Scale-effects on mean and standard deviation of the mechanical properties of condensed matter: an energy-based unified approach

The size effects on the mean values of the mechanical properties of condensed matter and on the related variances are analysed by means of a unified approach based on the multiscale character of energy dissipation. In particular, the scaling law for fragmentation energy density is obtained taking into account the self-similarity of fragments. It is based on a generalization of the three classical comminution laws that has been performed to evaluate the energy dissipation, computing volume and surface area of the particles for one- two- and three-dimensional fragmented objects. The result is general and can be applied to different fractal energy dissipation mechanisms, e.g., plasticity. Based on this approach, the scaling laws for mean and standard deviation values of the main mechanical properties of materials can be derived, like Young's and shear elastic moduli, ultimate normal and shear stresses and strains, fracture energy and toughness.     

Quantum metabolism explains the allometric scaling of metabolic rates

A general model explaining the origin of allometric laws of physiology is proposed based on coupled energy-transducing oscillator networks embedded in a physical d-dimensional space (d = 1, 2, 3). This approach integrates Mitchell''s theory of chemi-osmosis with the Debye model of the thermal properties of solids. We derive a scaling rule that relates the energy generated by redox reactions in cells, the dimensionality of the physical space and the mean cycle time. Two major regimes are found corresponding to classical and quantum behaviour. The classical behaviour leads to allometric isometry while the quantum regime leads to scaling laws relating metabolic rate and body size that cover a broad range of exponents that depend on dimensionality and specific parameter values. The regimes are consistent with a range of behaviours encountered in micelles, plants and animals and provide a conceptual framework for a theory of the metabolic function of living systems.     

Switching Energy of Ferromagnetic Logic Bits

Power dissipation in switching devices is believed to be the single most important roadblock to the continued downscaling of electronic circuits. There is a lot of experimental effort at this time to implement switching circuits based on magnets and it is important to establish power requirements for such circuits and their dependence on various parameters. This paper analyzes switching energy that is dissipated in the switching process of single-domain ferromagnets used as cascadable logic bits. We obtain generic results that can be used for comparison with alternative technologies or guide the design of magnet-based switching circuits. Two central results are established. One is that the switching energy drops significantly if the ramp time of an external pulse exceeds a critical time. This drop occurs more rapidly than what is normally expected of adiabatic switching for a capacitor. The other result is that under the switching scheme that allows for logic operations, the switching energy can be described by a single equation in both fast and slow limits. Furthermore, these generic results are used to discuss the practical consideration such as dissipation versus speed, increasing the switching speed and scaling. It is further explained that nanomagnets can have scaling laws similar to CMOS technology.     

Mixed mode modeling of a thin adhesive layer using a meso-mechanical model

A representative volume element is modeled using the finite element method. It is used to analyze mixed mode behavior of a thin adhesive layer. Two sources of dissipation is modeled; plasticity and decohesion. Macroscopic traction–separation laws are extracted from the simulations. The results indicate that a boundary of mode mix exists between a region where major plastic dissipation is present and a region where it is not. Without major plastic dissipation, the fracture energy is low and essentially governed by the cohesive properties. This is the case in peel dominated loading cases. In shear dominated loading cases plastic dissipation gives a substantial contribution to the fracture energy. The results show that pure shear loading gives the largest fracture energy.     

冷弯薄壁型钢框架-开缝钢板剪力墙力学性能研究

为研究适用于低层和多层冷弯薄壁型钢建筑的冷弯薄壁型钢框架-开缝钢板剪力墙(Cold-formed steel Framed Shear Wall with Slits,简称CFS-WS),该文开展了1面普通CFS-WS和3面加劲CFS-WS的拟静力试验,得到了CFS-WS的破坏形态、滞回曲线、骨架曲线和耗能能力等力学性能,提出了其抗剪承载力设计值。试验结果表明:CFS-WS加载时依靠竖缝间钢板“扭转-恢复-逆向扭转”和型钢框架变形来共同抵抗水平荷载和耗散能量,试件破坏时钢板撕裂,帽形柱端部屈曲;CFS-WS具有良好的承载力、塑性、延性和耗能能力,但其滞回曲线捏缩现象较为严重;加劲CFS-WS较普通CFS-WS而言,其抗剪刚度、承载能力和耗能能力更高,滞回曲线捏缩现象有所减轻。此外,通过加劲肋连接件将加劲肋和冷弯薄壁型钢梁柱连接成钢框架,可有效提高CFS-WS的前期抗剪刚度、承载力和耗能能力,大大改善结构的抗震性能。     

Experimental evidence and numerical simulation of size effects on the ductile fracture of metallic materials

The results of experimental tests investigating the size effects on single-edge-notched metallic specimens loaded in three-point bending are presented. Five different specimen scales were tested, with dimensions varying within the range 1:16. The samples were subjected to a fatigue pre-cracking to produce a sharp crack stemming from the notch root and, then, a quasi-static loading process was carried out up to the complete failure, in order to capture also the post-peak response. Notable size effects on the overall behaviour were obtained, with a variation of the failure mode from plastic collapse to ductile fracture and brittle failure by increasing the specimen size. An interpretation of the obtained size effects on ductile fracture is proposed based on numerical simulations carried out with a finite-element model that combines the cohesive method and the \(\hbox {J}_{2}\) plasticity to take into account all the possible mechanisms for energy dissipation. The best-fitting of the experimental results is obtained by scaling the mechanical properties with the specimen size, thus proving the need of considering size-dependent constitutive laws to correctly predict the ductile fracture. Finally, scale-invariant cohesive properties are derived on the base of the fractal approach to the size effect.     

薄钢板剪力墙结构试验研究及简化模型分析

通过对薄钢板剪力墙结构的低周反复荷载试验研究,分析了结构的受力机理、变形破坏模式、滞回曲线、延性指标、耗能能力等抗震性能指标。针对非加劲薄钢板剪力墙屈曲后受力性能,基于刚度等效、柱最大轴力等效和柱最大弯矩等效,提出一种构造简单又能考虑对边柱不利影响的三拉杆模型TSM(Three Strip Model),并与SM模型,精细有限元模型及试验结果进行了对比,结果表明,TSM模型具有很好的精度,可供工程设计应用。     

Plastic dissipation in mixed-mode fatigue crack growth along plastically mismatched interfaces

A new theory of fatigue crack growth in ductile solids has recently been proposed based on the total plastic energy dissipation per cycle ahead of the crack. This and previous energy based approaches in the literature suggest that the total plastic dissipation per cycle can be closely correlated with fatigue crack growth rates under mode I loading. In a recent paper, the authors have extended the dissipated energy approach to the case of fatigue crack growth in a homogeneous material under sustained mixed-mode loading conditions. The goal of the current study is to further extend the approach to mixed-mode fatigue delamination of ductile interfaces in layered materials. Attention is restricted to material combinations with identical elastic properties, but with mismatches in plastic properties (both yield strength and hardening modulus) across the interface. Such systems can occur in brazing, soldering, welding, and a variety of layered manufacturing applications, where high-temperature material deposition can result in a mismatch in mechanical properties between the deposited material and the substrate. In this study, the total plastic dissipation per cycle is obtained through plane strain elastic–plastic finite element analysis of a stationary crack in a general layered specimen geometry under constant amplitude, mixed-mode loading. Numerical results for a dimensionless plastic dissipation per cycle are presented over the full range of relevant material combinations and mixed-mode loading conditions. Results suggest that while applied mode-mix ratio is the dominant parameter, mismatches in yield strength and hardening modulus can have a significant effect on the total plastic dissipation per cycle, which is dominated by the weaker/softer material.     

A fractal model for the static coefficient of friction at the fiber-matrix interface

The physical, geometrical, and mechanical properties at the fiber/matrix interface of a fiber-reinforced composite material have a dominant effect on the overall mechanical behavior of these materials. Specifically, the toughening of these materials is largely attributed to the energy dissipation due to the frictional sliding of fibers at their interface with the matrix material. The micromechanisms involved with interfacial failure and sliding are currently not entirely understood, and the failure threshold is generally predicted using macro-scale friction laws which neglect the micromechanical aspects. The objective of this study is to explore the derivation of a macro-scale static coefficient of friction at the interface of a previously debonded fiber based on the micro-scale properties of the contacting surfaces. Presented results illustrate that the macro-scale static coefficient of friction obtained from the proposed micro-scale model is independent of the normal load and is therefore consistent with the classical Amontons-Coulomb phenomenological laws of friction.     

Impact response of elasto-plastic granular and continuum media: A comparative study

A comparative study of the impact response of three-dimensional ordered granular sphere packings and continuum half-spaces made of elastic-perfectly plastic materials is conducted. Energy dissipation and plastic zone volume are characterized, and scaling laws with respect to material properties, size and loading variables are derived for both continuum and discrete (granular) systems. Due to stress concentration at contacts, energy dissipation in granular systems occurs at much smaller impact loads than in continuum systems. At higher impact loads, the fraction of energy dissipated and the extent of plastic zone are much larger in the discrete system than in the continuum case. Though the size of plastic zone is much larger in discrete systems, the volume of material involved in dissipating a fraction of impact energy is comparable for continuum and granular systems.     

Derivation of Path Independent Coupled Mix Mode Cohesive Laws from Fracture Resistance Curves

A generalised approach is presented to derive coupled mixed mode cohesive laws described with physical parameters such as peak traction, critical opening, fracture energy and cohesive shape. The approach is based on deriving mix mode fracture resistance curves from an effective mix mode cohesive law at different mode mixities. From the fracture resistance curves, the normal and shear stresses of the cohesive laws can be obtained by differentiation. Since, the mixed mode cohesive laws are obtained from a fracture resistance curve (potential function), path independence is automatically satisfied. The effective mix mode cohesive law can have different shape and cohesive law parameters at different mode mixities so that the approach can be applied to various material failure models.     

高延性混凝土低矮剪力墙抗震性能试验研究及抗剪承载力计算

该文提出采用高延性混凝土（HDC）提高低矮剪力墙的抗震性能,设计并制作了5片剪跨比均为1.0的剪力墙,并通过拟静力试验,分析轴压比、水平分布钢筋及内置钢板对低矮剪力墙的破坏形态、延性和耗能能力的影响。试验结果表明:与高强混凝土剪力墙相比,HDC剪力墙的变形能力明显提高;HDC低矮剪力墙的耗能能力、变形能力随着轴压比的增大而减小,随水平分布钢筋数量的减小而减小;HDC与钢板协同工作提高了低矮剪力墙的承载能力和耗能能力。基于软化拉-压杆模型,并考虑HDC材料的受压软化特性,该文提出了高延性混凝土低矮剪力墙抗剪承载力的计算公式,计算结果与试验结果吻合较好。     

Characterizing delamination of fibre composites by mixed mode cohesive laws

A novel method is used for the determination of mixed mode cohesive laws and bridging laws for the characterisation of crack bridging in composites. The approach is based on an application of the J integral. The obtained cohesive laws were found to possess high peak stress values. Mixed mode cohesive stresses were found to depend on both the normal and tangential crack opening displacements. The bridging laws, which are to be used together with a mode mixity dependent crack tip fracture energy, were found to possess relative low bridging stresses; the peak normal bridging stress was approximately 2 MPa during pure Mode I and the maximum shear stress during pure Mode II was about 10 MPa.     

内嵌钢板及边缘框架相互作用对带连梁低屈服点钢板剪力墙结构受力性能的影响

为满足快速发展的高层建筑结构对抗震性能及空间灵活性的要求,将高耗能能力、高延性的低屈服点钢材与带连梁钢板剪力墙组合成新型带连梁低屈服点钢板剪力墙结构体系。采用有限元软件ABAQUS建立带连梁钢板剪力墙结构模型,结合国内外已有的典型试验结果验证数值方法的有效性。在此基础上,设计5个不同耦合度的低屈服点钢板剪力墙结构模型进行单调和循环加载,对比分析其损伤机制、承载性能及滞回耗能能力,探讨内嵌钢板与边缘框架的相互作用对结构及构件受力性能的影响,给出设计建议。结果表明:带连梁低屈服点钢板剪力墙结构内嵌钢板与边缘框架相互作用能够有效提高整体结构承载力、承载效率以及耗能能力。综合考虑材料利用率、承载能力及耗能能力,建议连梁耦合度控制在0.45以内。随着连梁耦合度的提高,边缘框架分担剪力多至60%,内部框架柱的轴力显著减小,连梁转角不断减小。因此,在带连梁低屈服点钢板剪力墙结构设计过程中应充分考虑内嵌钢板与边缘框架的相互作用,适当减小内嵌钢板设计厚度及边缘框架截面尺寸,提高材料利用率及设计经济性。同时,与纯框架抗侧性能相比,内嵌钢板与边缘框架的相互作用有效提高了边缘框架的初始抗侧刚度及承载力。     

Compression modeling of plain weave textile fabric using finite elements

Textile composite are used extensively in aerospace as they offer a 3D reinforcement in a single layer providing better mechanical properties in both in‐plane and transverse directions. This paper reports on the mechanical behavior of a plain weave textile fabric under the compressive loading. Unit cell geometry of the plain weave fabric structure is identified and its model is created using TexGen geometric modeling scheme developed by the University of Nottingham (U.K.). Later on its mechanical behavior is predicted using finite element modeling (FEM) based simulation software ABAQUS^® incorporating a transversely isotropic material law. Strain energy of the developed model has been compared with that of the published results and shows very good agreement. The analysis indicated that transverse‐longitudinal shear (TLS) modulus plays an important role in characterizing the behavior of the woven fabric under compression, while the friction between the yarns and longitudinal stiffness has less significant influence on compaction behavior. In order to ascertain the effectiveness of the developed model, exhaustive parametric studies have also been conducted to investigate the effect of transverse‐longitudinal shear modulus on some of the important parameters such as artificial strain energy, external work, frictional dissipation, internal energy, kinetic energy, strain energy and total energy of the model. The developed model has the capacity to predict and simulate the behavior of variety of fabric architectures based on their constituent yarn properties under various regimes of service loads.     

A nonlocal model of fracture by crazing in polymers

We derive and numerically verify scaling laws for the macroscopic fracture energy of polymers undergoing crazing from a micromechanical model of damage. The model posits a local energy density that generalizes the classical network theory of polymers so as to account for chain failure and a nonlocal regularization based on strain-gradient elasticity. We specifically consider periodic deformations of a slab subject to prescribed opening displacements on its surfaces. Based on the growth properties of the energy densities, scaling relations for the local and nonlocal energies and for the specific fracture energy are derived. We present finite-element calculations that bear out the heuristic scaling relations.     

The crack surface anomalous scaling and its connection with the size-scale effects

The size-scale effects is one of the most important research topics in solid mechanics. Several theories have been proposed in order to describe the scaling of mechanical properties in fracture mechanics of quasi-brittle materials such as concrete, rock, wood and a broad class of fibrous or particulate composites. In the last two decades they were investigated by means of several techniques, including renormalisation group theory, intermediate asymptotics, dimensional analysis, statistics of extremes among the others. One of the most successful approaches is the fractal one. It is based on the assumption of a fractal-like damage localization at the mesostructural level and on the linking of mechanical properties to the fractal dimensions of the damage domains. In particular, the fractal dimension of fracture surface an be linked to the scaling properties of toughness. On the other side, recent experimental researches have shown that fracture surfaces present an anisotropic propagation in the longitudinal and transverse directions. To describe such anisotropy, it does not appear sufficient to characterize the fracture surface by a single fractal dimension, but the anomalous scaling (Morel et al., Physical Review E 58, 6999–7005 [1998]) should be introduced. This approach has proved to be very effective in describing the R-curve behaviour (Morel et al., International Journal of Fracture 114, 307–325 [2002]). Dealing with the size-scaling effects, a scaling law for both fracture toughness and tensile strength has been recently proposed. In this work, we point out some inconsistencies of the proposed approach, suggesting a more consistent way to derive the scaling laws and a correction on the scaling exponent at the larger scales. The phenomenon of scaling in notched and un-notched structures is summarized in a unified framework and the anomalous scaling is applied to the case of unnotched specimens, showing how it captures correctly only the convexity of the scaling law in a bilogarithmic plane and not the real asymptotes, thus indicating that the anomalous scaling can not be considered as a satisfactory explanation to the size-scale effects.     

新型自复位变摩擦耗能装置理论研究与数值分析

提出一种兼具自复位、变摩擦和高耗能于一体的新型自复位变摩擦耗能装置,通过合理的构造措施,将SMA弹簧、摩擦材料和型钢集成一体,由SMA弹簧实现复位功能,变摩擦机构提供耗能作用,基于SMA力学特性和库伦摩擦理论建立该耗能装置的恢复力模型,并利用MATLAB对其力学性能进行数值分析。结果表明:所建立的恢复力模型能够较好地描述该耗能装置的力学特性,随着位移幅值的增加,其耗能能力逐渐增强,加载频率对其耗能能力影响不大,在应用中能够表现出稳定的耗能能力。     

Structural Relaxation Dynamics of ortho-Terphenyl

This paper analyzes molecular dynamicssimulation results on the small-molecule glass formerortho-terphenyl (OTP). The data can be describedwell using the coupling model of relaxation. Thedynamic susceptibility calculated from thedensity-density time correlation function is shown toapproximately conform to the scaling laws of modecoupling theory. Since the dynamic singularities ofmode coupling theory are absent in the coupling model,both approaches to high frequency structuralrelaxation can not be correct; the conformance to modecoupling theory indicates the non-uniqueness of modecoupling theory interpretation of data from fragileliquids. The non-cooperative relaxation time fordensity fluctuations in OTP is found to have the sameactivation energy as the shear viscosity in the hightemperature limit. This illustrates the relationshipbetween microscopic dynamic variables and the shorttime behavior of macroscopic properties, when theformer are analyzed according to the coupling model.     

A coefficient of restitution model for particle–surface collision of particles with a wide range of mechanical characteristics

The coefficient of restitution describes the energy dissipation resulting from particle-particle and particle–surface interactions in solid–fluid flows. The energy loss depends on the mechanical characteristics of the solid phase, therefore, to correctly predict the behavior of these systems it is necessary to use reliable coefficient values based on the properties of the particles. This paper investigated the energy dissipation in particle–surface collisions using 7 types of particles with a wide range of mechanical properties (Young's modulus between 1.38 × 10⁴ and 2.83 × 10⁹ Pa). Three empirical equations have been proposed to calculate the coefficient of restitution based on the impact velocity and the compressional wave velocity. The experimental results presented an inverse relation between the impact velocity and the coefficient of restitution. This effect was more pronounced for less elastic particles. The models presented an accurate fit to the experimental data and statistical analysis showed that the Power model presented the greater capacity to predict the coefficient of restitution from generic data. The experimental results showed the predominant effect of mechanical characteristics on the coefficient of restitution. In addition, the proposed equations are proved to be precise tools for predicting particle coefficients of restitution with a wide range of elasticity modulus at low velocities.