Multiscale modeling of oriented thermoplastic elastomers with lamellar morphology

Thermoplastic elastomers (TPEs) are block copolymers made up of “hard” (glassy or crystalline) and “soft” (rubbery) blocks that self-organize into “domain” structures at a length scale of a few tens of nanometers. Under typical processing conditions, TPEs also develop a “polydomain” structure at the micron level that is similar to that of metal polycrystals. Therefore, from a continuum point of view, TPEs may be regarded as materials with heterogeneities at two different length scales. In this work, we propose a constitutive model for highly oriented, near-single-crystal TPEs with lamellar domain morphology. Based on small-angle X-ray scattering (SAXS) and transmission electron microscopy (TEM) observations, we consider such materials to have a granular microstructure where the grains are made up of the same, perfect, lamellar structure (single crystal) with slightly different lamination directions (crystal orientations). Having identified the underlying morphology, the overall finite-deformation response of these materials is determined by means of a two-scale homogenization procedure. Interestingly, the model predictions indicate that the evolution of microstructure—especially the rotation of the layers—has a very significant, but subtle effect on the overall properties of near-single-crystal TPEs. In particular, for certain loading conditions—namely, for those with sufficiently large compressive deformations applied in the direction of the lamellae within the individual grains—the model becomes macroscopically unstable (i.e., it loses strong ellipticity). By keeping track of the evolution of the underlying microstructure, we find that such instabilities can be related to the development of “chevron” patterns.     

Equilibrium shapes of strained islands with non-zero contact angles

The equilibrium morphology of a strained island on an elastic substrate is determined. The island is assumed to partially wet the substrate (Volmer-Weber growth) and thus makes a non-zero contact angle with the surface. Both isotropic and anisotropic misfit strain are allowed. Two- and three-dimensional equilibrium island shapes are determined by using expressions for the elastic strain energy in the small-slope approximation. In this limit, the problem can be reduced to a singular integral-differential equation for the island thickness. We find that when there is a non-zero contact angle, all island shapes, for a given ratio of the elastic stress to surface energy, attain a form that is independent of the specific contact angle under an appropriate scaling. We show that for islands with non-zero contact angles, as the island volume increases, the shape approaches the geometry of a completely wetting island. But when the volume decreases, these islands approach a point while islands with a zero contact angle, approach a finite length line segment of zero volume. Multiple-hump equilibrium shapes are found. Single-humped islands are shown to have a lower chemical potential than multiple-humped islands, implying that they are the most stable. This conclusion is shown to be consistent with a stability analysis of the two-dimensional case. The effects of a tetragonal misfit strain on the three-dimensional island shape is investigated.     

Homogenization for wave propagation in periodic fibre-reinforced media with complex microstructure. I—Theory

The effective elastic properties of periodic fibre-reinforced media with complex microstructure are determined by the method of asymptotic homogenization via a novel solution to the cell problem. The solution scheme is ideally suited to materials with many fibres in the periodic cell. In this first part of the paper we discuss the theory for the most general situation—N arbitrarily anisotropic fibres within the periodic cell. For ease of exposition we then restrict attention to isotropic phases which results in a monoclinic composite material with 13 effective moduli and expressions for each of these are determined. In the second part of this paper we shall discuss results for a variety of specific microstructures.     

On the effective stress in unsaturated porous continua with double porosity

Using mixture theory we formulate the balance laws for unsaturated porous media composed of a double-porosity solid matrix infiltrated by liquid and gas. In this context, the term ‘double porosity’ pertains to the microstructural characteristic that allows the pore spaces in a continuum to be classified into two pore subspaces. We use the first law of thermodynamics to identify energy-conjugate variables and derive an expression for the ‘effective’, or constitutive, stress that is energy-conjugate to the rate of deformation of the solid matrix. The effective stress has the form , where σ is the total Cauchy stress tensor, B is the Biot coefficient, and is the mean fluid pressure weighted according to the local degrees of saturation and pore fractions. We identify other emerging energy-conjugate pairs relevant for constitutive modeling of double-porosity unsaturated continua, including the local suction versus degree of saturation pair and the pore volume fraction versus weighted pore pressure difference pair. Finally, we use the second law of thermodynamics to determine conditions for maximum plastic dissipation in the regime of inelastic deformation for the unsaturated two-porosity mixture.     

General integral equations of thermoelasticity in micromechanics of composites with imperfectly bonded interfaces

One considers a linear thermoelastic composite medium, which consists of a homogeneous matrix containing a statistically inhomogeneous random set of heterogeneities with various interface effects and subjected to essentially inhomogeneous loading by the fields of the stresses, temperature, and body forces (e.g., for a centrifugal load). The general integral equations connecting the stress and strain fields in the point being considered and the surrounding points are obtained for the random and deterministic fields of inclusions. The method is based on a centering procedure of subtraction from both sides of a new initial integral equation their statistical averages obtained without any auxiliary assumptions such as the effective field hypothesis (EFH), which is implicitly exploited in the known centering methods. The new initial integral equation is presented in a general form of perturbations introduced by the heterogeneities and taking into account both the spring-layer model and coherent imperfect one. Some particular cases, asymptotic representations, and simplifications of proposed equations as well as a model example demonstrating the essence of two-step statistical average scheme are considered. General integral equations for the doubly and triply periodical structure composites are also obtained.     

Micromechanical Analysis of the Trabecular Bone Stress State at the Interface with Metallic Biomedical Devices*

An iterative procedure for the stress analysis at interfaces between dissimilar materials is presented. The problem is specialised to the case of biomaterial interfaces with particular reference to materials which are characterised by tiny microstructures. The procedure is based on a recursive analysis of small size problems defined upon subdomains obtained by partitioning the whole structural domain. The kinematic boundary conditions are iteratively adjusted by using appropriate preconditioners. The numerical example reported in this paper shows that the procedure is effective regardless of the degree of material heterogeneity, in contrast with the results obtained by using a coarse mesh for the whole domain. The procedure seems to be a promising one for determining the structural strength of interfaces between trabecular bone and metal implants requiring accurate evaluation of stress at the scale level of the single microstructure exhibited by the bone.     

Micromechanics-based thermoelastic model for functionally graded particulate materials with particle interactions

Thermoelastic behavior of functionally graded particulate materials is investigated with a micromechanical approach. Based on a special representative volume element constructed to represent the graded microstructure of a macroscopic material point, the relation between the averaged strains of the particle and matrix phases is derived with pair-wise particle interactions, and a set of governing equations for the thermoelastic behavior of functionally graded materials is presented. The effective coefficient of thermal expansion at a material point is solved through the overall averaged strain of two phases induced by temperature change under the stress-free condition, and is shown to exhibit a weak anisotropy due to the particle interactions within the graded microstructure. When the material gradient is eliminated, the proposed model predicts the effective coefficient of thermal expansion for uniform composites as expected. If the particle interactions are disregarded, the proposed model recovers the Kerner model. The proposed semi-analytical scheme is consistent and general, and can handle any thermal loading variation. As examples, the thermal stress distributions of graded thermal barrier coatings are solved for two types of thermal loading: uniform temperature change and steady-state heat conduction in the gradation direction.     

压电压磁复合材料中正六边形孔边裂纹的反平面断裂问题

基于线性磁电弹性理论,利用Schwarz-Christoffel(CS)变换技术和Stroth公式,首次系统研究了压电压磁复合材料中含带两个不对称裂纹的正六边形孔口问题在部分渗透磁电边界条件下的解析解.当忽略磁场时,磁电非渗透裂纹和磁电渗透裂纹两种极端情况下的解析解答可退化为文献已有研究结果.数值结果揭示了正六边形孔口尺寸、裂纹长度以及力电载荷和磁载荷对能量释放率的影响规律.研究结果表明：减小孔口边长和裂纹长度可以提高材料的可靠性;机械载荷总是促进裂纹扩展;在磁电非渗透和磁电部分渗透边界条件下,负电场和负磁场会延缓裂纹的扩展,而正电场可以增强或阻碍裂纹的扩展,这取决于所施加的电场和磁场的强度以及机械载荷的水平;在磁电渗透边界条件下,电场和磁场对裂纹的扩展没有影响.     

Discrete contact mechanics of a fibrillar surface with backing layer interactions

The contact mechanics of a fibrillar micro-fabricated surface structure made of poly(dimethyl siloxane) (PDMS) is studied. The attachment and detachment of individual fibrils to and from a spherical indenter upon approach and retraction are detected as jumps in force and stiffness. A quantitative model describes the stiffness values by taking into account the deformation of the fibrils and the backing layer. The results emphasize the importance of long-range interactions in the contact mechanics of elastic materials and confirm some of the important concepts underlying the development of fibrillar adhesive materials.     

PVDF涂层建筑膜材单元结构力学性能的试验研究

使用PVDF涂层建筑膜材制成的结构,在承受外载荷情况下,力学行为非常复杂。在本文中,重点研究其单元结构在承受外载荷情况下的力学性能。首先,对PVDF涂层建筑膜材进行拉伸试验,测定其在常温和低温环境下膜的拉伸力学性能参数。然后,以制成的三角框架结构膜单元为对象,在常温条件下,从有限元分析和实际加载试验两方面计算得出结构单元在均布载荷下的位移、应变和应力分布。最后,对其进行强度验证,得出采用膜单元构建大型建筑是安全的结论。试验方法和结果可以应用于膜建筑结构的设计。     

The stability in neural networks with interneuronal transmission delays

1.IntroductionInthispaper,westudythefollowingmodelofaneuralwithnunits:inwhichfi(t)correspondstothemembranepotentialofthei-thunitattimet;h(xj)denotestheconversionofthemembranepotentialofthe.l-thunitsintoitsfiringrate:coildellotesthestrengthofthej-thunit;accorrespondStothetransmissiondelayalongtheaxonofthe.j-thunit;theConstantpid,enotestheexternalbiasorclampedinputfi-omoutsidethenetworktothei-thunit:hirepresentstheratewithwhichtheI-thLlnltwillresetitspotentialtotherestingstateinisolationwhendis…     

Boussinesq–Flamant problem in gradient elasticity with surface energy

The strain gradient elasticity theory with surface energy is applied to Boussinesq–Flamant problem. The solution for the vertical displacements at the surface of half space due to the surface normal line load is presented. The theory includes both volumetric and surface energy terms. Boussinesq–Flamant problem in the strain gradient elasticity is solved by means of Fourier transform. The results obtained show that the vertical displacements of half space in the gradient elasticity are some different from that in the classical elasticity and the effects of the strain gradient parameters (material characteristic lengths) on the vertical displacements do exist.     

采用分布式结构技术的组合仪表设计

阐述了采用分布式结构技术设计的组合仪表的组成、功能和原理方案，并对系统功能、信息交换、可靠性等特点进行了分析。该方案具有调试方便，增加和去掉或替换部分设备对全系统影响最小，每一功能部分不受其它功能故障的影响，对关键功能可提供备份的灵活性等优点。     

考虑附加结构的结构动力修改

本文分析了实际工程中可能出现的一些情况,提出了一种运用Rayleigh-Rjtz技术,结合模态综合方法的结构动力修改方案。文中采用相容位移函数代替结构主模态,并给出了相应的结构模态变换式和系统方程式。     

STABILITY ANALYSIS OF HOPFIELD NEURAL NETWORKS WITH TIME DELAY

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GLOBAL EXPONENTIAL STABILITY OF HOPFIELD NEURAL NETWORKS WITH VARIABLE DELAYS AND IMPULSIVE EFFECTS

A class of Hopfield neural network with time-varying delays and impulsive effects is concerned. By applying the piecewise continuous vector Lyapunov function some sufficient conditions were obtained to ensure the global exponential stability of impulsive delay neural networks. An example and its simulation are given to illustrate the effectiveness of the results.     

Synchronization in delayed map lattices with scale-free interactions

In this paper, we study synchronization of delayed map lattices with scale-free interactions. By numerical simulations and theoretical analysis, we find that time delays influence the network synchronization but the heterogeneity seems to have little effect on network synchronization, yet no synchronization happens with the homogeneously topological structures.     

Robust stability of a class of neural networks with time delays

A stability analysis of the equilibrium position for a given class of Hopfield neural networks with time delays is presented. The robustness of the equilibrium stability with respect to variations in the time delays, system parameters, and interconnection matrix is analyzed. Three approaches are presented which account in various ways for stability of the equilibrium with respect to these perturbations.Work conducted while visiting the University of Bremen, supported by the Deutscheforschungsgemeinschaft.