Zero-sound determination of texture transitions in flowing superfluid3He-A

The conditions have been measured for which the texture of the order parameter of superfluid³He-A is uniform and aligned with an applied superflow. At finite superflows, a finite parallel magnetic field is required to disrupt the uniform aligned texture. The shape of the uniform texture's phase boundary in av _s -H plane is similar to theoretical predictions, for which the state just outside of the phase boundary is a helical texture. However, substantial disagreements with the theory remain.     

A parallel-supercomputing investigation of the stiffness of aligned,short-fiber-reinforced composites using the Boundary Element Method

Computational experiments are carried out in three-dimensional, multi-fibre specimens with the objective of determining the influence of fibre volume fraction (ϕ) and aspect ratio (a_r) on the effective tensile modulus of aligned, discontinuous fibre-reinforced composites. The Boundary Element Method (BEM), implemented on a 1840-node Intel Paragon parallel supercomputer using a torus-wrap mapping, enables the prediction of the tensile behaviour of composite specimens consisting of up to 200 discrete aligned short fibres, randomly dispersed in an elastic matrix. Statistical averages of the computed effective longitudinal moduli are compared with the predictions of the Halpin–Tsai equation and are found to be in good agreement for low values of a_r and ϕ. However, as a_r and/or ϕ increase, the predictions of the Halpin–Tsai equation fall below the computed moduli. Consideration of the finite packing efficiency of the fibres as proposed by Lewis and Nielsen results in a generalized form of the Halpin–Tsai equation whose predictions are in very good agreement with the BEM calculations for the entire range of ϕ and a_r examined. The scatter in the computed moduli decreases with increasing number of fibres, reflecting the ‘homogenization’ of the specimen brought about by consideration of larger numbers of smaller fibres. This scatter grows with increasing ϕ and a_r, reflecting an increase in the magnitude and complexity of inter-fibre interactions. © 1997 by John Wiley & Sons, Ltd.     

A computational approach to the investigation of impact damage evolution in discontinuously reinforced fiber composites

 A micromechanical damage constitutive model for discontinuous fiber-reinforced composites is developed to perform impact simulation. Progressive interfacial fiber debonding and a crack-weakened model are considered in accordance with a statistical function to describe the varying probability of damage. Emanating from a constitutive damage model for aligned fiber-reinforced composites, a micromechanical damage constitutive model for randomly oriented, discontinuous fiber-reinforced composites is developed. The constitutive damage model is then implemented into a finite element program DYNA3D to simulate the dynamic behavior and the progressive damage of composites. Finally, numerical simulations for a biaxial loading test and a four-point bend impact test of composite specimens are performed to validate the computational model and investigate impact damage evolution in discontinuous fiber-reinforced composite structures. Furthermore, in order to address the influence of Weibull parameter S _o on the damage evolution in composites, parametric analysis is carried out. Received 29 April 2000     

Preferential cell response to anisotropic electro-spun fibrous scaffolds under tension-free conditions

Anisotropic alignment of collagen fibres in musculoskeletal tissues is responsible for the resistance to mechanical loading, whilst in cornea is responsible for transparency. Herein, we evaluated the response of tenocytes, osteoblasts and corneal fibroblasts to the topographies created through electro-spinning and solvent casting. We also evaluated the influence of topography on mechanical properties. At day 14, human osteoblasts seeded on aligned orientated electro-spun mats exhibited the lowest metabolic activity (P < 0.001). At day 5 and at day 7, no significant difference was observed in metabolic activity of human corneal fibroblasts and bovine tenocytes respectively seeded on different scaffold conformations (P > 0.05). Osteoblasts and corneal fibroblasts aligned parallel to the direction of the aligned orientated electro-spun mats, whilst tenocytes aligned perpendicular to the aligned orientated electro-spun mats. Mechanical evaluation demonstrated that aligned orientated electro-spun fibres exhibited significant higher stress at break values than their random aligned counterparts (P < 0.006) and random orientated electro-spun fibres exhibited significant higher strain at break values than the aligned orientated scaffolds (P < 0.006). While maintaining fibre structure, we also developed a co-deposition method of spraying and electro-spinning, which enables the incorporation of microspheres within the three-dimensional structure of the scaffold.     

Magnetic Properties of Ca3Ru2O7 Grown by a Floating Zone Method

We have succeeded in growing single crystals of Ca₃Ru₂O₇ by a floating zone method. The temperature dependence of magnetic susceptibility was measured in the temperature range from 2 to 300 K for the field along ab-plane and c-axis. The magnetic susceptibility shows anisotropic behavior. For T>55 K, the susceptibilities of both directions increase like the Curie–Weiss behavior with decreasing temperature. In the temperature range between 55 and 48 K, the susceptibility along ab-plane decreases steeply, while the one along c-axis is almost constant, which implies that the magnetic moment is aligned antiferromagnetically in the ab-plane. The susceptibilities drastically decrease in both directions at 48 K and are almost independent of temperature below 30 K.     

kFEM: Adaptive meshfree finite‐element methods using local kernels on arbitrary subdomains

We propose a novel finite‐element method for polygonal meshes. The resulting scheme is hp‐adaptive, where h and p are a measure of, respectively, the size and the number of degrees of freedom of each polygon. Moreover, it is locally meshfree, since it is possible to arbitrarily choose the locations of the degrees of freedom inside each polygon. Our construction is based on nodal kernel functions, whose support consists of all polygons that contain a given node. This ensures a significantly higher sparsity compared to standard meshfree approximations. In this work, we choose axis‐aligned quadrilaterals as polygonal primitives and maximum entropy approximants as kernels. However, any other convex approximation scheme and convex polygons can be employed. We study the optimal placement of nodes for regular elements, ie, those that are not intersected by the boundary, and propose a method to generate a suitable mesh. Finally, we show via numerical experiments that the proposed approach provides good accuracy without undermining the sparsity of the resulting matrices.     

A vectorized version of a sparse matrix-vector multiply

A fast vectorized algorithm is presented for a sparse matrix-vector multiply. It can be used when the matrix, A , can be represented as a multiplitting, A = ∑ A _e. In particular, it can be applied to a matrix-vector multiply arising in finite element techniques where the matrices A _e are associated with the individual element contributions to the global matrix A . The algorithm presented here uses a data structure which is based on the individual matrices A _e and can be applied both to symmetric and to non-symmetric matrices. This algorithm would be attractive for vector architecture similar to either the CYBER 205 or the CRAY and has been implemented for both regular and irregular finite element grids on the CYBER 205. Execution times and storage requirements are compared to standard sparse and band matrix-vector multiply algorithms.     

Scalable Manufacturing of Free-Standing,Strong Ti3C2Tx MXene Films with Outstanding Conductivity

Free-standing films that display high strength and high electrical conductivity are critical for flexible electronics, such as electromagnetic interference (EMI) shielding coatings and current collectors for batteries and supercapacitors. 2D Ti₃C₂T_x flakes are ideal candidates for making conductive films due to their high strength and metallic conductivity. It is, however, challenging to transfer those outstanding properties of single MXene flakes to macroscale films as a result of the small flake size and relatively poor flake alignment that occurs during solution-based processing. Here, a scalable method is shown for the fabrication of strong and highly conducting pure MXene films containing highly aligned large MXene flakes. These films demonstrate record tensile strength up to ≈570 MPa for a 940 nm thick film and electrical conductivity of ≈15 100 S cm⁻¹ for a 214 nm thick film, which are both the highest values compared to previously reported pure Ti₃C₂T_x films. These films also exhibit outstanding EMI shielding performance (≈50 dB for a 940 nm thick film) that exceeds other synthetic materials with comparable thickness. MXene films with aligned flakes provide an effective route for producing large-area, high-strength, and high-electrical-conductivity MXene-based films for future electronic applications.     

Higher‐order finite elements based on generalized eigenfunctions of the Laplacian

We present a new class of higher‐order finite elements based on generalized eigenfunctions of the Laplace operator, which are suitable for both product and simplicial geometries in ?^d. Due to simultaneous orthogonality of the generalized eigenfunctions under both the H and L² products and their almost negligible dependence on reference maps, such finite elements are an excellent choice for the discretization of second‐order elliptic problems by the hp‐FEM. Analysis is illustrated by numerical results and comparisons with other popular higher‐order finite elements are presented. The new elements are used to compute efficiently the model of an electrostatic micromotor. Copyright © 2007 John Wiley & Sons, Ltd.     

SOME NOVEL DEVELOPMENTS IN FINITE ELEMENT PROCEDURES FOR GRADIENT-DEPENDENT PLASTICITY

Improved algorithms are proposed for a gradient plasticity theory in which the Laplacian of an invariant plastic strain measure enters the yield function. Particular attention is given to the type of finite elements that can be used within the format of gradient-dependent plasticity. Assuming a weak satisfaction of the yield function, mixed finite elements are developed, in which the invariant plastic strain measure and the displacements are discretized. Two families of finite elements are developed: one in which the invariant plastic strain measure is interpolated using C¹-continuous polynomials, and one in which penalty-enhanced C⁰-continuous interpolants are used. The performance of both families of finite elements is assessed numerically in one-dimensional and two-dimensional boundary value problems. The regularizing effect of the used gradient enhancement in computations of elastoplastic solids is demonstrated, both for mesh refinement and for the directional bias of the grid lines.     

The influence of primary precipitates on the tensile strength of unidirectionally solidified (Fe,Cr)-(Cr,Fe)7C3 in-situ grown composites containing 30 wt % Cr

The influence is investigated of metal dendrites and primary carbide needles on the tensile strength of the (Fe, Cr)-(Cr, Fe)₇C₃ insitu grown composite cont-aining 30 wt % Cr. It is found that these irregularities in the aligned structure diminish the tensile strength of thein-situ composite both at room temperature and at 900°C. The maxima in the tensile strength versus composition curves occur at different compositions for these temperatures. A possible explanation of this behaviour is given.     

Large‐Scale Horizontally Aligned ZnO Microrod Arrays with Controlled Orientation,Periodic Distribution as Building Blocks for Chip‐in Piezo‐Phototronic LEDs

A novel method of fabricating large‐scale horizontally aligned ZnO microrod arrays with controlled orientation and periodic distribution via combing technology is introduced. Horizontally aligned ZnO microrod arrays with uniform orientation and periodic distribution can be realized based on the conventional bottom‐up method prepared vertically aligned ZnO microrod matrix via the combing method. When the combing parameters are changed, the orientation of horizontally aligned ZnO microrod arrays can be adjusted (θ = 90° or 45°) in a plane and a misalignment angle of the microrods (0.3° to 2.3°) with low‐growth density can be obtained. To explore the potential applications based on the vertically and horizontally aligned ZnO microrods on p‐GaN layer, piezo‐phototronic devices such as heterojunction LEDs are built. Electroluminescence (EL) emission patterns can be adjusted for the vertically and horizontally aligned ZnO microrods/p‐GaN heterojunction LEDs by applying forward bias. Moreover, the emission color from UV‐blue to yellow‐green can be tuned by investigating the piezoelectric properties of the materials. The EL emission mechanisms of the LEDs are discussed in terms of band diagrams of the heterojunctions and carrier recombination processes.     

A Computationally viable higher-order theory for laminated composite plates

A variational higher-order theory involving all transverse strain and stress components is proposed for the analysis of laminated composite plates. Derived from three-dimensional elasticity with emphasis on developing a viable computational methodology, the theory is well suited for finite element approximations as it incorporates both C⁰ and C^?1 continuous kinematic fields and Poisson boundary conditions. From the theory, a simple three-node stretching-bending finite element is developed and applied to the problem of cylindrical bending of a symmetric carbon/epoxy laminate for which an exact solution is available. Both the analytic and finite element results were found to be in excellent agreement with the exact solution for a wide range of the length-to-thickness ratio. The proposed higher-order theory has the same computational advantages as first-order shear-deformable theories. The present methodology, however, provides greater predictive capabilities, especially, for thick-section composites.     

Dual-mixed hp finite element methods using first-order stress functions and rotations

 A two-field dual-mixed variational formulation of three-dimensional elasticity in terms of the non-symmetric stress tensor and the skew-symmetric rotation tensor is considered in this paper. The translational equilibrium equations are satisfied a priori by introducing the tensor of first-order stress functions. It is pointed out that the use of six properly chosen first-order stress function components leads to a (three-dimensional) weak formulation which is analogous to the displacement-pressure formulation of elasticity and the velocity-pressure formulation of Stokes flow. Selection of stable mixed hp finite element spaces is based on this analogy. Basic issues of constructing curvilinear dual-mixed p finite elements with higher-order stress approximation and continuous surface tractions are discussed in the two-dimensional case where the number of independent variables reduces to three, namely two components of a first-order stress function vector and a scalar rotation. Numerical performance of three quadrilateral dual-mixed hp finite elements is presented and compared to displacement-based hp finite elements when the Poisson's ratio converges to the incompressible limit of 0.5. It is shown that the dual-mixed elements developed in this paper are free from locking in the energy norm as well as in the stress computations, both for h- and p-extensions. Received 22 October 1999     

Fiber-reinforced hyperelastic solids: a realizable homogenization constitutive theory

A new homogenization theory to model the mechanical response of hyperelastic solids reinforced by a random distribution of aligned cylindrical fibers is proposed. The central idea is to devise a special class of microstructures—by means of an iterated homogenization procedure in finite elasticity together with an exact dilute result for sequential laminates—that allows to compute exactly the macroscopic response of the resulting fiber-reinforced materials. The proposed framework incorporates direct microstructural information up to the two-point correlation functions, and requires the solution to a Hamilton–Jacobi equation with the fiber concentration and the macroscopic deformation gradient playing the role of “time” and “spatial” variables, respectively. In addition to providing constitutive models for the macroscopic response of fiber-reinforced materials, the proposed theory also gives information about the local fields in the matrix and fibers, which can be used to study the evolution of microstructure and the development of instabilities. As a first application of the theory, closed-form results for the case of Neo-Hookean solids reinforced by a transversely isotropic distribution of anisotropic fibers are worked out. These include a novel explicit criterion for the onset of instabilities under general finite-strain loading conditions.     

Creep fracture parameter C* solutions for semi-elliptical surface cracks in plates under tensile and bending loads

In order to predict and assess creep life for plate structures with semi-elliptic surface cracks under high temperature condition, the accurate calculation of the creep fracture mechanics parameter C* is a critical step. In this paper, the effects of crack sizes, plate geometries, and material creep properties on the parameter C* have been investigated under tensile and bending loads by extensive finite element analyses. Based on the results, the creep influence functions Hc for calculating C* values were obtained and fitted into equations for surface cracks in plates under both loads. The equations have been verified by finite element calculations. The C* solutions were obtained through these equations which are suitable for wide ranges of crack sizes, plate geometries, and materials.     

Elastic-plastic crack-tip-field numerical analysis integrated with moire interferometry

A novel method of integrating displacement field measurements from high-sensitive moire interferometry with the finite element method is introduced for the elastic-plastic fracture mechanics problems. The measured displacements normal to the crack in a fatigue-precracked specimen are input to a finite element model along a near-field boundary. In this paper the analysis is done for a power-law strain hardening material. The near-field region is discretized using 8-noded isoparametric quadrilateral elements. A validation procedure indicates that just the u _y -displacement (normal to the crack) as input is sufficient for an edge-cracked specimen whereas a center-cracked specimen requires both u _x - and u _x -displacement inputs. Results are obtained in the form of J-integral evaluations, HRR fields, and plastic zones. A significant CPU time saving is achieved when compared with the load-input case. Also the results indicate the existence of HRR field under large scale yielding.     

Influence of directional solidification variables on the cellular and primary dendrite arm spacings of PWA1484

A series of directional solidification experiments have been performed to elucidate the effects of thermal gradient G and growth velocity V on the solidification behavior and microstructural development of the multicomponent Ni-base superalloy PWA 1484. A range of aligned as-cast microstructures were exhibited by the alloy: (i) aligned dendrites with well developed secondary and tertiary arms; (ii) flanged cellular dendrites aligned with the growth direction and without secondary arms; and (iii) cells with no evidence of flanges or secondary arms. The role of the imposed process parameters on the primary arm spacings that developed in the Bridgman-grown samples were examined in terms of current theoretical models. The presence of secondary arms increases the spacings between dendrites and leads to a greater sensitivity of ₁ on G ^–1/2 V ^–1/4. The exponent of V was analyzed and found to depend upon the imposed gradient G. High withdrawal velocities and low thermal gradients were found to cause radial non-uniformity of the primary dendrite arm spacing. Such behavior was associated with off-axis heat flows.     

Effect of mode mixity on K-dominance and three dimensionality in cracked plates

The method of Coherent Gradient Sensing (CGS) in transmission, in conjunction with two and three dimensional finite element methods, is used to study the effect of mode mixity on crack tip stress fields. Using a two dimensional finite element analysis the outer bounds of the region of K-dominance were determined. A three dimensional finite analysis was utilized to study the effect of mode mixity on the three dimensional nature of the stress field in the immediate vicinity of the crack tip and to obtain an inner bound of the region of K-dominance. It was noted that increasing mode mixity leads to an increased rotation of the three dimensional zone, keeping its shape and size unchanged. In contrast, the region of K-dominance is seen to dramatically depend on mode mixity, both in shape and size. In addition, an analysis of the CGS interferograms was conducted to obtain an estimate of the regions of K-dominance experimentally. A least squares fit data analysis technique was used to extract fracture parameters, namely the stress intensity factors K _I, K _II and subsequently the crack tip phase angle, . The data points used for the least square fitting were obtained from the determined regions of K-dominance. The same fracture parameters were also evaluated from the finite element analysis, and good agreement was found between experimental measurements and finite element predictions.