The geometric nature of plasticity laws

This paper concerns the plasticity constitutive laws in small strain. In the thermodynamic approach developed here, the key concept is that of internal variables. The differential nature of plasticity law has been pointed out for a long time. If we unite the invariance condition of these laws in a state variable transformation, this involves, ultimately, that the natural mathematic frame of plasticity theory is Differential Geometry. The system state is defined as a point of a differentiable manifold. The state variable are the local coordinates of this point in a chart. The internal stresses are the components of a covariant vector of the cotangent bundle to internal state manifold and the elastic domain is a convex part of cotangent vector space. The plastic yield criteria such as von Mises condition define a Riemannian structure over the manifold. The metric element is identified with the internal dissipation element. Constitutive laws link the covariant derivatives of the thermodynamic stress with the state variable. Hardening modulus splits up in two parts, kinematic hardening and metric hardening. This last is defined by Christoffel connection coefficients. Applied to von Mises isotropic yield condition, the metric hardening is identified with isotropic hardening. The Baltov-Sawczuk model is also analysed. The use of appropriate polar coordinates simplifies significantly the computations. Generalization to a significant category of non-differentiable yield criteria, such as Tresca condition, is considered by introducting a metric tensor family. The adaptation of Drucker's postulate to the proposed model requires the introduction of parallel transport of the internal stress covector. Generally, this transport is different over distinctive paths joining two points. This fact expresses internal state manifold curvature. The Riemann-Christoffel tensor is computed for von Mises, Baltov-Sawczuk and Tresca models.     

Inhibitory activity of ginger rhizome on airway and uterine smooth muscle preparations

In this study, we describe the tracheal-relaxant and tocolytic activities of the methanol (ME) and aqueous (AQ) crude extracts of ginger (rhizome of Zingiber officinale) in an attempt to rationalize its traditional use in disorders of airways and uterine hyperactivity. Both of the ginger extracts dose-dependently relaxed K⁺ (80 mM) and carbachol (CCh, 1 μM)-induced contractions with more potency against K⁺, similar to that elicited by verapamil, a Ca²⁺ channel blocker. In isolated uterine preparations, the extracts suppressed the K⁺-induced contractions with respective EC₅₀ values of 0.03 mg/ml (0.02–0.05, 95% CI) and 0.05 mg/ml (0.04–0.06). Activity-directed fractionation of AQ yielded an organic and an aqueous fraction with the activities concentrated in the former. Both the crude extracts were found safe in mice up to the oral dose of 5 g/kg when tested for acute toxicity for 24 h. The study shows that ginger possesses tracheal and uterine smooth muscle relaxant activity, possibility mediated via Ca²⁺ channel blockade, justifying its use in disorders such as asthma, cough as well as in dysmenorrhoea and uterine and menstrual spasms and congestion.     

Hybrid gas-to-particle conversion and chemical vapor deposition for the production of porous alumina films

Porous alumina films can be found in a wide variety of materials, including filters, thermal insulation components, dielectrics, biomedical and catalyst supports, coatings and adsorbents. Production methods for these films are as equally diverse as their applications. In this work, a hybrid process based upon chemical vapor deposition and gas-to-particle conversion is presented as an alternative technique for producing porous alumina films, with the main advantages of solvent-free, low substrate-temperature operation. In this process, nanoparticles were produced in the vapor phase by reaction of aluminum acetylacetonate in the presence of oxygen. Downstream of this reaction zone, these nanoparticles were collected via thermophoresis onto a cooled substrate, forming a porous film. Some deposited films were subjected to post-processing in the form of annealing in air. Fourier-transform infrared spectra and X-ray energy-dispersive spectroscopy analysis confirmed the production of alumina at processing temperatures above 973 K. X-Ray diffraction revealed that the films were amorphous. Film thickness, ranging from 30 to 250 μm, and the average deposition rate were determined from scanning electron microscopy results. From transmission electron microscopy, the average primary particle size was determined to be approximately 18 nm and the formation of nanoparticle aggregates was evident. Annealing of the films at temperatures ranging from 523 to 1173 K in the presence of air did not have an effect on particle size. The specific surface area of the powder composing the films ranged from 10 to 185 m² g⁻¹, as determined from nitrogen gas adsorption by the Brunauer–Emmett–Teller method.     

An orthogonal basis for the hyperbolic hybrid polynomial space

Motivated by the wide usage of the Tchebyshev basis and Legendre basis in the algebra polynomial space, we construct an orthogonal basis with the properties of the H-Bézier basis in the hyperbolic hybrid polynomial space, which is similar to the Legendre basis and holds remarkable properties. Moreover, we derive the transformation matrices that map the H-Bézier basis and the orthogonal basis forms into each other. An example for approximating the degree reduction of the H- Bézier curves is sketched to illustrate the utility of the orthogonal basis.     

An ideal topology type convergent theorem on scale effect algebras

The famous Antosik-Mikusinski convergent theorem on the Abel topological groups has very extensive applications in measure theory, summation theory and other analysis fields. In this paper, we establish the theorem on a class of effect algebras equipped with the ideal topology. This paper shows also that the ideal topology of effect algebras is a useful topology in studying the quantum logic the- ory.     

Application of Code Approach for Emergency Evacuation in a Rail Station

This paper presents an emergency evacuation analysis during a mid-platform train fire in an underground rail station. A time-based evacuation scenario is developed taking into account the stairway inaccessibility due to smoke blockage. The calculation approach in NFPA 130 is then applied to a parametric study of this time-based scenario and its reliability is examined using a micro-simulation model. Both methods give consistent predictions of the exiting times. The results demonstrate that with the division of the station into two zones, the exiting time could not meet the code requirements, whereas it does meet the required exiting time without the division. Such division is due to smoke blockage and creates an uneven ratio of the occupant load to the available exiting capacity. This shows that appropriate consideration of the fire and smoke effects is important for station egress evaluation. Other issues such as the fire growth rate and the pre-evacuation time are also discussed.     

Residual Stress Simulation of Injection Molding

In this study, distribution and history of residual stresses in plaque-like geometries are simulated based on linear thermoviscoelastic model, which helps to understand the mechanics and evolution of the residual stresses in the injection molding process. The numerical calculation of direction, combined with the specified boundary conditions. Results show that the stress variation across the thickness exhibits a high surface tensile value changing to a compressive peak value close to the surface, with the core region experiencing a parabolic tensile peak. Residual stress distribution throughout the thickness is almost same along the flowpath and the final residual stresses value near the gate is lower than the value near the end of flowpath.     

Theoretical Investigation of Time Suboptimal Control of Industrial Manipulators Along Specified Paths

A method for the time suboptimal control of an industrial manipulator from an initial position and orientation to a final position and orientation as it moves along a specified path is proposed. Nonlinear system equations that describe the manipulator motion are linearized at each time step along the path. A method which gives the control inputs (joint angular velocities) for time suboptimal control of the manipulator is developed. In the formulation, joint angular velocity and acceleration limitations are also taken into consideration. A six degree of freedom elbow type manipulator is used in numerical examples to verify the method developed.     

Mechanical properties of iron processed by severe plastic deformation

In the present study, the mechanical properties of Fe processed via severe plastic deformation (equal-channel angular pressing (ECAP)) at room temperature were investigated for the first time. The grain size of annealed Fe, with an initial grain size of about 200 μm, was reduced drastically during ECAP. After eight passes, the grain size reaches 200 to 400 nm, as documented by means of transmission electron microscopy (TEM). The value of microhardness during pressing increases 3 times over that of the starting material after the first pass and increases slightly during subsequent pressing for higher-purity Fe. Examination of the value of microhardness after eight passes as a function of post-ECAP annealing temperature shows a transition from recovery to recrystallization, an observation that resembles the behavior reported for heavily deformed metals and alloys. The tensile and compression behaviors were examined. In tension, a drop in the engineering stress-engineering strain curve beyond maximum load was observed both in the annealed Fe and the ECAP Fe. This drop is related to the neck deformation. The fracture surface, examined by scanning electron microscopy (SEM), shows vein patterns, which is different from the dimples found on the fracture surface of annealed Fe. In compression, an initial strain-hardening region followed by a no-strain-hardening region was observed in the ECAP Fe. The yield strength in tension of the ECAP Fe was observed to be higher than that in compression. The strengthening mechanisms and softening behavior are discussed.