Constitutive equations in Cosserat elasticity

Summary A new theory for the constitutive equations in Cosserat elasticity is proposed. It is based on the assumption that the rotation vector depending on the displacement vector should be coupled with a rotation vector independent of the displacement vector. This eliminates the indeterminancies in stress and couple-stress encountered earlier.     

Gradients in polymeric materials

In this paper we consider the structure and properties of polymeric materials possessing spatial gradients as well as potential applications of such materials.These gradients may be generated by varying the chemical nature of the monomers, the molecular constitution of the polymers and the supramolecular structure or morphology of the polymers. Gradients in each of these categories are possible for single-phase as well as heterophase systems. Such gradients are associated with gradients in properties.The properties considered are chemical, mechanical, biomedical and transport properties. Structural gradients in the polymeric system may lead to a desired gradient in a single property, or to a combination of more than one property which may assume optimum values in different regions of the material. In the latter case, one of the properties is frequently related to mechanical integrity.Possible applications of gradient polymeric systems include platic gasoline tanks, biomedical implants, and damping materials for a wide frequency range.     

Constitutive equations of creep under changing multiaxial stresses for materials with different behavior in tension and compression

A theory of creep that describes kinematic hardening of polycrystalline materials with different behavior in tension and compression is presented. A structure of the equivalent effective stress in the equation for creep deformation as well as structures of the equivalent effective stress in the describing creep hardening and of equivalent back stress in the describing thermal softening are based on three independent material characteristics obtained from uniaxial tension tests, uniaxial compression tests, and pure torsion tests for different values of constant stress at constant temperatures. A satisfactory agreement is obtained between the theoretical results and the experimental data of the creep under multiaxial loading with constant stresses for isothermal processes as well as under uniaxial nonproportional and multiaxial nonproportional loadings for both isothermal and nonisothermal conditions. Materialgleichungen für das Kriechen unter veräderlichen mehrachsigen Spannungszuständen für Materialien mit unterschiedlichem Verhalten unter Zug- und Druckbelastung Zusammenfassung Eine Kriechtheorie zur Beschreibung der kinematischen Verfestigung polykristalliner Materialien mit unterschiedlichem Verhalten unter Zug- und Druckbelastung wird vorgestellt. Die Gleichungen für die Kriechverformung und die Kriechverfestigung werden in Abhängigkeit von der äquivalenten effektiven Spannung formuliert. Die Gleichung zur Beschreibung der thermischen Erweichung hängt von einer äquivalenten Rückspannung ab. Alle Gleichungen basieren auf drei unabhängigen Materialeigenschaften, die aus einachsigen Zug-, einachsigen Druck- sowie reinen Torsionsversuchen für unterschiedliche konstante Spannungen und konstante Temperaturen bestimmt werden können. Es wird eine befriedigende Übereinstimmung dieser Theorie mit experimentellen Daten sowohl für Kriechen unter mehrachsiger Beanspruchung mit konstanten Spannungen in isothermen Prozessen als auch für einachsige und mehrachsig-nichtproportionale Belastungen unter isothermen und nichtisothermen Bedingungen gefunden.The research described in this paper is sponsored by the Alexander von Humboldt Foundation. The first writer wishes to thank Dr. Oleg Artyushenko, Ms. Oksana Kovalenko and Mrs. Elena Novichenko for helpful advises and fruitful discussions.     

Constitutive relationships for anisotropic viscous materials

Constitutive relationships for anisotropic materials are considered to describe the viscous flow of fiber-reinforced, thermoplastic composites during forming. The fully anisotropic and the orthotropic cases are first presented. The special case of a transversely isotropic viscous material, which is of particular interest to the deformation of assemblies of oriented fibers suspended in a viscous fluid, is then investigated and the correspondence between two approaches found in the literature on the subject is established.     

高分子吸油材料的研究进展

对吸油树脂的结构、吸油机理及性能评价进行了简单介绍。着重对聚合所用单体、交联情况、聚合条件等方面对吸油树脂的研究进展进行了全面的综述,并对最新的重要研究成果进行了阐述。     

高分子辐射材料的研究进展

介绍了高分子辐射材料的开发研究现状,重点论述了高分子防辐射屏蔽材料、辐射聚 合材料、辐射交联材料和辐射接枝材料的研究发展。     

Constitutive equations of symmetrical triple layer piezoelectric benders

Piezoelectric triple layer benders, with a structure of two piezoelectric top and bottom layers sandwiched by a non-piezoelectric elastic central layer, are one of the most commonly used piezoelectric devices. In this paper, we present the derivation of the constitutive equations of a symmetrical triple layer piezoelectric bender under different excitation conditions. The constitutive equations are presented by a 4x4 matrix with an external moment M, an external tip force F, a uniform load p, and an applied electric voltage V as the extensive parameters, with the generated tip angular deflection (slope) alpha, tip deflection delta, volume displacement v, and electric charge Q as the internal parameters. Further analysis on the electromechanical behavior of the triple layer piezoelectric bender can be made on the constitutive equations.     

聚合物基纳米复合材料的研究进展

对聚合物基纳米复合材料的研究进展进行了介绍,报道了有关聚合物基纳米复合材料制备方法的研究进展情况,并分别对聚合物/粘土纳米复合材料、环氧树脂基纳米复合材料、聚酯纳米复合材料、聚合物/碳纳米管纳米复合材料的研究发展情况给予了评述,同时对每种体系特点和存在的问题进行了论述,最后着重指出纳米复合材料制备方法、应用以及开发新的聚合物基纳米复合体系是今后的主要研究方向.     

Constitutive potentials for dilutely voided nonlinear materials

Constitutive relations are derived for an incompressible, isotropic power-law matrix material containing a dilute concentration of spherical voids. The derivation is made for a nonlinearly viscous material used to characterize steady creep. However, the theory applies equally well to small strain nonlinear elasticity (deformation theory), and an extension to a rate-independent flow theory is also discussed. The starting point and key element in the formulation is the potential function for an isolated spherical void in an infinite block of power-law material. Approximate, but accurate, representations for this potential function are given. The overall constitutive relation governing the behavior of the dilutely voided solid is obtained simply and directly using the void potential. An assessment of the range of validity of the dilute concentration results is obtained using numerical solutions to the problem of a spherical void centered in a sphere of finite radius made of the power-law material. The potential function is also given for a dilute concentration of aligned penny-shaped cracks in the same power-law material.     

导热高分子材料研究进展

讨论了提高聚合物导热性能的途径－合成高导热系数的结构聚合物,用高导热无机填料对聚合物进行填充复合。综述了导热高分子材料的研究成果：聚合物导热的基本概念和影响其导热性能的因素及导热系数的预测理论;聚合物基导热复合材料的选材、复合技术及其应用。指出了导热高分子材料的研究方向－－纳米导热填料的研究和开发;聚合物树脂基体的物理化学改性;聚合物基体与导热填料复合新技术的研究和开发;复合材料导热模型的建立、导热机理（特别是聚合物基体与导热填料界面的结构与性能对材料导热性能的影响）及导热通路的形成等;探索高导热本体聚合物材料的制备方法和途径等。对导热高分子材料的研究和开发有重要意义。     

Dynamic overstresses in fibrous polymeric materials

We have considered the problem of the dynamic stress redistribution in fibrous materials brought about by the failure of a single element. Our model consists of a number of aligned adjacent chains of harmonically coupled masses. Neighboring masses on adjacent chains are also coupled by shear-carrying springs. Depending upon the scope and assignment of parameters, the model might apply to aligned polymer chains in a crystal or amorphous environment, to filaments in a fiber, or to a fibrous composite material. At time t = 0, an intra-chain spring is broken and the motion of the masses in the local environment is followed by molecular dynamics. The dynamic loads carried by bonds in chains neighboring the defect oscillate with decreasing amplitude, ultimately reaching asymptotic values that can also be calculated exactly by harmonic analysis. We find that the maximum of the excess load carried by a spring in a chain adjacent to a defect is about two times the asymptotic value for two-dimensional arrays of chains and somewhat larger for three-dimensional arrays. The dependence of these quantities on the magnitude of the shear carrying spring constant is explored. These results have implications for a number of theoretical approaches to fiber and composite strength which use load-sharing models based on asymptotic values.     

Constitutive equations for the nonlinear elastic response of rubbers

Summary A constitutive model is derived for the elastic behavior of rubbers at three-dimensional deformations with finite strains. An elastomer is thought of as an incompressible network of flexible chains bridged by permanent junctions that move affinely with the bulk medium. The constraints imposed by surrounding macromolecules on configurations of an individual chain are introduced by combining the Flory–Erman and Erman–Monnerie approaches. To describe inter-chain interactions in a tractable way, the conventional picture of a tube where a chain is confined is replaced by geometrical restrictions on the positions of its ends and center of mass. The constraints on the chain ends are formulated within the traditional Flory concept, whereas those on the position of center of mass are described following the Ronca–Allegra scenario. Stress–strain relations for a network of constrained chains are derived by using the laws of thermodynamics. The constitutive equations involve four adjustable parameters with transparent physical meaning. The material constants are found by fitting experimental data on elastomers at uniaxial and equi-biaxial tensions and pure shear. It is demonstrated that (i) the model provides an acceptable prediction of stresses in a test with one deformation mode, when its parameters are found by matching observations in an experiment with another mode, and (ii) material constants are affected by chemical composition of elastomers in a physically plausible way.     

Nanostructuring polymeric materials by templating strategies

This contribution summarizes efforts in designing, assembling/synthesizing, and structurally and functionally characterizing nanostructured materials using anodized aluminum oxide (AAO) as a thin-film template. Optical waveguide spectroscopy, using a nanoporous template as the guiding structure, is a particularly powerful analytical tool. The layer-by-layer approach for the fabrication of multilayer assemblies is shown to allow the fabrication of nanotube arrays. In addition to using dendrimers as building blocks, semiconducting nanomaterial (e.g., quantum dot) hybrid architectures with very interesting photophysical properties can be assembled. These can be employed, for example, in biosensing applications. Other strategies for using the AAO layers as templates include the growth of polymeric nanorod arrays from different functional monomers, which, after the dissolution of the template, are still able to guide light. This opens up novel concepts for integrated optics platforms with nanostructured materials.     

Fatigue crack propagation in polymeric materials

In order to gain a better understanding of matrix-controlled fatigue failure processes in non-metallic materials a series of fatigue tests were performed on several different polymer materials representing different classes of mechanical response. Fatigue crack propagation rates between 5×10^–6 in. cycle^–1 (127 nm cycle^–1) and 4×10^–4 in. cycle^–1 (10 300 nm cycle^–1) were measured in nylon, polycarbonate, ABS resin, low-density polyethylene and polymethyl methacrylate. A strong correlation was found between the fatigue crack propagation rate and the stress intensity factor range prevailing at the advancing crack tip. Whereas metals exhibit comparable fatigue growth rates for a given stress intensity range when normalised with respect to their static elastic modulus, the polymer materials exhibited a 1300-fold difference in crack growth rate for a given normalised stress intensity range. This observation dramatically illustrates the importance of understanding molecular motion and energy dissipation processes in polymer materials as related to their chemistry and architecture. The relative behaviour of the different polymer materials could be generally correlated with their reported damping characteristics.     

Constitutive equation for a class of non-simple elastic materials

Summary Initial yield is the upper limit of the purely elastic deformation behaviour of an elasticplastic solid. Thus the choice of the constitutive equation describing the purely elastic deformation behaviour determines the initial yield function. The constitutive equation of a simple elastic material is only compatible with von Mises yield criterion, a conclusion which applies also to the classical infinitesimal theory. A more general form of constitutive equation for an elastic material is formulated by way of the concept of a stress loading function, the proposed constitutive equation being quadratic in the stress. The two loading coefficients associated with the stress loading function are assumed to be deriveable from a generalised isotropic yield criterion which is now assumed to hold over the entire range of deformation, and in this context is referred to as the stress intensity function. The proposed constitutive equation has the same representation in terms of the left Cauchy-Green deformation tensor as that for a simple elastic material. Using the Cayley-Hamilton theorem, this representation is rearranged and expressed in terms of a measure of finite strain which is defined to be one quarter of the difference between the left Cauchy-Green deformation tensor and its inverse. In this way the strain properties of the proposed constitutive equation are formulated by way of the concept of a strain response function. The three response coefficients associated with the strain response function are assumed to be deriveable from a generalised, isotropic, strain intensity function. The predictions of the proposed constitutive equation are considered in the context of the combined stressing of a thin sheet of incompressible material. In this way, it is shown that the proposed constitutive equation is not limited in the same way as the constitutive equation of a simple elastic material.     

Constitutive equations for amended non-Gaussian network models of rubber elasticity

New constitutive equations based on an amended form of the Kuhn–Grün probability distribution function due to Jernigan and Flory are derived from the standard James–Guth (JG) 3-chain and Arruda–Boyce (AB) 8-chain non-Gaussian molecular network models. The kinematics describing the stretch of a 1-chain model in an affine deformation shows that the relative stretch of a single molecular chain initially oriented along the diagonal of a cube is determined by the first principal invariant of the Cauchy–Green deformation tensor. The Kuhn–Grün probability distribution for a randomly oriented chain and its more general amended form due to Wang and Guth, are functions of only the relative chain stretch. Hence, any non-Gaussian network model for which the configurational entropy of all chains may be uniform is characterized by an elastic response function that depends on only the first principal invariant of the Cauchy–Green deformation tensor. Both the regular and amended AB 8-chain models are characterized by specific response functions in this class; the regular and amended JG 3-chain models, however, are not. An amended form of the phenomenological composite 3-chain/8-chain model suggested by Wu and van der Giessen is introduced. Analytical relations for several kinds of homogeneous deformations of the standard and amended models are compared with a variety of experimental data by others. It is found that results for the amended 3-chain and 8-chain models do not vary significantly from results for the corresponding regular models. The composite model, on the other hand, shows excellent overall agreement with the diverse data, including equibiaxial deformations for which other models show greater variance; but it offers no improvement in comparison with data for plane strain compression. Some remarks relating the chain parameters of the 3-chain and 8-chain network models, and the limiting chain and continuum stretches for these models are discussed in an appendix.