Some exact solutions for a class of compressible non-linearly elastic materials

In this paper we consider exact solutions for plane and axisymmetric deformations for a class of compressible elastic materials we call coharmonic. The coharmonic materials are derived from the harmonic materials by using Shield's inverse deformation theorem. The governing equations for the coharmonic material show the same kind of simplification associated with the harmonic materials. The equations reduce to first-order linear equations depending on an arbitrary harmonic function. They are intractable in general, so various ansätze are investigated. Boundary value problems for the coharmonic materials are compared with the same problems for harmonic materials. For certain boundary value problems, the harmonic materials exhibit well-known problematic behaviour which limits their use as models of material behaviour. The corresponding solutions for the coharmonic materials do not display these non-physical features.     

Energy Splitting Theorems for Materials with Memory

We extend to materials with fading memory and materials with internal variables a result previously established for materials with instantaneous memory: the additive decomposability of the total energy into an internal and a kinetic part, and a representation of the latter and the inertial forces in terms of one and the same mass tensor.     

微孔压电弹性动力学的能量原理

根据古典阴阳互补和现代对偶互补的基本思想,通过作者早已提出一条简单而统一的新途径,系统地建立了微孔压电弹性动力学的能量原理,给出一个重要的以卷积表示的积分关系式,可以认为,在力学上它是广义虚功原理的表式,从该式出发,不仅能得到微孔压电弹性动力学的虚功原理和互等定理,而且通过作者所给出的一系列广义Legendre变换,能系统地导出成互补关系的11类变量、9类变量、6类变量和3类变量简化Gurtin型变分原理的泛函,同时,通过这条新途径,还能清楚地阐明这些原理之间的内在联系。     

Singular stress field near the edge of interface of bonded dissimilar materials with an interlayer

For bonded dissimilar materials, the free-edge stress singularity usually prevails near the intersection of the free-surface and the interface. When two materials are bonded by using an adhesive, an interlayer develops between the two bonded materials. When a ceramic and a metal are bonded, the residual stress develops because of difference in the coefficient of thermal expansion. An interlayer may be inserted between the two materials to defuse the residual stress. Stress field near the intersection of the interface and free-surface in the presence of the interlayer is then very important for evaluating the strength of bonded dissimilar materials.In this study, stress distributions on the interface of bonded dissimilar materials with an interlayer were calculated by using the boundary element method to investigate the effect of the interlayer on the stress distribution. The relation between the free-edge singular stress fields of bonded dissimilar materials with and without an interlayer was investigated numerically. It was found that the influence of the interlayer on the stress distributions was confined within a small area of the order of interlayer thickness around the intersection of the interface and the free-surface when the interlayer was very thin. The stress distribution near the intersection of the interface and the free-surface was controlled by the free-edge stress singularity of the bonded dissimilar materials without the interlayer. In this case, the interlayer can be called free-edge singularity-controlled interlayer. If a stress distribution on the interface is known for one thickness of an interlayer h, stress distributions on the interface for other values of h can be estimated.     

The effective properties of piezoelectric composite materials with transversely isotropic spherical inclusions

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Extracting inter-particle forces in opaque granular materials: Beyond photoelasticity

This paper presents the first example of inter-particle force inference in real granular materials using an improved version of the methodology known as the Granular Element Method (GEM). GEM combines experimental imaging techniques with equations governing particle behavior to allow force inference in cohesionless materials with grains of arbitrary shape, texture, and opacity. This novel capability serves as a useful tool for experimentally characterizing granular materials, and provides a new means for investigating force networks. In addition to an experimental example, this paper presents a precise mathematical formulation of the inverse problem involving the governing equations and illustrates solution strategies.     

摩擦副材料对二烷基二硫代氨基甲酸钼添加剂摩擦学特性的影响

选择等离子喷涂钼合金层、渗氮层以及镀铬层为摩擦副材料 ,以全配方矿物基发动机油 SJ/ 5 W- 30作为基础润滑油 ,研究了上述 3种摩擦副材料对油溶性二烷基二硫代氨基甲酸钼 (Mo DTC)添加剂摩擦学特性的影响 .结果表明 :Mo DTC的摩擦学特性与摩擦副材料类型有关 ;采用喷钼层、渗氮层及镀铬层作为摩擦副材料 ,Mo DTC均表现出减摩和抗磨作用 ,对渗氮层的减摩抗磨效果最佳 .X射线光电子能谱分析表明 :摩擦副材料类型对添加剂中的 Mo和 S的化学状态和相对含量均有影响 ;摩擦副材料类型不同时 ,Mo DTC摩擦学行为的差异与其在磨损表面形成的 Mo S2 以及 Mo O3 、Fe S和磷酸盐等物质的含量有关     

Transverse loading of cellular topologically interlocked materials

Topologically interlocked materials (TIMs) are a class of materials made by a structured assembly of an array of identically shaped and sized unit elements that are held in a confining framework. The assembly can resist transverse forces in the absence of adhesives between the unit elements. The present study focuses on topologically interlocked materials with cellular unit elements. The resulting materials achieve their properties by a combination of deformation of the individual unit elements and their contact interaction. Drop tower tests were conducted to characterize the mechanical behavior of the cellular TIMs made of an intrinsically brittle base material. The TIMs were found to exhibit perfect softening, independent of the relative density of the cellular units. The analysis of the experiments revealed a positive correlation between strength and toughness in contrast to more conventional materials. An analytical model for the prediction of the observed material behavior is developed. Model predictions are in agreement with experimental data. The implications of the present findings for the design of these novel materials are discussed.     

Spontaneous Mixed-Mode Fracture in Bonded Similar and Dissimilar Materials

In this paper, we report on an experimental study of spontaneous, mixed-mode, crack propagation in weakly bonded similar and dissimilar materials. A unique experimental configuration is proposed to induce spontaneous crack growth events along the interfaces. The cracks nucleate from tiny circular holes and are triggered by an exploding wire. They subsequently propagate under the action of a constant, far-field load. Dynamic photoelasticity in conjunction with high speed photography is used to capture the real-time isochromatics associated with crack propagation. In the case of identical materials, crack propagation is anti-symmetric with respect to the crack nucleation point while strong asymmetry is observed for the case of dissimilar materials. In both cases, cracks propagate at constant velocity from the initiation point. The time histories of dynamic stress intensity factors and of energy release rates of the propagating cracks along the bonded similar materials are also reported.     

Surface effects on mechanical behavior of elastic nanoporous materials under high strain

This paper studies surface effects on the mechanical behavior of nanoporous materials under high strains with an improved anisotropic Kelvin model. The stress-strain relations are derived by the theories of Euler-Bernoulli beam and surface elasticity. Meanwhile, the influence of strut (or ligament) size on the mechanical properties of nanoporous materials is discussed, which becomes a key factor with consideration of the residual surface stress and the surface elasticity. The results show that the decrease in the strut diameter and the increase in the residual surface stress or the surface elasticity can both lead to an increase in the carrying capacity of nanoporous materials. Furthermore, mechanical behaviors of anisotropic nanoporous materials in different directions (the rise direction and the transverse direction) are investigated. The results indicate that the surface effects in the transverse direction are more obvious than those in the rise direction for anisotropic nanoporous materials. In addition, the present results can be reduced to the cases of conventional foams as the strut size increases to micron-scale, which confirms validity of the model to a certain extent.     

On Macrocrack–Microdefect Interaction

A review is given of studies devoted to problems and methods of evaluating the effective resistance to macrocrack growth in materials with microdamages and in materials reinforced with small rigid inclusions under mechanical and thermal loads. Also an analysis is made of the three-dimensional interaction of penny-shaped microcracks and macrocracks in isotropic and transversely isotropic materials. Related publications based on methods and models other than those used by the authors are reviewed.     

非均匀颗粒材料的类固-液相变行为及本构方程

以非均匀颗粒介质为研究对象，采用三维离散元方法对其在不同密集度和剪切速率下的动 力过程进行了数值模拟，分析了其在由瞬时接触的快速流动向持续接触的准静态流动的转变 过程及其行为特点. 通过对不同材料性质下相变过渡区内颗粒材料的宏观应力、接触时间数、 配位数、团聚颗粒数量、有效摩擦系数等参量的计算，更加全面地描述了非均匀颗粒材料在 类固-液相变过程中的基本特征. 基于以上数值计算结果，建立了一个适用于颗粒材料 类固态、类液态以及其相变过程的本构方程，并通过剪切室实验结果验证了它的合理性.     

缺陷对脆性材料碎裂过程的影响

采用特征线方法模拟脆性材料中应力波的传播过程,采用内聚力模型模拟断裂点的断裂过程,运用C++语言开发了一个模拟脆性圆环发生一维膨胀碎裂过程的实用工具ExpRing,简要给出了该程序的理论基础和使用说明。采用此程序模拟了具有初始缺陷的脆性圆环在均匀膨胀作用下的碎裂过程,探讨了不同应变率下,缺陷分布特征对碎裂过程和平均碎片尺寸的影响。计算结果表明:(1)在一定的应变率范围内,等间距分布的点缺陷会控制断裂点的位置及碎片个数,在碎片尺寸 应变率曲线上形成一个缺陷控制碎裂平台;(2)点缺陷的间距和弱化程度将影响缺陷控制碎裂平台的宽度和位置;(3)具有缺陷的脆性材料的表观强度呈现应变率硬化特征;(4)在一定的应变率范围内,正弦分布型缺陷同样导致缺陷控制碎裂的现象。     

钢纤维对铜基金属陶瓷摩擦材料力学和摩擦学性能的影响

研究了钢纤维含量及长径比对汽车离合器用Cu基金属陶瓷摩擦材料硬度、力学性能及摩擦磨损性能的影响．结果表明,钢纤维同Cu基体结合良好,钢纤维可增加金属陶瓷的硬度和弯曲强度;钢纤维含量及长径比对Cu基金属陶瓷摩擦材料的摩擦磨损性能具有明显影响;随着钢纤维含量和长径比的增大,摩擦系数对比压的敏感性减弱;当钢纤维含量为10％～30％时,长径比较大的SF-1钢纤维增强Cu基金属陶瓷摩擦材料的综合摩擦磨损性能较优,相应的偶件磨损较轻微．     

Coupled hydro-mechanical effects in a poro-hyperelastic material

Fluid-saturated materials are encountered in several areas of engineering and biological applications. Geologic media saturated with water, oil and gas and biological materials such as bone saturated with synovial fluid, soft tissues containing blood and plasma and synthetic materials impregnated with energy absorbing fluids are some examples. In many instances such materials can be examined quite successfully by appeal to classical theories of poroelasticity where the skeletal deformations can be modelled as linear elastic. In the case of soft biological tissues and even highly compressible organic geological materials, the porous skeleton can experience large strains and, unlike rubberlike materials, the fluid plays an important role in maintaining the large strain capability of the material. In some instances, the removal of the fluid can render the geological or biological material void of any hyperelastic effects. While the fluid component can be present at various scales and forms, a useful first approximation would be to treat the material as hyperelastic where the fabric can experience large strains consistent with a hyperelastic material and an independent scalar pressure describes the pore fluid response. The flow of fluid within the porous skeleton is defined by Darcy's law for an isotropic material, which is formulated in terms of the relative velocity between the pore fluid and the porous skeleton. It is assumed that the form of Darcy's law remains unchanged during the large strain behaviour. This approach basically extends Biot's theory of classical poroelasticity to include finite deformations. The developments are used to examine the poro-hyperelastic behaviour of certain one-dimensional problems.     

含柔性涂层的颗粒增强复合材料弹性模量估计

采用线弹簧型弱界面模型来模拟柔性涂层,研究柔性涂层对复合材料宏观弹性模量的影响。首先利用Mori-Tanaka方法和弱界面球形夹杂问题的弹性解,获得单夹杂内部的平均应力和平均应变,进而求得具有柔性涂层的复合材料的宏观弹性模量,并研究界面柔度对复合材料弹性模量的影响。     

二维材料纳米尺度摩擦行为及其机制

二维材料是指厚度仅有单层或数层原子的晶体或非晶材料,其优异的物理、力学和化学性能给纳米尺度超薄固体润滑材料的设计和发展带来了新的契机。同时,二维材料独特而简单的拓扑结构也为深入了解摩擦的微观机制提供了一个理想的对象。本文综述了以石墨烯为主的二维材料纳米尺度摩擦和磨损研究的进展。根据相对运动形式的不同,我们分别介绍了二维材料的层间滑动和表面摩擦行为,并详细阐述了这些独特行为背后的微观物理机制;同时我们还重点介绍了若干种影响和调控二维材料表面摩擦性能的典型方法和策略,以及二维材料纳米尺度的磨损行为及其失效模式。最后,我们还对纳米尺度二维材料摩擦研究进行了小结,并展望了该领域尚待探索的若干研究方向。     

圆柱夹层多孔材料的主动散热性能研究与优化设计

通过推导不同边界条件的圆柱状夹层多孔材料散热指标,研究了一种特殊结构的圆柱状夹层多孔材料主动散热问题。这种圆柱夹层材料的每一层胞体个数相同,胞体尺寸随着外径的增大而增大,从而保持每一层胞体的相对密度相同。通过计算两种不同换热边界条件下圆柱夹层多孔材料的散热性能,比较并分析了与夹层材料层数相对应的最大散热效率和最优相对密度等指标,并最终得到这些工况下的最优质量。通过分析得到,无论哪种边界条件,正六边形胞体的夹层结构散热性能优于其他构型。同时当为达到某一限定散热效率值时,正六边形胞体结构的质量最小,正六边形构型的多孔材料具有明显的综合性能优势。     

Analysis of spherical indentation of materials with plastically graded surface layer

In the present work, a comprehensive parametric study for establishing contact mechanics of instrumented normal spherical indentation on homogeneous materials and materials with plastically graded surface layer (PGSL) was undertaken by dimensional analysis and finite element modeling. The spherical indentation response for homogeneous materials can be described only by two dimensionless parameters: strain hardening exponent and a unified parameter that can describe effects of both the normalized yield strength and the normalized indentation depth. The influences of these two parameters were investigated for a wide range of engineering materials, and the results may be used as an estimate of loading response and pile-up/sink-in behavior when the material properties are known. In the materials with PGSL, a linear gradient in yield strength, and no variation in elastic modulus and strain hardening exponent were explored. The indentation response of the materials with PGSL can be described only by three dimensionless parameters: the normalized indentation depth, the dimensionless strength gradient parameter, and the normalized PGSL thickness. The effects of these three parameters were studied systematically. The normalized pile-up/sink-in parameter is found to be an increasing function of the strength gradient parameter. The normalized pile-up/sink-in parameter increases (decreases) with increasing PGSL thickness for a fixed positive (negative) gradient case at large indentation depth. The results also indicate that the materials with positive PGSL can bear more loads and have significantly more resistance to contact crack formation.     

Mode III stress intensity factors for edge-cracked circular shafts,bonded wedges,bonded half planes and DCB’s

Antiplane shear deformation of several edge-cracked geometries is considered. Analytical expressions are derived for the mode III stress intensity factor (SIF) of circular shafts with edge cracks, bonded half planes containing an interfacial edge crack, bonded wedges with an interfacial edge crack and also DCB’s. The results are extracted for simple isotropic materials as well as anisotropic materials and also bonded dissimilar materials and it is shown that the same expressions are obtained for the SIF under the same geometries but with different above-mentioned material properties. Different boundary conditions are assumed and the SIF relations are derived in each case. As the special cases, the SIF’s of the two bonded quarter planes containing an edge crack at the interface and infinite strip with a semi-infinite edge crack are extracted which coincide with the results cited in the literature.