Local Area Ratio Research Articles

Nonlinearly elastic maps: Energy minimizing configurations of membranes on prescribed surfaces

We propose a model for nonlinearly elastic membranes undergoing finite deformations while confined to a regular frictionless surface in R 3 \mathbb {R}^3 . This is a physically correct model of the analogy sometimes given to motivate harmonic maps between manifolds. The proposed energy density function is convex in the strain pair comprising the deformation gradient and the local area ratio. If the target surface is a plane, the problem reduces to 2-dimensional, polyconvex nonlinear elasticity addressed by J. M. Ball. On the other hand, the energy density is not rank-one convex for unconstrained deformations into R 3 \mathbb {R}^3 . We show that the problem admits an energy-minimizing configuration when constrained to lie on the given surface. For a class of Dirichlet problems, we demonstrate that the minimizing deformation is a homeomorphism onto its image on the given surface and establish the weak Eulerian form of the equilibrium equations.

Development of multi-filament textured-powder Bi-2212/Ag wire with enhanced local area ratio

The performance and cost of Bi-2212/Ag wire is limited by the large area fraction of Ag matrix (∼3:1) that is required in the conventional oxide-powder-in-tube fabrication process. An alternative process is being developed in which fine-powder Bi-2212 is uniaxially compressed to form a bar tetrahedral bar with a Ag-alloy foil cladding. The fine powder naturally textures under compression (aligns the a-b planes perpendicular to the direction of compaction). Earlier work demonstrated that a symmetric billet of trapezoidal-cross-section textured-powder (TP) bars draws conformally so that the local area ratio is preserved.

Existence of Weak Solutions for Non-Simple Elastic Surface Models

We consider a class of models for nonlinearly elastic surfaces in this work. We have in mind thin, highly deformable structures modeled directly as two-dimensional nonlinearly elastic continua, accounting for finite membrane and bending strains and thickness change. We assume that the stored-energy density is polyconvex with respect to the second gradient of the deformation, and we require that it grow unboundedly as the local area ratio approaches zero. For sufficiently fast growth, we show that the latter is uniformly bounded away from zero at an energy minimizer. With this in hand, we rigorously derive the weak form of the Euler-Lagrange equilibrium equations.

Development of Multi-Filament Textured-Powder Bi-2212/Ag Wire With Enhanced Local Area Ratio

The performance and cost of Bi-2212/Ag wire is limited by the large fraction of Ag matrix (~3:1) that is required in the oxide-powder-in-tube fabrication process. An alternative fabrication process is being developed in which fine-powder Bi-2212 is uniaxially compressed to form bars with a thin Ag foil sheath. The fine powder naturally textures (aligns the a-bplanes perpendicular to the direction of compaction) with texture >80% using 200 MPa compression. A billet is formed by stacking trapezoidal-cross-section bars in a symmetric 8-12-16 pattern around an Ag rod and enclosed in an Ag-wall extrusion can. The billet is extruded and drawn to fine wire. Results are presented on present status of the development and testing.

The corrosion behavior of Mg-9Al-xRE magnesium alloys modified by friction stir processing

The combination of rare earth (RE) alloying and friction stir processing (FSP) was demonstrated to be favorable in improving the corrosion resistance of Mg-9Al alloys. The microstructure and corrosion behavior of the modified Mg-9Al-xRE alloys were documented in this paper. Electrochemical measurements revealed that the corrosion resistance of as-cast Mg-9Al-xRE alloys in 3.5 wt% NaCl solution was weaken with the addition of RE elements. It is found that the formation of a large amount of coarse strip-like Al-RE precipitates is responsible for the accelerated dissolution of anodic magnesium matrix. However, the corrosion resistance of FSPed Mg-9Al-xRE alloys was improved when the RE element was added and the improvement was further enhanced with the increasing amount of RE addition. This is mainly attributed to the alternation in the corrosion behavior of magnesium alloys owing to the refined and redistributed precipitates in α-Mg matrix. The refinement of cathodic precipitates enlarges the local area ratio of anode and cathode and retards the severe galvanic corrosion tendency in magnesium alloys. In addition, the presence of a large amount of fine Al-RE precipitates is favorable in accumulative growing of the corrosion product layer during the corrosion propagation, and thus improves the stability and compactness of this protective layer.

On the equivalence of local and global area-constraint formulations for lipid bilayer vesicles

Lipid bilayer membranes are commonly modeled as area-preserving fluid surfaces that resist bending. There appear to be two schools of thought in the literature concerning the actual area constraint. In some works the total or global area (GA) of the vesicle is a prescribed constant, while in others the local area ratio is assigned to unity. In this work we demonstrate the equivalence of these ostensibly distinct approaches in the specific case when the equilibrium configuration is a smooth, closed surface of genus zero. We accomplish this in the context of the Euler-Lagrange equilibrium equations, constraint equations and the second-variation with admissibility conditions, for a broad class of models - including the phase-field type.

Navier–Stokes Equations Interacting with a Nonlinear Elastic Biofluid Shell

We study a moving boundary value problem consisting of a viscous incompressible fluid moving and interacting with a nonlinear elastic fluid shell. The fluid motion is governed by the Navier–Stokes equations, while the fluid shell is modeled by a bending energy which extremizes the Willmore functional and a membrane energy with density given by a convex function of the local area ratio. The fluid flow and shell deformation are coupled together by continuity of displacements and tractions (stresses) along the moving surface defining the shell. We prove the existence and uniqueness of solutions in Sobolev spaces for a short time.

Image analysis of superconducting composites

Image analysis of multifilament superconducting materials can yield quantitative analysis of many critical parameters that affect conductor performance. The techniques for analysis are described, and examples of each of the techniques applied to samples from the Superconducting Super Collider Laboratory (SSCL) vendor qualification program are presented. SSCL has image analysis capabilities over the range of 0.5* to 10,000*. Transmission electron microscopy (TEM) analysis equipped with the same image analysis system at Sandia National Laboratory extends these capabilities to over 150,000*. Among the analysis routines for composite materials are the local area ratio, barrier volume fraction, barrier inside perimeter, barrier outside perimeter, barrier thickness filament roundness, filament area, filament perimeter, transmission X-ray negative analysis, and feature position analysis TEM work also provides analysis of alpha -phase titanium precipitate volume fraction, precipitate thickness, and precipitate spacing.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>