A multiscale analysis of the mechanical behavior of a thermo-oxidized c/epoxy lamina

The mechanical behavior of carbon-fiber-reinforced polymer matrix composites having undergone a thermo-oxidation process is studied. The purpose is to perform a multiscale analysis of the consequences of oxidation on the intrinsic mechanical properties of the external composite ply and on the internal mechanical states experienced by the structure under mechanical loads. The effective mechanical properties of oxidized composite plies are determined according to the Eshelby–Kr?ner self-consistent homogenization procedure, depending on evolution of the oxidation process. The results obtained are compared with estimates found by the finite-element method. The macroscopic mechanical states are calculated for a unidirectional composite and laminates. The macroscopic stresses in each ply of the structure are determined by the classical lamination theory and the finite-element method, whereas the local stresses in the carbon fiber and epoxy matrix are calculated by using an analytical stress concentration relation.     

机械故障模糊诊断中模糊矩阵的可视化处理与分析

通过对机械故障诊断中的模糊矩阵及采用不同数学模型运算后的结果进行可视化处理,得到二维图谱和三维图谱,使故障与征兆之间的关系更加明确     

Algorithm for computing the mechanical impedances of reinforcing ribs of various shapes

The problem is considered of finding the mechanical impedances of reinforcing ribs of various shapes. The rib is modeled by a narrow plate. The thickness of the rib (the thickness of the plate from which the rib is made) is thus considered small as compared with the height of the rib (the width of the plate). The height of the rib h is assumed small as compared with the lengths of waves propagating in the material of the plate. One of the edges of the rib is assumed to be free of stresses. The matrix giving the relation between the stresses and the velocities of displacements on the second (loaded) edge is called the impedance matrix. An algorithm is proposed for computing the coefficients of the expansion of the impedance matrix in a Taylor series in powers of h. The method is illustrated by the computation of the mechanical impedances of rectilinear and annular reinforcing ribs.     

细胞骨架与细胞外基质的力学建模与分析

细胞和生物组织需要适应人体内复杂的力学生物学环境,一方面要被动地承受外部环境中的机械力,另一方面在组织生长、修复等生理过程中要积极主动地产生机械力调整自身的结构和形态.细胞和生物组织的力学性质主要由细胞骨架和细胞外基质决定,它们在微观上都是生物聚合物交联形成的复杂的、各向异性的三维网络结构.这方面早期的力学研究主要集中在通过各种网络模型,理解其普遍存在的非线性响应和硬化行为.近年来随着实验方法、理论建模和计算机模拟技术的大幅进步,这些生命介质的力学性质及其潜在的力学机理得到了更深入的理解.该文回顾了近些年细胞骨架和细胞外基质研究方面取得的部分进展,主要侧重动态交联属性、生物聚合物力学化学耦合赋予的主动材料属性、交联网络塑性和断裂,以及力学训练引发的自适应网络重构.发展细胞骨架与细胞外基质的力学模型与计算方法,分析该类生命介质的复杂力学行为,理解这些力学行为的潜在机制,可以加深我们对细胞和组织的力学生物学认识,并为人造生物材料和细胞组织工程提供基础和参考.     

Gyroscopic stabilization of nonconservative systems

The problem is considered of the stabilization of a mechanical system having only nonconservative positional forces by adding gyroscopic forces. The gyroscopic stabilization is proved to be always realizable in the case of a degenerate matrix of nonconservative forces and even number of coordinates. If the matrix of nonconservative forces is nonsingular then a possibility of the gyroscopic stabilization is established for all systems whose number of coordinates is divisible by four. For a nonautonomous systemwith nonconservative positional forces and dissipative forces with complete dissipation, some sufficient conditions are obtained for stabilization up to the exponential stability by addition of gyroscopic forces.     

Design of planar articulated mechanisms using branch and bound

This paper considers an optimization model and a solution method for the design of two-dimensional mechanical mechanisms. The mechanism design problem is modeled as a nonconvex mixed integer program which allows the optimal topology and geometry of the mechanism to be determined simultaneously. The underlying mechanical analysis model is based on a truss representation allowing for large displacements. For mechanisms undergoing large displacements elastic stability is of major concern. We derive conditions, modeled by nonlinear matrix inequalities, which guarantee that a stable equilibrium is found and that buckling is prevented. The feasible set of the design problem is described by nonlinear differentiable and non-differentiable constraints as well as nonlinear matrix inequalities.To solve the mechanism design problem a branch and bound method based on convex relaxations is developed. To guarantee convergence of the method, two different types of convex relaxations are derived. The relaxations are strengthened by adding valid inequalities to the feasible set and by solving bound contraction sub-problems. Encouraging computational results indicate that the branch and bound method can reliably solve mechanism design problems of realistic size to global optimality.     

The combinatorial complexity of masterkeying

We consider the combinatorial complexity of the algorithmic design of mechanical master key locking systems. Such locking systems use pin tumblers and profile elements (wards) to realize the functional dependencies given by a key/cylinder matrix. We prove that even very restricted versions of the masterkeying problem are NP-complete. We show that the general masterkeying problem can be defined by an integer linear program whose number of variables and restrictions is polynomial in the size of the key/cylinder matrix and the size of the locking system. Heuristic solutions are also discussed.     

Penetration of a wetting front in a porous medium interacting with the flow

We analyse a model for incompressible flows through a porous medium, characterized by a mechanical interaction between the flow and the solid matrix and by the presence of a wetting front penetrating in a dry medium. Received February 19, 1996     

Measuring the stresses in fibers of a loaded composite material by the method of infrared spectroscopy

Conclusions 1. Actual stresses in reinforcement fibers of a loaded composite have been measured by infrared spectroscopy.2. It has been shown that the plain rule of mixtures, not accounting for changes in mechanical properties of the matrix during processing of a composite, does not apply to a hot molded polyethylene-polypropylene composite.3. It is suggested that around the reinforcement fibers there exists an ordered layer of the matrix material capable of carrying a heavy load. A method is proposed, furthermore, for calculating the mechanical characteristics of the composite with such a layer. The volume fraction and the thickness of this hardened layer have been estimated from experimental data.Paper presented at the Third All-Union Conference on Polymer Mechanics in Riga, 1976.A. F. Ioffe Physicotechnical Institute, Academy of Sciences of the USSR, Leningrad. Translated from Mekhanika Polimerov, No. 5, pp. 832–837, September–October, 1977.     

Modeling of the mechanical characteristics of chaotically reinforced GRP

Experimental results on the mechanical properties under tension and compression of composites based on a phenol-formaldehyde binder reinforced with short glass fibers are reported. Unidirectional structures, in which the reinforcing elements had different orientations with respect to the external load, were studied, as well as chaotically reinforced composites. In addition, the mechanical properties of the polymer matrix and of the reinforcing elements as well as the bond strength between them were also determined. An analysis of the results obtained in the tension experiments is presented, based on a model in which the frictional mechanism of interaction between the polymer matrix and the reinforcing elements is utilized. The quantitative relationships deduced give results agreeing with those obtained experimentally.     

Main features of the viscoelastic behavior of carbon fiber-reinforced plastics with a polymer matrix: Model study and calculation

It was shown that below the glass transition temperature of the amorphous matrix, its viscoelastic behavior in a composite is described by the Halpin-Tsao equation for composites, as modified by Nielsen, with a sufficient degree of reliability. However, when the matrix passes into the highly elastic and especially the viscous flow state characteristics of thermoplastic matrices, a significant difference is observed in the experimental and calculated temperature curves of the elastic and matrix loss moduli. It is possible to hypothesize that this is due to hindrance of plastic deformation of the matrix in the composite not accounted for in the Halpin-Tsao model. Using simple models of the one-sided coating and sandwich type, it was shown that consideration of the stress state of a matrix in contact with a rigid coating can result in the same kind of effects as in a composite, namely, apparent toughening of the matrix in the highly elastic region and shifting of the maximum of the mechanical loss modulus to the high-temperature region.Institute of Macromolecular Compounds. Russian Academy of Sciences, St. Petersburg, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 33, No. 5, 690–703, September–October, 1997.     

Change in the Surface Properties of Carbon Fibers as a Result of Plasmochemical Modification

The influence of plasmochemical modification of carbon fibers on their surface properties and compatibility with the PTFE matrix is investigated. It is shown that the thin PTFE coating formed on the carbon fiber surface improves the wetting of the fibers by PTFE. As a result, the mechanical characteristics of PTFE-based composites are improved.     

异常情况时的Liapunov-Kozlov法

Kozlov将Liapunov第一方法推广到非线性力学系统,用来研究保守力和耗散力场中,运动力学系统平衡位置的不稳定性.在平衡位置分析惯性张量的异常,或者Rayleigh耗散函数系数矩阵的异常.在稳定性分析中,实际上不可能应用Liapunov逼近法,因为平衡位置的存在条件,和运动微分方程解的唯一性条件,均无法得到满足.Kozlov的广义Liapunov第一方法,不仅适用上面提及的条件,此外,还知道同样的代数表达式得到满足.给出了3个关于平衡位置的不稳定性定理.用一个例子,举例说明了得到的结果.     

Influence of fiber structure modification on the mechanical properties of flax fiber-epoxy composites

The mechanical characteristics of flax fibers were optimized by using the NaOH treatment process to improve the properties of composite materials. Shrinkage of the fibers during this treatment had a significant effect on the structure and, as a result, on the mechanical properties of the fibers and the composites based on them. Due to the higher mechanical strength and stiffness of flax fibers after NaOH treatment under isometric conditions, the strength and stiffness of composites in general increase. Further, NaOH treatment leads to a rougher surface morphology, as shown, e.g., for jute fibers, compared with the surface of untreated fibers without improved fiber/matrix adhesion.     

Extension of quantum information by using entropy of deterministic functions

The concept of entropy of random variables first defined by Shannon has been generalized later in various ways by mathematicians who so obtained new measures of uncertainty, again for random variables. Recently, the author suggested another extension which provides a meaningful definition for the entropy of deterministic functions, both in the sense of Shannon and of Renyi. These measures of uncertainty are different from those which are utilized by physicists in the study of chaotic dynamics, like the Kolmogorov entropy for instance.

The aim of this paper is to go a step further, and to derive measures of uncertainty for operators, by using exactly the same rationale. After a short background on the entropies of deterministic functions, one obtains successively the entropy of a constant square matrix operator, the entropy of a varying square matrix operator, the entropy of the kernel of an integral transformation, and the entropy of differential operators defined by square matrices.

Then one carefully exhibits the relation which exists between these results and the quantum mechanical entropy first introduced by Von Neumann, and one so obtains a new generalized quantum mechanical entropy which applies to matrics which are not necessarily density matrices. Finally, some illustrative examples for future applications are outlined.     

Modeling of fiber-reinforced PMMA at different scales

This paper deals with the modeling of fiber-reinforced PMMA. Focus is on the macroscopic mechanical response with emphasis on the fracture properties such as the ultimate strength and the fracture energy. In order to capture the macroscopic mechanical response of PMMA, a finite element formulation is presented. While the elastic response of the fibres and that of the surrounding matrix are modelled in standard manner, i.e., by standard bulk material models, the relevant failure modes such as cracking of the fibres are accounted for by means of the so-called Strong Discontinuity Approach (SDA). Since the fibres are relatively small, their fracture mechanical properties crucially depend on their geometry, i.e., they show a pronounced size effect. Based on numerical analyses of fibres with different geometries, the aforementioned size effect is naturally incorporated into the formulation [1]. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

桥联理论研究的最新进展

欲根据组分材料——纤维和基体性能参数预报复合材料的强度,必须解决3个方面的问题.首先,必须准确计算出纤维和基体中的内应力;其次,必须基于这些内应力,建立起复合材料的有效破坏判据,即细观力学强度理论;最后,必须根据独立测试的基体性能,准确定义其现场强度输入数据,因为后者无法测量.复合材料强度预报之所以困难,在于所涉及的每一个问题都极具挑战.由黄争鸣创建和发展的桥联理论,系统给出了这3方面问题的有效解决方案.该文简要介绍这些解决方案,包括桥联理论的最新进展及有待进一步研究的课题.     

Mechanical properties of a polyamide 6-reinforced PTFE composite

Polytetrafluoroethylene (PTFE) blends with polyamide 6 (PA6) in various ratios were prepared in a corotating twin-screw extruder, where PTFE acted as a polymer matrix and PA6 as a disperse phase, and the morphology and mechanical properties of the blends were investigated by using SEM. With increasing content of PA6 in the blends, their flexural properties improved. The interfacial adhesion promoted the creation of an interphase between the PTFE and PA6 and led to improved mechanical properties of the material. The mechanical properties of the blends were optimum at 30 vol.% PA6. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 45, No. 3, pp. 419-426, May-June, 2009.