Some Remarks on Equivalence of Moduli of Smoothness

The present paper investigates polynomials for which the inverse inequality for moduli of smoothness holds. The technique for approach is different from the previous works for splines and is elegantly organized.     

Upper Estimates in Direct Inequalities for Bernstein-Type Operators

We obtain explicit upper estimates in direct inequalities with respect to the usual sup-norm distance for Bernstein-type operators. Our approach combines analytical and probabilistic techniques based on representations of the operators in terms of stochastic processes. We illustrate our results by considering some classical families of operators, such as Weierstrass, Szàsz, and Bernstein operators.     

Effect of the Rounding Radius of Supports on the Accuracy of Determining the Interlayer Shear Modulus of Reinforced Plastics from Short-Beam Bending Tests

The accuracy of determining the elastic constants of reinforced plastics is estimated based on bending tests of short beams using the results of a numerical experiment with known elastic constants of the specimen material. Several combination variants for the initial values of the shear modulus and support radius are considered. It is shown that the calculation error of the shear modulus is considerably higher than that of the elastic modulus A decrease in the shear modulus increases the accuracy of its determination. The radius of supports affects this accuracy insignificantly.     

Cellular solid behaviour of liquid crystal colloids 2. Mechanical properties

This paper presents the results of a rheological study of thermotropic nematic colloids aggregated into cellular structures. Small sterically stabilised PMMA particles dispersed in a liquid crystal matrix densely pack on cell interfaces, but reversibly mix with the matrix when the system is heated above . We obtain a remarkably high elastic modulus, , which is a nearly linear function of particle concentration. A characteristic yield stress is required to disrupt the continuity of cellular structure and liquify the response. The colloid aggregation in a “poor nematic” MBBA has the same cellular morphology as in the “good nematic” 5CB, but the elastic strength is at least an order of magnitude lower. These findings are supported by theoretical arguments based on the high surface tension interfaces of a foam-like cellular system, taking into account the local melting of nematic liquid and the depletion locking of packed particles on interfaces. Received 13 March 2000 and Received in final form 6 June 2000     

Tensile modulus of polymer/CNT nanocomposites by effective volume fraction of nanoparticles as a function of CNT properties in the network

In this article, the effects of filler network and interphase between polymer matrix and nanoparticles on the tensile modulus of polymer/carbon nanotubes (CNT) nanocomposites are assumed by the effective volume fraction of nanoparticles. By this approach, the Takayanagi model is developed for polymer/CNT nanocomposites above percolation threshold. Also, the effective factors for filler network including the number (N ), aspect ratio (α ) and percolation threshold (? _p ) of CNT are correlated to three main parameters. The developed model is evaluated for some reported samples from previous papers, and the influences of main parameters on the modulus are examined. The acceptable predictability of the developed model for modulus of nanocomposites is illustrated by experimental results. The “α ” and “N ” parameters play positive roles in the modulus, while an inverse relation is observed between the modulus and the percolation threshold. The reasonable effects of these parameters on the tensile modulus of polymer/CNT nanocomposites are also discussed. Copyright © 2017 John Wiley & Sons, Ltd.     

Orthotropic elastic behaviors and yield strength of fused deposition modeling materials: Theory and experiments

This work is devoted to study the mechanical behaviors of polylactic acid (PLA) materials from additive manufacturing, and an orthotropic model is established to predict the mechanical properties under arbitrary printing orientation. Firstly, the morphology of PLA material is analyzed by using scanning electron microscopy, from which the orthotropic behavior of PLA material is obtained. Three printing planes are adopted, and on each printing plane different printing angles may be selected. The mechanical parameters, including Young's modulus, yielding stress, and Poisson's ratio, for material under different printing directions are determined via quasi-static experiments. Secondly, the orthotropic constitutive model of PLA materials under different printing angles is thus obtained, and the prediction method of orthotropic mechanical properties is built based on the coordinate transformation matrix, where the orthotropic coordinate transformation matrix is acquired by attitude angles (i.e., Euler angle, the rotation angle of the local coordinate system relative to the global coordinate system). Finally, the theoretical prediction method was verified, and high-quality printing methods were recommended. In addition, the obtained results of the model show that: for PLA material, the orthotropic hypothesis model is superior to the transverse isotropic hypothesis one. This present method is not only suitable for predicting the constitutive model of printed specimens in any direction but also for other materials of fused deposition modeling.     

A Flexible Organic Single Crystal with Plastic-Twisting and Elastic-Bending Capabilities and Polarization-Rotation Function

Flexible organic single crystals capable of plastic or elastic deformations have a variety of potential applications. Although the integration of plasticity and elasticity in a crystal is theoretically possible and it may cause rich and complex deformations which are highly demanded for potential applications, the integration is hard to realize in practice. Here, we show that through utilizing different modes of external forces for influencing molecular packing in different crystallographic directions, plastic helical twisting and elastic bending can both be achieved for a crystal, and they can even be realized simultaneously. Detailed crystallographic analyses and contrast experiments disclose the mechanisms behind these two kinds of distinct deformations and their mutual compatibility. Based on the plastically twistable nature of the crystal, a new application field of flexible organic single crystals, namely polarization rotators, is successfully opened up.     

用环形剪切方法分析环氧树脂的固化过程

应用动态粘弹谱仪的环形剪切方法,在恒定的温度条件下,对环氧树脂的固化潜伏期、凝胶化时间和固化过程进行了分析测定.根据计算机处理的数据绘出样品粘度和剪切模量随时间变化的关系谱图,为研究环氧树脂的固化全过程提供了一种有效的表征方法.     

Hydrogen bond-reinforced double-network hydrogels with ultrahigh elastic modulus and shape memory property

Development of tough hydrogels has greatly expanded their applications as load-bearing materials. However, the elastic modulus of tough hydrogels is usually lower than 1 MPa. It remains a challenge to design tough hydrogels with high modulus. We report here a series of tough double-network (DN) hydrogels with ultrahigh elastic modulus (up to 200 MPa) by forming robust hydrogen bonds between the first poly(acrylic acid) network and the second poly(N-isopropyl acrylamide) network. The dense cooperative hydrogen bonds greatly reduce the segmental mobility and thus improve the rigidity of gel matrix. Owing to the dynamic nature of hydrogen bonds, the modulus of hydrogels is strongly influenced by temperature and pH, affording the gels shape memory property. The strategy by forming robust noncovalent bonds between interpenetrating networks should be applicable to other systems for designing tough and versatile hydrogels with diverse promising applications. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2018 , 56, 1281–1286     

Orthogonal Dual‐Triggered Shape‐Memory DNA‐Based Hydrogels

DNA‐based shape‐memory hydrogels revealing switchable shape recovery in the presence of two orthogonal triggers are described. In one system, a shaped DNA/acrylamide hydrogel is stabilized by duplex nucleic acids and pH‐responsive cytosine‐rich, i‐motif, bridges. Separation of the i‐motif bridges at pH 7.4 transforms the hydrogel into a quasi‐liquid, shapeless state, that includes the duplex bridges as permanent shape‐memory elements. Subjecting the quasi‐liquid state to pH 5.0 or Ag⁺ ions recovers the hydrogel shape, due to the stabilization of the hydrogel by i‐motif or C‐Ag⁺‐C bridged i‐motif. The cysteamine‐induced transformation of the duplex/C‐Ag⁺‐C bridged i‐motif hydrogel into a quasi‐liquid shapeless state results in the recovery of the shaped hydrogel in the presence of H⁺ or Ag⁺ ions as triggers. In a second system, a shaped DNA/acrylamide hydrogel is generated by DNA duplexes and bridging Pb²⁺ or Sr²⁺ ions‐stabilized G‐quadruplex subunits. Subjecting the shaped hydrogel to the DOTA or KP ligands eliminates the Pb²⁺ or Sr²⁺ ions from the respective hydrogels, leading to shapeless, memory‐containing, quasi‐liquid states that restore the original shapes with Pb²⁺ or Sr²⁺ ions.