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。     

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 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.     

Deformation of single‐walled carbon nanotubes by interaction with graphene: A first‐principles study

The interaction between single‐walled carbon nanotubes (SWNTs) and graphene were studied with first‐principles calculations. Both SWNTs and single‐layer graphene (SLG) or double‐layer graphene (DLG) display more remarkable deformations with the increase of SWNT diameter, which implies a stronger interaction between SWNTs and graphene. Besides, in DLG, deformation of the upper‐layer graphene is less than in SLG. Zigzag SWNTs show stronger interactions with SLG than armchair SWNTs, whereas the order is reversed for DLG, which can be interpreted by the mechanical properties of SWNTs and graphene. Density of states and band structures were also studied, and it was found that the interaction between a SWNT and graphene is not strong enough to bring about obvious influence on the electronic structures of SWNTs. © 2015 Wiley Periodicals, Inc.     

Heterostructured composite of NiFe-LDH nanosheets with Ti4O7 for oxygen evolution reaction

Developing oxygen evolution reaction (OER) electrocatalyst based on earth-abundant materials holds great promise for ascertaining water-splitting to surmount its deprived kinetics. In this regard, NiFe-LDH (layered double hydroxide) receives considerable attention owing to their layered structure. However, they still suffer from poor electronic conductivity and structural stability. We combined NiFe-LDH nanosheets with Magnéli phase Ti₄O₇ into a heterostructured composite. A series of analyses reveal that decorating Ti₄O₇ facilitates charge transfer to enhance the conductivity of NiFe-LDH-Ti₄O₇. During electrochemical measurement, Ni²⁺ is transformed to metastable Ni³⁺ (Ni (OH)→ NiOOH) before the OER onset potential. Thus, the presence of Ni³⁺ as the main active sites could improve the chemisorption of OH^? to facilitate OER. As a result, the NiFe-LDH-Ti₄O₇ catalyst delivers as low as onset potential (1.43 V). Combining the holey structure (NiFe-LDH and Ti₄O₇) and the defect engineering generated on NiFe-LDH-Ti₄O₇ as a synergistic effect improves the OER performance. The inclusion of Ti₄O₇ in the composite leads to more vacancy sites, as evidenced by the extended X-ray absorption fine structure (EXAFS) analysis. The obtained defective structure with a low coordination environment would improve the electronic conductivity and facilitate the adsorption process of H₂O onto metal cations, thereby increasing the intrinsic catalytic activity of NiOOH. The strong coupling of NiFe-LDH and Ti₄O₇ also increases the stability, and the heterostructured composite helps maintain the structural robustness of the LDH.     

Characterisation and effect of polymer network deformation in reverse-mode polymer-stabilised cholesteric texture

In reverse-mode polymer-stabilised cholesteric texture (PSCT), the dynamic response is derived from local director reorientation governed by dielectric coupling effect/self-assembly and polymer network deformation. A double exponential rise/decay model is proposed to investigate the underlying physical mechanisms. Through simulation of the transient rise and decay processes, the polymer network deformation in PSCT can be quantitatively evaluated. Less deformation and faster restoration speed of the polymer network can suppress hysteresis. These results provide useful guidelines for future PSCT fabrication and performance optimisation.