Application of piece‐wise linear weight functions for 2D 8‐node quadrilateral element in contact problems

The present study is a continuation of our previous work with the aim to reduce problems caused by standard higher order elements in contact problems. The difficulties can be attributed to the inherent property of the Galerkin method which gives uneven distributions of nodal forces resulting in oscillating contact pressures. The proposed remedy is use of piece‐wise linear weight functions. The methods to establish stiffness and/or mass matrix for 8‐node quadrilateral element in 2D are presented, i.e. the condensing and direct procedures. The energy and nodal displacement error norms are also checked to establish the convergence ratio. Interpretation of calculated contact pressures is discussed. Two new 2D 8‐node quadrilateral elements, QUAD8C and QUAD8D, are derived and tested in many examples, which show their good performance in contact problems. Copyright © 2004 John Wiley & Sons, Ltd.     

A three‐dimensional computational procedure for reproducing meshless methods and the finite element method

A flexible computational procedure for solving 3D linear elastic structural mechanics problems is presented that currently uses three forms of approximation function (natural neighbour, moving least squares—using a new nearest neighbour weight function—and Lagrange polynomial) and three types of integration grids to reproduce the natural element method and the finite element method. The addition of more approximation functions, which is not difficult given the structure of the code, will allow reproduction of other popular meshless methods. Results are presented that demonstrate the ability of the first‐order meshless approximations to capture solutions more accurately than first‐order finite elements. Also, the quality of integration for the three types of integration grids is compared. The concept of a region is introduced, which allows the splitting of a domain into different sections, each with its own type of approximation function and spatial integration scheme. Copyright © 2004 John Wiley & Sons, Ltd.     

A variationally consistent αFEM (VCαFEM) for solution bounds and nearly exact solution to solid mechanics problems using quadrilateral elements

A variationally consistent alpha finite element method (VC αFEM) for quadrilateral isoparametric elements is presented by constructing an assumed strain field in which the gradient of the compatible strain field is scaled with a free parameter α. The assumed strain field satisfies the orthogonal condition and the Hellinger–Reissner variational principle is used to establish the discretized system of equations. It is shown that the strain energy is a second‐order continuous function of α, and the VC αFEM can produce both lower and upper bounds to the exact solution in the strain energy for all elasticity problems by choosing a proper α∈[0, α_upper]. Based on this bound property, an exact‐α approach has been devised to give an ultra‐accurate solution that is very close to the exact one in the strain energy. Furthermore, the exact‐α approach also works well for volumetric locking problems, by simply replacing the strain gradient matrix by a stabilization matrix. In addition, a regularization‐α approach has also been suggested to overcome possible hourglass instability. Intensive numerical studies have been conducted to confirm the properties of the present VC αFEM, and a very good performance has been found in comparing to a large number of existing FEM models. Copyright © 2010 John Wiley & Sons, Ltd.     

A three‐dimensional finite element method with arbitrary polyhedral elements

The ‘variable‐element‐topology finite element method’ (VETFEM) is a finite‐element‐like Galerkin approximation method in which the elements may take arbitrary polyhedral form. A complete development of the VETFEM is given here for both two and three dimensions. A kinematic enhancement of the displacement‐based formulation is also given, which effectively treats the case of near‐incompressibility. Convergence of the method is discussed and then illustrated by way of a 2D problem in elastostatics. Also, the VETFEM's performance is compared to that of the conventional FEM with eight‐node hex elements in a 3D finite‐deformation elastic–plastic problem. The main attraction of the new method is its freedom from the strict rules of construction of conventional finite element meshes, making automatic mesh generation on complex domains a significantly simpler matter. Copyright © 2006 John Wiley & Sons, Ltd.     

A three‐dimensional C1 finite element for gradient elasticity

In gradient elasticity strain gradient terms appear in the expression of virtual work, leading to the need for C¹ continuous interpolation in finite element discretizations of the displacement field only. Employing such interpolation is generally avoided in favour of the alternative methods that interpolate other quantities as well as displacement, due to the scarcity of C¹ finite elements and their perceived computational cost. In this context, the lack of three‐dimensional C¹ elements is of particular concern. In this paper we present a new C¹ hexahedral element which, to the best of our knowledge, is the first three‐dimensional C¹ element ever constructed. It is shown to pass the single element and patch tests, and to give excellent rates of convergence in benchmark boundary value problems of gradient elasticity. It is further shown that C¹ elements are not necessarily more computationally expensive than alternative approaches, and it is argued that they may be more efficient in providing good‐quality solutions. Copyright © 2008 John Wiley & Sons, Ltd.     

Updated Lagrangian free surface flow simulations with natural neighbour Galerkin methods

In this paper, a new method to simulate free surface fluid flows within an updated Lagrangian framework is described. It is based on the use of a meshless technique coined as natural element method (NEM) or, more recently, as natural neighbour Galerkin method. The position of the flow front or the geometry of the fluid domain is handled by invoking the geometrical concept of α‐shape of the cloud of points, thus avoiding the explicit definition of the boundary of the domain as it evolves. This method also avoids the traditional need of remeshing typical in finite element simulations of this kind of processes. Three types of fluid behaviour have been considered, namely a purely Newtonian fluid, a non‐Newtonian short fibre‐reinforced thermoplastic, and finally a Norton–Hoff viscoplastic behaviour. Benchmark examples showing the performance of the technique are included in the paper. Copyright © 2004 John Wiley & Sons, Ltd.     

In Situ Encapsulating α‐MnS into N,S‐Codoped Nanotube‐Like Carbon as Advanced Anode Material: α → β Phase Transition Promoted Cycling Stability and Superior Li/Na‐Storage Performance in Half/Full Cells

Incorporation of N,S‐codoped nanotube‐like carbon (N,S‐NTC) can endow electrode materials with superior electrochemical properties owing to the unique nanoarchitecture and improved kinetics. Herein, α‐MnS nanoparticles (NPs) are in situ encapsulated into N,S‐NTC, preparing an advanced anode material (α‐MnS@N,S‐NTC) for lithium‐ion/sodium‐ion batteries (LIBs/SIBs). It is for the first time revealed that electrochemical α → β phase transition of MnS NPs during the 1st cycle effectively promotes Li‐storage properties, which is deduced by the studies of ex situ X‐ray diffraction/high‐resolution transmission electron microscopy and electrode kinetics. As a result, the optimized α‐MnS@N,S‐NTC electrode delivers a high Li‐storage capacity (1415 mA h g^?1 at 50 mA g^?1), excellent rate capability (430 mA h g^?1 at 10 A g^?1), and long‐term cycling stability (no obvious capacity decay over 5000 cycles at 1 A g^?1) with retained morphology. In addition, the N,S‐NTC‐based encapsulation plays the key roles on enhancing the electrochemical properties due to its high conductivity and unique 1D nanoarchitecture with excellent protective effects to active MnS NPs. Furthermore, α‐MnS@N,S‐NTC also delivers high Na‐storage capacity (536 mA h g^?1 at 50 mA g^?1) without the occurrence of such α → β phase transition and excellent full‐cell performances as coupling with commercial LiFePO₄ and LiNi_0.6Co_0.2Mn_0.2O₂ cathodes in LIBs as well as Na₃V₂(PO₄)₂O₂F cathode in SIBs.     

Study of autoabsorption for total α and β counting

The RaMsEs Group (Radioprotection et Mesures Environnementales) of the IPHC performs research and offers services mainly in the field of radioactivity measurements and sample analysis. This report will describe some of our recent experience using a semiautomatic evaporation system to prepare large area thin deposits for total α and β counting and gives experimental and simulated results for the autoabsorption coefficients.     

3D Hollow α‐MnO2 Framework as an Efficient Electrocatalyst for Lithium–Oxygen Batteries

Lithium–oxygen (Li–O₂) batteries are attracting more attention owing to their superior theoretical energy density compared to conventional Li‐ion battery systems. With regards to the catalytically electrochemical reaction on a cathode, the electrocatalyst plays a key role in determining the performance of Li–O₂ batteries. Herein, a new 3D hollow α‐MnO₂ framework (3D α‐MnO₂) with porous wall assembled by hierarchical α‐MnO₂ nanowires is prepared by a template‐induced hydrothermal reaction and subsequent annealing treatment. Such a distinctive structure provides some essential properties for Li–O₂ batteries including the intrinsic high catalytic activity of α‐MnO₂, more catalytic active sites of hierarchical α‐MnO₂ nanowires on 3D framework, continuous hollow network and rich porosity for the storage of discharge product aggregations, and oxygen diffusion. As a consequence, 3D α‐MnO₂ achieves a high specific capacity of 8583 mA h g^?1 at a current density of 100 mA g^?1, a superior rate capacity of 6311 mA h g^?1 at 300 mA g^?1, and a very good cycling stability of 170 cycles at a current density of 200 mA g^?1 with a fixed capacity of 1000 mA h g^?1. Importantly, the presented design strategy of 3D hollow framework in this work could be extended to other catalytic cathode design for Li–O₂ batteries.     

Mechanochemical Synthesis of γ‐Graphyne with Enhanced Lithium Storage Performance

γ‐Graphyne is a new nanostructured carbon material with large theoretical Li⁺ storage due to its unique large conjugate rings, which makes it a potential anode for high‐capacity lithium‐ion batteries (LIBs). In this work, γ‐graphyne‐based high‐capacity LIBs are demonstrated experimentally. γ‐Graphyne is synthesized through mechanochemical and calcination processes by using CaC₂ and C₆Br₆. Brunauer–Emmett–Teller, atomic force microscopy, X‐ray photoelectron spectroscopy, solid‐state ¹³C NMR and Raman spectra are conducted to confirm its morphology and chemical structure. The sample presents 2D mesoporous structure and is exactly composed of sp and sp²‐hybridized carbon atoms as the γ‐graphyne structure. The electrode shows high Li⁺ storage (1104.5 mAh g^?1 at 100 mA g^?1) and rate capability (435.1 mAh g^?1 at 5 A g^?1). The capacity retention can be up to 948.6 (200 mA g^?1 for 350 cycles) and 730.4 mAh g^?1 (1 A g^?1 for 600 cycles), respectively. These excellent electrochemical performances are ascribed to the mesoporous architecture, large conjugate rings, enlarged interplanar distance, and high structural integrity for fast Li⁺ diffusion and improved cycling stability in γ‐graphyne. This work provides an environmentally benign and cost‐effective mechanochemical method to synthesize γ‐graphyne and demonstrates its superior Li⁺ storage experimentally.     

Hierarchical α‐MnO2 Nanowires@Ni1‐xMnxOy Nanoflakes Core–Shell Nanostructures for Supercapacitors

A facile two‐step solution‐phase method has been developed for the preparation of hierarchical α‐MnO₂ nanowires@Ni_1‐xMn_xO_y nanoflakes core–shell nanostructures. Ultralong α‐MnO₂ nanowires were synthesized by a hydrothermal method in the first step. Subsequently, Ni_1‐xMn_xO_y nanoflakes were grown on α‐MnO₂ nanowires to form core–shell nanostructures using chemical bath deposition followed by thermal annealing. Both solution‐phase methods can be easily scaled up for mass production. We have evaluated their application in supercapacitors. The ultralong one‐dimensional (1D) α‐MnO₂ nanowires in hierarchical core–shell nanostructures offer a stable and efficient backbone for charge transport; while the two‐dimensional (2D) Ni_1‐xMn_xO_y nanoflakes on α‐MnO₂ nanowires provide high accessible surface to ions in the electrolyte. These beneficial features enable the electrode with high capacitance and reliable stability. The capacitance of the core–shell α‐MnO₂@Ni_1‐xMn_xO_y nanostructures (x = 0.75) is as high as 657 F g^?1 at a current density of 250 mA g^?1, and stable charging‐discharging cycling over 1000 times at a current density of 2000 mA g^?1 has been realized.     

Oxidation protective coatings for γ‐TiAl – recent trends

Engine designers show continued interest in γ‐TiAl based titanium aluminides as light–weight structural materials to be used at moderately elevated temperatures. Although alloy development has made significant progress in terms of mechanical properties and environmental resistance, protective coatings have been developed that help to extend the lifetime of these alloys significantly. The major challenge of coating development is to prevent the formation of fast growing titania. Furthermore, changes of coating chemistries at high temperatures have to be considered in order to avoid rapid degradation of the coatings due to interdiffusion between substrate and coating. The paper describes recent work of the authors on different coatings produced by means of magnetron sputter technique. Thin ceramic Ti‐Al‐Cr‐Y‐N layers tested at 900 °C exhibited poor oxidation resistance. In contrast, intermetallic Ti‐Al‐Cr, Si‐based and aluminum rich Ti‐Al coatings were tested at exposure temperatures up to 950 °C for 1000h resulting in reasonable and partially excellent oxidation behaviour.     

Identification of the anthelix motif in the TGF‐β superfamily by molecular 3D‐Rapid Prototyping

3D‐Rapid Prototyping (3D‐RP) is a novel technique for the construction of highly accurate three‐dimensional polyamide models of biomolecules. This method has been shown to be a valuable tool in the modeling of protein‐protein‐interactions as well as in the analysis of surface topography. Using this technique we were recently able to identify a so far unknown structure on the concave side of bone morphogenetic protein 2 (BMP‐2). Since this structure is the imprint of a left‐handed helix we have called this negative an unthelix. Obviously this novel structural feature of BMP‐2 may act as a binding side for endogenous ligands. BMP‐2 belongs to the highly conserved Transforming Growth Factor‐β (TGF‐β) superfamily, a large group of multifunctional peptides controlling differentiation, proliferation and repair in multicellular organism. The protomer structures of all members share a cystine‐knot motif as a characteristic feature. The question therefore arose whether a) the novel anthelical motif found in BMP‐2 is a common structural feature of this family and b) if there are any differences in terms of pitch and radius of the anthelix. As anthelical structures are difficult to visualize and nearly impossible to quantify using 3D molecular visualization software we constructed models of BMP‐2, BMP‐7 and TGF‐β2 from X‐ray crystallographic data by 3D‐Rapid Prototyping (3D‐RP). The anthelix motif was found in BMP‐2, BMP‐7 and TGF‐β2 with similar values for pitch (ca. 8‐10 nm) and radius (ca. 0.5‐0.7 nm). In contrast the anthelical motif was not found in a 3D‐RP model of human chorionic gonadotropin (HCG) which is also a member of the cystine‐knot family but doesn’t belong to the TGF‐β superfamily. These results were corroborated by measurements of the intersubunit angle of these dimeric proteins (141‐149°) and the distances between the center of mass (1.68‐1.96 nm) of the subunits both of which appear to be determinants of the anthelical pitch. We conclude that the anthelical groove on the concave side is a common structural motif of BMP‐2, BMP‐7 and TGF‐β2 and maybe of the whole group of the TGF‐β superfamily.     

Analysis of three‐dimensional crack initiation and propagation using the extended finite element method

An Erratum has been published for this article in International Journal for Numerical Methods in Engineering 2005, 63(8): 1228. We present a new formulation and a numerical procedure for the quasi‐static analysis of three‐dimensional crack propagation in brittle and quasi‐brittle solids. The extended finite element method (XFEM) is combined with linear tetrahedral elements. A viscosity‐regularized continuum damage constitutive model is used and coupled with the XFEM formulation resulting in a regularized ‘crack‐band’ version of XFEM. The evolving discontinuity surface is discretized through a C⁰ surface formed by the union of the triangles and quadrilaterals that separate each cracked element in two. The element's properties allow a closed form integration and a particularly efficient implementation allowing large‐scale 3D problems to be studied. Several examples of crack propagation are shown, illustrating the good results that can be achieved. Copyright © 2005 John Wiley & Sons, Ltd.     

Constraint‐corrected J–R curve based on three‐dimensional finite element analyses

Three‐dimensional (3D) finite element analyses are carried out on single‐edge bend [SE(B)] specimens for which the J‐integral resistance curves (J–R curves) have been experimentally determined to develop the constraint‐corrected J–R curves for the X80 grade pipe steel. The constraint parameters considered in this study include Q_HRR, Q_SSY, Q_{SSY_m}, Q_LM, Q_BM1, Q_BM2, A₂, h and T_z. The constraint‐corrected J–R curves were developed on the basis of the constraint parameters obtained from finite element analysis and experimentally determined J–R curves associated with deeply cracked and medium‐cracked SE(B) specimens and validated against shallow‐cracked SE(B) specimens. The analysis results indicate that all the constraint parameters considered in this study except Q_HRR, Q_SSY, Q_{SSY_m} and Q_LM lead to reasonably accurate constraint‐corrected J–R curves if the crack extensions are relatively small (≤0.7 mm). For larger crack extensions (≤1.5 mm), the Q_BM1‐based constraint‐corrected J–R curve leads to the most accurate predictions of J among all the constraint parameters considered.     

H+‐Insertion Boosted α‐MnO2 for an Aqueous Zn‐Ion Battery

Rechargeable Zn/MnO₂ batteries using mild aqueous electrolytes are attracting extensive attention due to their low cost, high safety, and environmental friendliness. However, the charge‐storage mechanism involved remains a topic of controversy so far. Also, the practical energy density and cycling stability are still major issues for their applications. Herein, a free‐standing α‐MnO₂ cathode for aqueous zinc‐ion batteries (ZIBs) is directly constructed with ultralong nanowires, leading to a rather high energy density of 384 mWh g^?1 for the entire electrode. Greatly, the H⁺/Zn²⁺ coinsertion mechanism of α‐MnO₂ cathode for aqueous ZIBs is confirmed by a combined analysis of in situ X‐ray diffractometry, ex situ transmission electron microscopy, and electrochemical methods. More interestingly, the Zn²⁺‐insertion is found to be less reversible than H⁺‐insertion in view of the dramatic capacity fading occurring in the Zn²⁺‐insertion step, which is further evidenced by the discovery of an irreversible ZnMn₂O₄ layer at the surface of α‐MnO₂. Hence, the H⁺‐insertion process actually plays a crucial role in maintaining the cycling performance of the aqueous Zn/α‐MnO₂ battery. This work is believed to provide an insight into the charge‐storage mechanism of α‐MnO₂ in aqueous systems and paves the way for designing aqueous ZIBs with high energy density and long‐term cycling ability.     

Probing the Domain Architecture in 2D α‐Mo2C via Polarized Raman Spectroscopy

MXenes are emerging 2D materials with intriguing properties such as excellent stability and high conductivity. Here, a systematic study on the Raman spectra of 2D α‐Mo₂C (molybdenum carbide), a promising member in MXene family, is conducted. Six experimentally observed Raman modes from ultrathin α‐Mo₂C crystal are first assigned with the assistance of phonon dispersion calculated from density functional theory. Angle‐resolved polarized Raman spectroscopy indicates the anisotropy of α‐Mo₂C in the b–c plane. Raman spectroscopy is further used to study the unique domain structures of 2D α‐Mo₂C crystals grown by chemical vapor deposition. A Raman mapping investigation suggests that most of the α‐Mo₂C flakes contain multiple domains and the c‐axes of neighboring domains tend to form a 60° or 120° angle, due to the weak Mo? C bonds in this interstitial carbide and the low formation energy of the carbon chains along three equivalent directions. This study demonstrates that polarized Raman spectroscopy is a powerful and effective way to characterize the domain structures in α‐Mo₂C, which will facilitate the further exploration of the domain‐structure‐related properties and potential applications of α‐Mo₂C.