多尺度复合材料力学研究进展

多尺度复合材料力学是运用多尺度分析思想研究空间分布非均匀材料力学性能的学科, 近年来,多 组分、多层级先进材料的蓬勃发展和微纳米实验观测手段的不断进步,有力地推动了该学科的研究,论文围绕非均 匀材料力学性能的多尺度分析,首先从微纳米尺度到宏观尺度综述了常用的理论分析方法;接着分别针对非均匀 连续介质和离散体系介绍了常用的多尺度计算模拟方法;然后结合本课题组在纳米复合材料、抗冲击吸能材料、随 机网络材料和多层级自相似材料等方面的研究工作,举例说明了如何综合运用多种方法对各种复杂材料系统进行 多尺度分析;最后,展望了该领域还需进一步发展和完善的若干方向。     

Establishing foundations of the mechanics of nanocomposites (Review)

A general idea of the mechanics of nanocomposites that allows formulating a system of approaches and methods of analysis in this area is given. The place of mechanics in materials research and the structural levels that divide mechanics into macromechanics, mesomechanics, micromechanics, and nanomechanics are discussed. A brief historical sketch of the nanomaterial technology is presented. Examples of different nanotechnologies and nanomaterials are given. Typical nanomaterials and their properties are described. Matrices and reinforcements of nanocomposite materials as well as their properties are considered separately. A classification of nanocomposites is proposed. Special attention is given to modeling in the structural mechanics of nanocomposites, the principles of continualization and homogenization, edge and near-surface effects, validity limits of the continuum approach, and two-sided estimates. A discussion is given of two basic models within the framework of the basic approach as a set of concepts, models, and problem statements and of the development of methods adequately describing mechanical phenomena in nanocomposites. The presented material is mainly taken from the book A. N. Guz, J. J. Rushchitsky, and I. A. Guz, Introduction to the Mechanics of Nanocomposites [in Russian], S. P. Timoshenko Inst. Mech., Kyiv (2010)     

On two models in the three-dimensional theory of stability of composites

A comparative analysis is made of the infinite-fiber and finite-fiber models in the three-dimensional theory of stability of composites. The results analyzed have been obtained using the three-dimensional linearized theory of stability of deformable bodies. A historical sketch is given of the theory of stability for and approaches used in the mechanics of laminated and fibrous composite materials Translated from Prikladnaya Mekhanika, Vol. 44, No. 8, pp. 3–31, August 2008.     

Coupling the finite element method and molecular dynamics in the framework of the heterogeneous multiscale method for quasi-static isothermal problems

Multiscale models are designed to handle problems with different length scales and time scales in a suitable and efficient manner. Such problems include inelastic deformation or failure of materials. In particular, hierarchical multiscale methods are computationally powerful as no direct coupling between the scales is given. This paper proposes a hierarchical two-scale setting appropriate for isothermal quasi-static problems: a macroscale treated by continuum mechanics and the finite element method and a microscale modelled by a canonical ensemble of statistical mechanics solved with molecular dynamics. This model will be implemented into the framework of the heterogeneous multiscale method. The focus is laid on an efficient coupling of the macro- and micro-solvers. An iterative solution algorithm presents the macroscopic solver, which invokes for each iteration an atomistic computation. As the microscopic computation is considered to be very time consuming, two optimisation strategies are proposed. Firstly, the macroscopic solver is chosen to reduce the number of required iterations to a minimum. Secondly, the number of time steps used for the time average on the microscale will be increased with each iteration. As a result, the molecular dynamics cell will be allowed to reach its state of thermodynamic equilibrium only in the last macroscopic iteration step. In the preceding iteration steps, the molecular dynamics cell will reach a state close to equilibrium by using considerably fewer microscopic time steps. This adapted number of microsteps will result in an accelerated algorithm (aFE-MD-HMM) obtaining the same accuracy of results at significantly reduced computational cost. Numerical examples demonstrate the performance of the proposed scheme.     

基于分子动力学模拟的多晶结构微观热-力耦合行为的计算

基于分子动力学模拟,建立了一套可用于表征微观下多晶结构热-力耦合行为的算法框架。该算法的要点是将连续模型和分子模拟耦合起来,并使守恒定律在微观连续模型和原子层次上都得到满足,与利用传统的连续介质力学建立晶界与晶粒的本构方程相比,本模型中的连续流是通过原子模型准确计算得到的,从而避免了使用经验的本构方程。     

Inhomogeneous shearing of strain-stiffening rubber-like hollow circular cylinders

The purpose of this paper is to investigate the effects of strain-stiffening for the classical problems of axial and azimuthal shearing of a hollow circular cylinder composed of an incompressible isotropic non-linearly elastic material. For some specific strain-energy densities that give rise to strain-stiffening in the stress–stretch response, the stresses and resultant axial forces are obtained in explicit closed form. While such results are well known for classical constitutive models such as the Mooney–Rivlin and neo-Hookean models, our main focus is on materials that undergo severe strain-stiffening in the stress–stretch response. In particular, we consider in detail two phenomenological constitutive models that reflect limiting chain extensibility at the molecular level and involve constraints on the deformation. The amount of shearing that tubes composed of such materials can sustain is limited by the constraint. Numerical results are also obtained for an exponential strain-energy that exhibits a less abrupt strain-stiffening effect. Potential applications of the results to the biomechanics of soft tissues are indicated.     

A Molecular-Statistical Basis for the Gent Constitutive Model of Rubber Elasticity

Molecular constitutive models for rubber based on non-Gaussian statistics generally involve the inverse Langevin function. Such models are widely used since they successfully capture the typical strain-hardening at large strains. Limiting chain extensibility constitutive models have also been developed on using phenomenological continuum mechanics approaches. One such model, the Gent model for incompressible isotropic hyperelastic materials, is particularly simple. The strain-energy density in the Gent model depends only on the first invariant I ₁ of the Cauchy–Green strain tensor, is a simple logarithmic function of I ₁ and involves just two material parameters, the shear modulus μ and a parameter J _m which measures a limiting value for I ₁−3 reflecting limiting chain extensibility. In this note, we show that the Gent phenomenological model is a very accurate approximation to a molecular based stretch averaged full-network model involving the inverse Langevin function. It is shown that the Gent model is closely related to that obtained by using a Padè approximant for this function. The constants μ and J _m in the Gent model are given in terms of microscopic properties. Since the Gent model is remarkably simple, and since analytic closed-form solutions to several benchmark boundary-value problems have been obtained recently on using this model, it is thus an attractive alternative to the comparatively complicated molecular models for incompressible rubber involving the inverse Langevin function. This revised version was published online in June 2006 with corrections to the Cover Date.     

The fluid-structure interaction between a tensioned elastica and a flotation guide

Fluid-structure interaction between a flotation-guide and a tensioned elastic beam was investigated theoretically and experimentally. The work is inspired by manufacturing of thin flexible materials such as paper, foils and tape, collectively known as web. The mechanics of the web was modeled as an elastica beam, and solved in a Eulerian reference system by using the finite element method. The fluid mechanics in the beam/flotation-guide interface was modeled with two different fluid mechanics approaches with and without height averaging of the flow variables. The fluid models were solved with a finite volume approach. A stacked, iterative coupling algorithm was used to obtain coupled solutions. Experiments were performed to verify the two FSI models. The experiments showed that the supply pressure inside the flotation-guide must be at least equal to the belt-wrap pressure of the web for flotation to occur, as expected. The effects of large web deformations and using the height-averaged fluid model were analyzed by varying design parameters such as web wrap angle, flotation-guide radius, supply pressure, and the distribution of the pressure supply holes. This work showed that the height-averaged fluid mechanics model fails to predict the two-dimensional flow near the exit regions, which develops for cases where the web-reverser clearance tends to have large diverging variations. It was also shown that in order to keep the applied web tension at a constant level, the arc length of the web between the supports must change.     

针尖的分子生物物理力学研究进展

围绕包括扫描探针显微镜在内的各种探针技术下核酸、蛋白质等生物分子及生物材料的生物力学与力 - 电耦合实验研究, 较系统地总结了分子层次或纳米尺度下生物分子和材料的力学性能的扫描探针显微镜、光镊、磁镊等探针技术的实验研究方法和主要进展, 进而探讨了在``针尖'这个极小、极特殊环境下的分子生物物理力学研究状况.通过介绍借助探针技术研究相关生物物质的结构、力学、电学等性能以及提出的一些理论模型, 指出探针技术在生物分子（包括遗传物质和蛋白质）力学性能、纳米生物材料结构及分子仿生等研究中的广泛意义.提出多场耦合作用下的针尖的生物物理力学研究必定是将来研究的重点;将针尖的分子生物力学的物理实验研究与分子物理力学理论、计算科学相结合, 发展分子物理力学虚拟实验技术是本领域的一个重要发展方向.      

A novel atomistic approach to determine strain-gradient elasticity constants: Tabulation and comparison for various metals, semiconductors, silica, polymers and the (Ir) relevance for nanotechnologies

Strain-gradient elasticity is widely used as a suitable alternative to size-independent classical continuum elasticity to, at least partially, capture elastic size effects at the nanoscale. In this work, borrowing methods from statistical mechanics, we present mathematical derivations that relate the strain-gradient material constants to atomic displacement correlations in a molecular dynamics computational ensemble. Using the developed relations and numerical atomistic calculations, the strain-gradient constants are explicitly determined for some representative semiconductor, metallic, amorphous and polymeric materials. This method has the distinct advantage that amorphous materials can be tackled in a straightforward manner. For crystalline materials we also employ and compare results from both empirical and ab initio based lattice dynamics. Apart from carrying out a systematic tabulation of the relevant material parameters for various materials, we also discuss certain subtleties of strain-gradient elasticity, including: the paradox associated with the sign of the strain-gradient constants, physical reasons for low or high characteristic length scales associated with the strain-gradient constants, and finally the relevance (or the lack thereof) of strain-gradient elasticity for nanotechnologies.     

Mechanics of biomolecules

Over the last few years molecular biomechanics has emerged as a new field in which theoretical and experimental studies of the mechanics of proteins and nucleic acids have become a focus, and the importance of mechanical forces and motions to the fundamentals of biology and biochemistry has begun to be recognized. In particular, single-molecule biomechanics of DNA extension, bending and twisting; protein domain motion, deformation and unfolding; and the generation of mechanical forces and motions by biomolecular motors has become a new frontier in life sciences. There is an increasing need for a more systematic study of the basic issues involved in molecular biomechanics, and a more active participation of researchers in applied mechanics. Here we review some of the advances in this field over the last few years, explore the connection between mechanics and biochemistry, and discuss the concepts, issues, approaches and challenges, aiming to stimulating a broader interest in developing molecular biomechanics.     

位错动力学方法在辐照损伤力学中的应用

核能是人类最理想的清洁能源之一,在世界能源结构中发挥着巨大作用。核裂变或核聚变导致的辐照环境会引起材料的辐照损伤,进而显著影响材料的力学性能,造成辐照硬化、脆化、蠕变、肿胀等现象。无论是预测辐照材料的服役寿命,还是设计新型的抗辐照材料,都迫切需要建立强辐照环境下的塑性力学和损伤力学理论。分子动力学方法为理解辐照材料中的原子级相互作用机理提供了诸多有价值的信息,然而受限于时空尺度难以直接用于力学理论模型的建立。晶体塑性有限元方法可用于预测辐照材料的力学响应,但是往往需要基于已知的物理模型,并且拟合实验数据。位错动力学方法是联系纳米力学与连续介质力学的桥梁,是揭示大量微结构的累积相互作用机理,建立基于物理机制的塑性力学和损伤力学理论的强有力手段。位错动力学方法起源于上个世纪八十年代,起初主要用于研究位错间的短程和长程相互作用、计算位错运动引起的塑性变形、硬化、软化、变形局部化等。本文将展示三种耦合位错动力学和辐照损伤场的方法,并系统地综述研究者近年来使用该方法在理解辐照硬化、塑性变形局部化、晶界效应、温度效应、和发展多尺度耦合方法等方面取得的进展。     

Microscopic modelling of orientation kinematics of non-spherical particles suspended in confined flows using unilateral mechanics

The properties of reinforced polymers strongly depend on the microstructural state, that is, the orientation state of the fibres suspended in the polymeric matrix, induced by the forming process. Understanding flow-induced anisotropy is thus a key element to optimize both materials and process. Despite the important progresses accomplished in the modelling and simulation of suspensions, few works addressed the fact that usual processing flows evolve in confined configurations, where particles characteristic lengths may be greater than the thickness of the narrow gaps in which the flow takes place. In those circumstances, orientation kinematics models proposed for unconfined flows must be extended to the confined case. In this short communication, we propose an alternative modelling framework based on the use of unilateral mechanics, consequently exhibiting a clear analogy with plasticity and contact mechanics. This framework allows us to revisit the motion of confined particles in Newtonian and non-Newtonian matrices. We also prove that the confined kinematics provided by this model are identical to those derived from microstructural approaches (Perez et al. (2016) [1]).     

位错动力学方法在辐照损伤力学中的应用

核能是人类最理想的清洁能源之一,在世界能源结构中发挥着巨大作用。核裂变或核聚变导致的辐照环境会引起材料的辐照损伤,进而显著影响材料的力学性能,造成辐照硬化、脆化、蠕变、肿胀等现象。无论是预测辐照材料的服役寿命,还是设计新型的抗辐照材料,都迫切需要建立强辐照环境下的塑性力学和损伤力学理论。分子动力学方法为理解辐照材料中的原子级相互作用机理提供了诸多有价值的信息,然而受限于时空尺度难以直接用于力学理论模型的建立。晶体塑性有限元方法可用于预测辐照材料的力学响应,但是往往需要基于已知的物理模型,并且拟合实验数据。位错动力学方法是联系纳米力学与连续介质力学的桥梁,是揭示大量微结构的累积相互作用机理,建立基于物理机制的塑性力学和损伤力学理论的强有力手段。位错动力学方法起源于上个世纪八十年代,起初主要用于研究位错间的短程和长程相互作用、计算位错运动引起的塑性变形、硬化、软化、变形局部化等。本文将展示三种耦合位错动力学和辐照损伤场的方法,并系统地综述研究者近年来使用该方法在理解辐照硬化、塑性变形局部化、晶界效应、温度效应、和发展多尺度耦合方法等方面取得的进展。     

Micro-potential model for stress-strain hysteresis of micro-cracked materials

While developing models for nonlinear mechanical and acoustical behavior of micro-cracked materials, it is common to start from a purely phenomenological approach. Most approaches essentially assume the material to have certain given “mathematical” properties, that lead to an acceptable equation of state (stress-strain relation) containing nonlinearity and hysteresis. In this paper, we formulate a deeper physical insight on the subject of mechanical hysteresis based on physical and measurable material properties. The theory developed in this paper interprets real images of crack networks in micro-inhomogeneous materials, obtained via electron microscopy, and uses this interpretation to build up a micro-potential model for a medium containing elementary cracks with known properties. It is found that the hysteretic contribution of each crack strongly depends on its average rest opening and its asperity. As a result, a distribution of cracks with different properties yields the physical basis for a slightly more complex version of the commonly used Preisach-Mayergoyz space in rock mechanics. The effect of a uniform distribution of the crack properties on the stress-strain relation is shown as an example.     

Experimental analysis of propagation of fatigue crack on gears

Gears of different sizes and with different systems of loading are indispensable components of machines and devices. When optimizing such gear assemblies, on of the most important parameters is their required service life. To calculate the service life as precisely and reliably as possible, researchers need to use the required mathematical models for describing loading, the geometry, properties of materials and fracture mechanics parameters. The accuracy and reliability of the gear model assemblies can be compared only with appropriate experimental results. To this end, the authors have used and developed a series of methods and test pieces. A comparison of results has shown that the models and approaches are adequate.     

Some applications of molecular rheology: Polymer formulation and molecular design

“Molecular rheology” is the missing link between the macromolecular structure of polymeric materials and their viscoelastic properties in the melt state. It complements the engineering or continuum mechanics aspects of rheology, which generally ignores the molecular details of the objects under study. The pioneering vision of the diffusion and relaxation processes of flexible macromolecular chains initiated by P.-G. de Gennes has lead to very effective and predictive models of viscoelasticity of polymer melts, which go far beyond academic interest.We present, in this paper, two very different examples of application of molecular rheology: molecular design of block copolymers corresponding to expected end-user properties (which are directly linked to linear viscoelastic properties) and formulation of blends of linear polymers in order to get strain-hardening effects in non-linear viscoelasticity usually obtained with long-chain branched (LCB) materials.     

Convection and diffusion of polymer network strands

A review of several important constitutive equations is herein conducted with an eye towards determining those most suitable for use in modelling polymer melt processing. General principles are invoked for a priori screening of the equations without needing detailed comparison of the model predictions with experimental data. These principles, which are derived from continuum mechanics, thermodynamics and molecular kinetic theory, and dela with convection and diffusion of entangled polymer strands during flow, are: (1) During sudden deformations, the stress is a unique function of the total strain. (2) The second law of thermodynamics holds for all deformations. (3) The constitutive equation can be derived from a plausible molecular model which describes the convection and diffusion. (4) The model parameters can be determined by a reasonable number of rheometric experiments. Based on these principles, it is concluded that separable free energy models are the most promising. These are either BKZ integral models with a kernel factorable into a time-dependent and a strain-dependent part. or sets of Maxwell-type differential equations that employ a generalized convected derivative, and that are linear in stress in the absence of flow.     

细分曲面边界元法的黏附吸声材料结构拓扑优化分析

等几何分析采用样条基函数构造几何模型和实施变量近似,实现了计算机辅助设计和辅助工程的无缝连接,并已广泛应用于弹性力学、电磁场和位势问题等领域.然而直接采用等几何方法难以构造复杂模型,限制了该方法在大规模实际工程问题上的应用.细分曲面法可用于克服这一问题,该方法对传统模型的离散网格进行细分和拟合操作,构造出极限光滑曲面,连续性更高,对复杂结构的适用性更强.该方法主要有以下优点:(1)适用于任意拓扑结构;(2)数值计算稳定;(3)实施简单;(4)局部细化与连续性控制.由于该方法在复杂结构模型构造方面具有较强的灵活性和便利性,已被广泛应用于航空航天、汽车、动画、游戏制作等建模领域.将细分曲面法与边界元法相结合进行结构声学分析,几何场与物理场均采用箱样条基函数进行插值近似.以黏附吸声材料结构的声散射问题为例,建立吸声材料分布拓扑优化数学模型,并采用移动渐进线算法进行设计变量更新,最终获得最优材料分布.