupled harmonic oscillators

The article deals with processes which occur in coupled oscillator chains following an initial impulse imparted to any one of the atoms. In considering one-dimensional chains of coupled harmonic oscillators, their obvious deficiencies are analyzed and taken into account. The effects which energy dissipation losses and transverse vibrations have on propagation of collision waves through a one-dimensional atom chain are evaluated. It stands to reason, of course, to consider only small transverse displacements of atoms in a chain, since otherwise the simplest models become obviously inadequate.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 46–50, January–February, 1971.     

A continuum-molecular model of oriented polymer region formation in elastomer nanocomposite

An approach for constructing a continuum-molecular model of a polymer material is proposed. The approach has the following advantages. It combines the convenience of dealing with the continuum representation, which permits numerically analyzing complicated processes at the nanolevel with the characteristic time measured in minutes. In addition, the model contains molecular representations which permit calculating the continuum properties with the specific features of interaction between links of molecular chains taken into account. Moreover, the state of the material can be inhomogeneous at the scale level that is several times greater than the dimension of a single link of the polymer chain.     

On energy balance and the structure of radiated waves in kinetics of crystalline defects

Traveling waves, with well-known closed form expressions, in the context of the defects kinetics in crystals are excavated further with respect to their inherent structure of oscillatory components. These are associated with, so called, Frenkel–Kontorova model with a piecewise quadratic substrate potential, corresponding to the symmetric as well as asymmetric energy wells of the substrate, displacive phase transitions in bistable chains, and brittle fracture in triangular lattice strips under mode III conditions. The paper demonstrates that the power expended theorem holds so that the sum of rate of working and the rate of total energy flux into a control strip moving steadily with the defect equals the rate of energy sinking into the defect, in the sense of N.F. Mott. In the conservative case of the Frenkel–Kontorova model with asymmetric energy wells, this leads to an alternative expression for the mobility in terms of the energy flux through radiated lattice waves. An application of the same to the case of martensitic phase boundary and a crack, propagating uniformly in bistable chains and triangular lattice strips, respectively, is also provided and the energy release is expressed in terms of the radiated energy flux directly. The equivalence between the well-known expressions and their alternative is established via an elementary identity, which is stated and proved in the paper as the zero lemma. An intimate connection between the three distinct types of defects is, thus, revealed in the framework of energy balance, via a structural similarity between the corresponding variants of the ‘zero’ lemma containing the information about radiated energy flux. An extension to the dissipative models, in the presence of linear viscous damping, is detailed and analog of the zero lemma is proved. The analysis is relevant to the dynamics of dislocations, brittle cracks, and martensitic phase boundaries, besides possible applications to analogous physical contexts which are marked by macroscopic energy release through emission of waves and possibly linear viscous damping.     

黏弹性材料等效分数阶微观结构标准线性固体模型

从黏弹性材料微观链结构出发,以橡胶基黏弹性材料超弹性理论分子网链高斯(Gauss)统计模型和黏滞流动理论为基础,研究黏弹性材料的微观结构、填料等对黏弹性性能的影响.用温频等效原理描述温度对黏弹性材料力学性能的影响,建立了可以有效描述黏弹性材料耗能特性的等效分数阶微观结构标准线性固体模型.采用动态热机械分析仪(DMA)对高聚物黏弹性材料力学性能、耗能能力进行测试.试验表明:在低温区域,储能模量较大,随着温度的升高,储能模量下降显著;能量损耗因子在高温和低温区域数值较小,在玻璃化转变温度附近数值较高.根据测试数据对所提等效分数阶微观结构标准线性固体模型进行验证,该力学模型能够较好地描述黏弹性材料储能模量和能量损耗因子随温度的变化趋势.用9050A和ZN22黏弹性材料对模型的有效性进一步验证,结果表明:9050A和ZN22黏弹性材料具有较好的耗能能力,所提出的等效分数阶微观结构标准线性固体模型能够准确地描述微观结构和填料对黏弹性材料宏观性能的影响,能够准确地描述黏弹性材料在不同温度和频率下的动态力学性能.     

青藏铁路冻土区环境问题对工程安全可靠性影响

当大涡模拟用于研究化学反应流动时，传统的滤波方法会导致化学反应项不封闭. 为克服这 个困难，发展了条件滤波大涡模拟方法. 在选择适当的条件变量后，条件滤波的化学反 应项可以表达为一个封闭项. 但同时也带来了新的问题：条件滤波耗散或条件滤波扩散项的 不封闭. 为解决这一问题，采用了直接数值模拟方法研究了它们在大小尺度上的统计特 性. 研究结果表明：条件滤波耗散和扩散对于大尺度的依赖主要体现在大尺度标量场中扩散 层结构的影响，同时小尺度脉动的变化几乎与条件滤波扩散无关，而它对条件滤波耗散却显 现出明显的作用. 在构造条件滤波耗散的亚格子模型时，小尺度脉动的作用不容忽视.