Existence of strong minimizers for the Griffith static fracture model in dimension two

We consider the Griffith fracture model in two spatial dimensions, and prove existence of strong minimizers, with closed jump set and continuously differentiable deformation fields. One key ingredient, which is the object of the present paper, is a generalization to the vectorial situation of the decay estimate by De Giorgi, Carriero, and Leaci. This is based on replacing the coarea formula by a method to approximate $SB{D}^p$ functions with small jump set by Sobolev functions, and is restricted to two dimensions. The other two ingredients will appear in companion papers and consist respectively in regularity results for vectorial elliptic problems of the elasticity type and in a method to approximate in energy $GSB{D}^p$ functions by $SB{V}^p$ ones.     

MECHANICAL ANALYSIS OF TOROFLUX

流动环是一款魔术玩具,具有丰富的力学行为。制作流动环时应用了预应力储存技术,使得环内部储存了弹性弯曲变形能。一经外界扰动,流动环会迅速张开,进入一种新的稳定平衡状态;若给张开的流体环输入某种形式的能量,环会合拢,恢复原有的稳定平衡状态。本文从能量的角度对流动环张开与合拢等现象进行力学分析。     

Microfluidic fabrication of water-in-water droplets encapsulated in hydrogel microfibers

By combining microfiber spinning techniques with aqueous two phase system (ATPS), a rapid and simple strategy to fabricate water-in-water (w/w) droplets encapsulated in microfibers was proposed for the first time. Hydrophilic environment in hydrogel and the fiber format facilitates higher biocompatibility, convenient manipulation of the droplets and recycling of the contents inside droplets, which would have promising development in biological, pharmacological and environmental fields.     

ZnO nanowire lines and bundles: Template-deformation-guided alignment for patterned field-electron emitters

One-dimensional ZnO materials have been promising for field-emission (FE) application, but how to facially control the alignment of ZnO emitters is still a great challenge especially for patterned display application. Here, we report the fabrication of novel ZnO nanowire (NW) line and bundle arrays for patterned field-electron emitters. The effects of PS template size and heating time on the resulted ZnO nanoarrays were systematically studied. The deformation degree of PS templates was controlled and hence utilized to adjust the alignment of electrochemically deposited ZnO arrays. It was found that the length of NW lines and the density of NW bundles can effectively tuned by the PS template heating time. The optimal FE performance with turn-on electric field as low as of 4.4 V μm⁻¹ and the field-enhancement factor as high as of 1450 were achieved through decreasing the screening effect among the patterned field-electron emitters.     

纵横载荷作用下功能梯度梁的弯曲和过屈曲

基于一阶非线性梁理论和物理中面概念,导出了纵横向载荷作用下功能梯度材料(FGM)梁非线性弯曲和过屈曲问题的控制方程,并获得了该问题的精确解;据此解研究了梯度材料性质、外载荷、横向剪切变形以及边界条件等因素对功能梯度材料梁非线性力学行为的影响,分析中假设功能梯度材料性质只沿梁厚度方向,并按成分含量的幂指数函数形式变化。结果表明:纵横载荷共同作用下,功能梯度梁的弯曲构形将有无限多个;随着梯度指数的增大,梁的变形减小,临界载荷升高;随着长高比的增大,横向剪切变形的影响减小。     

小实验大道理 ——从热缩片小制品DIY看高分子材料的熵致形变

A little experiment concerning the pyrocondensation materials was introduced in this paper. The aim was to help the public understand the principles of entropy induced deformation of polymer materials.     

A micrometer head integrated microfluidic device for facile droplet size control and automatic measurement of a droplet size

A novel microfluidic droplet generator is proposed, which can control the droplet size through turning an integrated micrometer head with ease, and the size of the produced micro-droplet can be automatically and real-time monitored by an open-sourced software and off-the-shelf hardware.     

A theory of finite tensile deformation of double-network hydrogels

A continuum damage model was developed to describe the finite tensile deformation of tough double-network (DN) hydrogels synthesized by polymerization of a water-soluble monomer inside a highly crosslinked rigid polyelectrolyte network. Damage evolution in DN hydrogels was characterized by performing loading-unloading tensile tests and oscillatory shear rheometry on DN hydrogels synthesized from 3-sulfopropyl acrylate potassium salt (SAPS) and acrylamide (AAm). The model can explain all the mechanical features of finite tensile deformation of DN hydrogels, including idealized Mullins effect and permanent set observed after unloading, qualitatively and quantitatively. The constitutive equation can describe the finite elasto-plastic tensile behavior of DN hydrogels without resorting to a yield function. It was showed that tensile mechanics of DN hydrogels in the model is controlled by two material parameters which are related to the elastic moduli of first and second networks. In effect, the ratio of these two parameters is a dimensionless number that controls the behavior of material. The model can capture the stable branch of material response during neck propagation where engineering stress becomes constant. Consistent with experimental data, by increasing the elastic modulus of the second network the finite tensile behavior of the DN hydrogel changes from necking to strain hardening.     

Dynamic stability of externally pressurized elastic rings subjected to high rates of loading

Of interest here is the influence of loading rate on the stability of structures where inertia is taken into account, with particular attention to the comparison between static and dynamic buckling. This work shows the importance of studying stability via perturbations of the initial conditions, since a finite velocity governs the propagation of disturbances. The method of modal analysis that determines the fastest growing wavelength, currently used in the literature to analyze dynamic stability problems, is meaningful only for cases where the velocity of the perfect structure is significantly lower than the associated wave propagation speeds.     

Annulation-Induced Hidden Reactivity of the 1,2,4-Triazole Backbone

Triazoles are an important class of compounds with widespread applications. Functionalization of the triazole backbone is thus of significant interest. In comparison to 1,2,3-triazoles, C−H activation-functionalization of the congeners 1,2,4-triazoles is surprisingly underdeveloped. Indeed, no such C−H activation-functionalization has been reported for 4-substituted 1,2,4-triazole cores. Furthermore, although denitrogenative ring-opening of 1,2,3-triazoles is well-explored, 1,2,4-triazole/triazolium substrates have not been known to exhibit N−N bond-cleaving ring-opening reactivity so far. In this work, we unveiled an unusual hidden reactivity of the 1,2,4-triazole backbone involving the elusive N−N bond-cleaving ring-opening reaction. This new reactivity was induced by a Satoh-Miura-type C−H activation-annulation at the 1,2,4-triazole motif appended with a pyridine directing group. This unique reaction allowed ready access to a novel class of unsymmetrically substituted 2,2′-dipyridylamines, with one pyridine ring fully-substituted with alkyl groups. The unsymmetrical 2,2′-dipyridylamines were utilized to access unsymmetrical boron-aza-dipyridylmethene fluorescent dyes. Empowered with desirable optical/physical properties such as large Stokes shifts and suitable hydrophobicity arising from optimal alkyl chain length at the fully-substituted pyridine-ring, these dyes were used for intracellular lipid droplet-selective imaging studies, which provided useful information toward designing suitable lipid droplet-selective imaging probes for biomedical applications.