Trans-scale mechanics: looking for the missing links between continuum and micro/nanoscopic reality

Problems involving coupled multiple space and time scales offer a real challenge for conventional frame-works of either particle or continuum mechanics. In this paper, four cases studies （shear band formation in bulk metallic glasses, spallation resulting from stress wave, interaction between a probe tip and sample, the simulation of nanoindentation with molecular statistical thermodynamics） are provided to illustrate the three levels of trans-scale problems （problems due to various physical mechanisms at macro-level, problems due to micro-structural evolution at macro/micro-level, problems due to the coupling of atoms/ molecules and a finite size body at micro/nano-level） and their formulations. Accordingly, non-equilibrium statistical mechanics, coupled trans-scale equations and simultaneous solutions, and trans-scale algorithms based on atomic/molecular interaction are suggested as the three possible modes of trans-scale mechanics.

New approach based on continuum damage mechanics with simple parameter identification to fretting fatigue life prediction

A new continuum damage mechanics model for fretting fatigue life prediction is established. In this model, the damage evolution rate is described by two kinds of quantities. One is associated with the cyclic stress characteristics obtained by the finite element （FE） analysis, and the other is associated with the material fatigue property identified from the fatigue test data of standard specimens. The wear is modeled by the energy wear law to simulate the contact geometry evolution. A two-dimensional （2D） plane strain FE implementation of the damage mechanics model and the energy wear model is presented in the platform of ABAQUS to simulate the evolutions of the fatigue damage and the wear scar. The effect of the specimen thickness is also investigated. The predicted results of the crack initiation site and the fretting fatigue life agree well with available experimental data. Comparisons are made with the critical plane Smith- Watson-Topper （SWT） method.

Thermodynamic Consistency of Plate and Shell Mathematical Models in the Context of Classical and Non-Classical Continuum Mechanics and a Thermodynamically Consistent New Thermoelastic Formulation

Inclusion of dissipation and memory mechanisms, non-classical elasticity and thermal effects in the currently used plate/shell mathematical models require that we establish if these mathematical models can be derived using the conservation and balance laws of continuum mechanics in conjunction with the corresponding kinematic assumptions. This is referred to as thermodynamic consistency of the mathematical models. Thermodynamic consistency ensures thermodynamic equilibrium during the evolution of the deformation. When the mathematical models are thermodynamically consistent, the second law of thermodynamics facilitates consistent derivations of constitutive theories in the presence of dissipation and memory mechanisms. This is the main motivation for the work presented in this paper. In the currently used mathematical models for plates/shells based on the assumed kinematic relations, energy functional is constructed over the volume consisting of kinetic energy, strain energy and the potential energy of the loads. The Euler’s equations derived from the first variation of the energy functional for arbitrary length when set to zero yield the mathematical model(s) for the deforming plates/shells. Alternatively, principle of virtual work can also be used to derive the same mathematical model(s). For linear elastic reversible deformation physics with small deformation and small strain, these two approaches, based on energy functional and the principle of virtual work, yield the same mathematical models. These mathematical models hold for reversible mechanical deformation. In this paper, we examine whether the currently used plate/shell mathematical models with the corresponding kinematic assumptions can be derived using the conservation and balance laws of classical or non-classical continuum mechanics. The mathematical models based on Kirchhoff hypothesis (classical plate theory, CPT) and first order shear deformation theory (FSDT) that are representative of most mathematical models for plates/shells are investigated in this paper for their thermodynamic consistency. This is followed by the details of a general and higher order thermodynamically consistent plate/shell thermoelastic mathematical model that is free of a priori consideration of kinematic assumptions and remains valid for very thin as well as thick plates/shells with comprehensive nonlinear constitutive theories based on integrity. Model problem studies are presented for small deformation behavior of linear elastic plates in the absence of thermal effects and the results are compared with CPT and FSDT mathematical models.

Continuum Mechanics of Space Seen from the Aspect of General Relativity An Interpretation of the Gravity Mechanism

A mechanical structure of space is suggested. On the supposition that a space as vacuum has a physical fine structure like continuum, it enables us to apply a continuum mechanics to the so-called ＂vacuum＂ of space. A space is an infinite continuum and its structure is determined by Riemannian geometry. Assuming that space is an infmite continuum, the pressure field derived from the geometrical structure of space is newly obtained by applying both continuum mechanics and General Relativity to space. A fundamental concept of space-time is described that focuses on theoretically innate properties of space including strain and curvature. As a trial consideration, gravity can be explained as a pressure field induced by the curvature of space.

A Hybrid Local/Nonlocal Continuum Mechanics Modeling of Damage and Fracture in Concrete Structure at High Temperatures

This paper proposes a hybrid peridynamic and classical continuum mechanical model for the high-temperature damage and fracture analysis of concrete structures.In this model,we introduce the thermal expansion into peridynamics and then couple it with the thermoelasticity based on the Morphing method.In addition,a thermomechanical constitutive model of peridynamic bond is presented inspired by the classic Mazars model for the quasi-brittle damage evolution of concrete structures under high-temperature conditions.The validity and effectiveness of the proposed model are verified through two-dimensional numerical examples,in which the influence of temperature on the damage behavior of concrete structures is investigated.Furthermore,the thermal effects on the fracture path of concrete structures are analyzed by numerical results.

Ductile Fracture Characterization for Medium Carbon Steel Using Continuum Damage Mechanics

This paper presents the ductility characterization for a medium carbon steel, for two microstructural conditions, that has been evaluated using the continuum damage mechanics theory, as proposed by Kachanov and developed by Lemaitre. Tensile tests were carried out using loading-unloading cycles in order to capture the gradual deterioration of the elastic modulus, which may be linked to the ductile damage increase with increasing plastic strain. The mechanical parameters for the isotropic damage evolution equation were obtained and then used as inputs for a plasticity-damage coupled nu- merical algorithm, validated through numerical simulations of the experimental tensile tests. A comparison between the SAE 1050 steels studied and two carbon steel alloys (obtained from the literature), provided some basic understanding of the influence of the carbon level on the evolution of the damage parameters. An empiric relationship for this set of parameters, which can provide useful data for preliminary studies envisaging prediction of ductile failure in carbon steels, is also presented.

EFFECTS OF PHASE CONTINUITY ON RHEOLOGY OF TWO-PHASE ROCKS: A CONTINUUM MECHANICL MODEL

Based on continuum mechanics, we have developed a model for semi quantitative estimating effects of phase continuity on flow strength of two phase rocks including partially melted or crystallized rocks. Calculations of the bulk flow strength of composite rocks as functions of the volume fraction, geometrical shape and continuity of the constitutive phases involve in numerically solving two non linear equations and thus are easy to be performed. The model has been justified by a good agreement between the predicted and measured results on diabase (64% clinopyroxene and 36% plagioclase) in the range of experimental temperatures and strain rates. It is believed that the present model could provide an approximate estimate for the rheological evolution of magmatic rocks during their life cycle of melting crystallization deformation.

Variable Curvature Modeling Method of Soft Continuum Robots with Constraints

The inherent compliance of continuum robots holds great promise in the fields of soft manipulation and safe human–robot interaction.This compliance reduces the risk of damage to the manipulated object and its surroundings.However,continuum robots possess theoretically infinite degrees of freedom,and this high flexibility usually leads to complex deformations when subjected to external forces and positional constraints.Describing these complex deformations is the main challenge in modeling continuum robots.In this study,we investigated a novel variable curvature modeling method for continuum robots,considering external forces and positional constraints.The robot configuration curve is described using the developed mechanical model,and then the robot is fitted to the curve.A ten-section continuum robot prototype with a length of 1 m was developed in order to validate the model.The feasibility and accuracy of the model were verified by the ability of the robot to reach target points and track complex trajectories with a load.This work was able to serve as a new perspective for the design analysis and motion control of continuum robots.

基于连续介质损伤力学的钛合金耐压球壳极限强度分析

本文在连续介质损伤力学理论框架下,以深海载人装备耐压球壳结构为研究对象,开展Bonora损伤模型适用性研究。首先,设计TA31钛合金加载卸载试验,依据试验结果,分析Bonora模型参数对材料应力应变响应的影响规律;随后,提出一种模型参数校准方法,依据试验数据确定TA31钛合金的模型参数;最后,将Bonora模型通过VUMAT子程序的形式嵌入到有限元软件中,开展钛合金球壳结构的极限强度分析,并与传统方法进行对比。研究结果表明,在耐压球壳极限强度分析中,引入Bonora模型可以准确模拟耐压球壳结构的失效模式和破坏压力。该模型在材料本构关系中考虑了屈服强度、抗拉强度以及最大塑性应变的影响,结构失效的物理意义更加明确,对材料性能的优化与提升具有指导意义。

土力学的连续性假设及其在建模中的应用

为了弥补土力学中缺失连续性假设这一重要理论缺陷,在对多个学科中的连续性概念进行系统地梳理考究的基础上,提出了土力学中连续性假设的恰当表述,进而厘清了土的本构模型的概念、种类、属性和建模思路。研究结果表明:连续介质力学和多孔介质流体动力学的连续性假设为土力学的连续性假设提供了有益参考,但都有一定的缺陷;用混合物理论的观点和方法描述土的连续性比较合适,且可以避开在定义孔隙率时遇到的困扰;“连续”是一个相对的概念,当外部特征尺寸远大于介质内部特征尺寸时,就可以把研究对象看作连续介质;现有土的各种本构模型均以连续介质力学为基础,总体上属于唯象模型。阐明了本构关系的概念、种类和建模思路:本构关系是物质宏观性质的数学模型;土的本构模型包括持水、渗水、渗气、传热、屈服、变形、强度、细观结构演化、热力学效应、相变规律等多方面的内容,而不仅限于应力-应变关系;土的本构关系的研究应针对具体土类,抓住主要影响因素,建立解决主要问题的数学模型。

深潜器钛合金室温蠕变-疲劳损伤模型及数值研究

针对钛合金深潜器耐压壳在实际作业过程中疲劳与蠕变损伤相互促进的现象,本文提出了适用于室温环境下钛合金材料的蠕变-疲劳损伤模型和数值模拟方法。基于连续损伤力学理论建立了蠕变-疲劳损伤模型,并通过单轴蠕变-疲劳试验标定了参数;将该模型用子程序进行定义,通过有限元软件二次开发模拟了紧凑拉伸试件蠕变-疲劳损伤演化过程,并将数值模拟结果与试验结果对比。试验结果表明:超过90%的数据点预测结果的相对误差包络在±50%范围内,紧凑拉伸试件蠕变-疲劳寿命的模型预测结果与试验值误差为2.9%。本文所提出的模型和数值模拟方法可以很好地描述钛合金结构的室温蠕变-疲劳失效过程。

基于理性扩展热力学的L-S热声弹性理论框架

本文基于连续介质力学和理性扩展热力学分析流程,将L-S(Lord and Shulman)热弹性理论与声弹性理论相结合,建立L-S热声弹性理论的基本框架,包括运动学、力学与热力学、本构方程与演化方程、基本场方程四部分。在运动学部分,区分了Lagrange描述和Euler描述,以及3种不同的状态和构形,同时针对热声弹性情况定义了两类从自然状态到初始状态的转变过程;在力学与热力学部分,给出了质量守恒定律、动量守恒定律、角动量守恒定律、能量守恒定律以及熵产不等式,从而引出经典不可逆热力学的局限性;在本构方程与演化方程部分,介绍了扩展不可逆热力学原理,并基于理性扩展热力学流程,推导了从自然状态到初始状态、从初始状态到最终状态的热声弹性本构方程与演化方程,将热流作为本构自变量并考虑了热流与应变和温度的相关性;在最后一部分给出了基本场方程的运动方程形式和适用于数值模拟的一阶速度-应力-热流-温度微分方程。

二维材料层间切向熵力的连续介质模型

层间相互作用对二维材料的界面力学行为影响显著,特别是在力热耦合环境下,二维材料搭接结构中存在层间切向熵力,可用于构筑新型纳米机械器件.基于薄板振动理论,并结合能量均分定理,构建了描述二维材料层间切向熵力的连续介质模型.该模型揭示了不同条件下由热振动梯度引起的切向熵力之间的内在联系,为研究二维材料层间切向熵力提供了新的视角,也为纳米器件的设计提供了理论支撑.

连续介质力学的类比思维教学法——黏弹性力学vs.广义热传导

类比是重要创新思维方式,能发挥类比思维教育价值,强化学生类比思维训练,有助于创新人才培养。本文以黏弹性力学和广义热传导教学模块为抓手,展现类比思维教学法在连续介质力学课程运用的设计案例。首先,基于力学弹性单元和黏性单元,采用串并联方法,推导黏弹性力学Maxwell模型和Kelvin-Voigt模型。其次,给出广义热传导Cattaneo-Vernotte模型和Green-Naghdi模型,介绍Green-Naghdi模型热位移概念的起源。随后,通过类比方法引入热学“弹性”单元和“黏性”单元,运用串并联方法实现Cattaneo-Vernotte模型和Green-Naghdi模型的重构,澄清黏弹性力学和广义热传导各模型间的对应类比关系。最后,分析热学基本方程与力学基本方程的差异,指出:对研究对象间差异性的关注也是基于类比方法启发创新思维的重要手段。

不同数值方法模拟皮质骨结构弯曲断裂的准确性

背景:当前针对皮质骨结构的断裂模拟主要有基于单元瞬时失效、连续损伤力学以及扩展有限元理论3种方法。虽然断裂模拟文献众多,但却鲜有研究比较3种断裂方法的模拟精度。目的:探究3种数值方法模拟皮质骨结构弯曲断裂的准确性与适用性。方法:首先针对大鼠股骨样本进行三点弯曲实验,然后依据样本微观扫描影像建立大鼠股骨有限元模型,分别采用3种数值方法模拟皮质骨结构在三点弯曲载荷下的断裂,通过将预测断裂载荷及断裂模式与实验结果进行对比,以判定各方法模拟皮质骨结构弯曲断裂的准确性。结果与结论:①由于单元失效策略不同,3种数值方法针对同一股骨有限元模型预测所得断裂进程存在明显差异;②结果显示基于连续损伤力学理论的断裂模拟与实验结果一致性更好;③通过与实验对比可以找到更适合模拟皮质骨结构弯曲断裂的数值方法,通过观测不同数值方法预测断裂参数差异并解析差异存在的原因,能够为各数值方法确定断裂模拟的适用范围,以提高仿真精度。

Curved Space-Time at the Planck Scale

This paper presents a physically plausible and somewhat illuminating first step in extending the fundamental principles of mechanical stress and strain to space-time. Here the geometry of space-time, encoded in the metric tensor, is considered to be made up of a dynamic lattice of extremely small, localized fields that form a perfectly elastic Lorentz symmetric space-time at the global (macroscopic) scale. This theoretical model of space-time at the Planck scale leads to a somewhat surprising result in which matter waves in curved space-time radiate thermal gravitational energy, as well as an equally intriguing relationship for the anomalous dispersion of light in a gravitational field.

Malus’ Law Derived from Deterministic Particle Behavior

A polarized beam of energy is usually interpreted as a set of particles, all having the same polarization state. Difference in behavior between the one and the other particle is then explained by a number of counter-intuitive quantum mechanical concepts like probability distribution, superposition, entanglement and quantized spin. Alternatively, I propose that a polarized beam is composed of a set of particles with a cosine distribution of polarization angles within a polarization area. I show that Malus’ law for the intensity of a beam of polarized light can be derived in a straightforward manner from this distribution. I then show that none of the above-mentioned counter-intuitive concepts are necessary to explain particle behavior and that the ontology of particles, passing through a polarizer, can be easily and intuitively understood. I conclude by formulating some questions for follow-up research.

Fatigue Reliability Analysis of Fiber-Reinforced Laminated Composites by Continuum Damage Mechanics

This paper investigates the reliability of composite laminates with various lay-ups under fatigue loading.The prediction of failure probability of composite laminates subjected to different loads involves many uncertainties associated with mechanical properties,loading,and boundary conditions.Failure in the composite material is truly hard to trace because there are individual faults in each ply,and we face a stochastic process due to the scatter in the mechanical properties.The continuum damage mechanics(CDM),as a powerful approach,is applied to model the damage of fiber,matrix,and fiber/matrix debonding.This method defines criteria for damage detection and determines safe zones.The material constitutive equations are executed using a subroutine inAbaqus.The first-order reliability method and second-order reliability method have been applied to examine the reliability of laminated composites.The results are compared with those of the Monte Carlo simulation.Different composite laminates under different stress levels are considered for the failure probability investigation.The limit state functions and random variables have been determined based on the CDM model.Finally,the effects of the number of cycles,applied stress,and stacking sequence of the laminate on the reliability and fatigue life in fiber-reinforced laminated composites are assessed.

基于连续介质力学的接触轮橡胶超弹性模型研究

针对橡胶超弹性导致恒切深砂带的磨削材料去除深度与理论材料去除深度产生误差的问题,基于连续介质力学理论模型的本构方程对橡胶超弹性特性下的应力-应变关系进行分析,对比确定了适用于钢轨打磨作业的Mooney-Rivlin理论模型,揭示了橡胶超弹性和线弹性的关系和差异,利用仿真验证了上述理论模型的正确性。

ATOMISTIC/CONTINUUM SIMULATION OF INTERFACIAL FRACTURE PART Ⅱ:ATOMISTIC/DISLOCATION/CONTINUUM SIMULATION

Coupled atomistic/dislocation/continuum simulation of interfacial fracture is performed in this paper.The model consists of a nanoscopic core made by atomistic assembly and a surrounding elastic continuum with discrete dislocations. Atomistic dislocations nucleate from the crack tip and move to the continuum layer where they glide according to the dislocation dynamics curve.An atoms/continuum overlapping belt is devised to facilitate the transition between the two scales.The continuum constraint on the atomic assembly is imposed through the mechanics at- mosphere along the overlapping belt.Transmissions of mechanics parameters such as displacements,stresses,masses and momenta across the belt are realized.The present model allows us to explore interfacial fracture processes under different mode mixity.The effect of atomistic zigzag interface on the fracture process is revealed:it hinders dislocation emission from the crack tip,especially under high mode mixity.