Planar interface between a chiral medium and a metal: Surface wave excitation

Abstract

The feasibility of excitation of surface waves at a single planar interface is demonstrated numerically. The interface separates a chiral medium from an isotropic and achiral medium; this latter could be a metal. Both media are characterized by their dielectric permittivity and their magnetic permeability. The chiral is also specified by its chiral parameter. As a result it is found that surface wave excitation is theoretically possible. The range of values of the chiral parameter in which surface waves can be excited is very narrow and depends on the constants of both media. The condition that at least one of the media must be dissipative seems to be necessary to have excitation. To obtain these results, the dispersion relation of the interface is deduced. Chiral media are described by the Drude–Born–Fedorov constitutive equations. The exact dependence of the fields on the chiral parameter is kept in the computation.     

Material ratchetting of beam under steady axial load and cyclic bending

Abstract

The purpose of this paper is to extend the applicability of the complete differential elasto‐plastic constitutive equations of the endochronic theory to describe the material ratchetting of a beam under a steady axial load and cyclic bending. Based on the assumption of the linear distribution of the through‐thickness strain of a beam under cyclic bending, the stress‐strain behavior of each through‐thickness point can be found theoretically. Experimental data of a lead alloy under a steady axial load and cyclic bending from Hyde et al. are used for comparison with theoretical predictions. It is shown that the theoretical results are in agreement with the experimental data.     

Generalised constitutive equations for densification of metal matrix coated fibre composites

Abstract

The present paper completes a study of constitutive equations for the consolidation processing of continuous fibre reinforced metal matrix composite materials. It builds on an earlier paper in which physically based constitutive equations were derived for the case of symmetrical, isostatic loading. In the present paper, constitutive equations are developed for in plane, general stress states. The total deformation of the consolidating composite is expressed as the sum of a conventional deviatoric creep term, together with a dilatational term, which was derived using a variational method previously published. The equations contain only two material parameters, which are the conventional creep coefficient and exponent for the fibre coating material (in this case, Ti-6Al-4V). The resulting equations have been implemented into finite element software enabling the simulation of practical consolidation processes. The model has been verified by comparing predicted results with those obtained from independent micromechanical models. A number of experimental tests have been carried out, and the model is used to predict the rates of densification for a range of experimental pressure and temperature histories. Good comparisons have been achieved.     

Internal symmetry groups for perfect elastoplasticity under axial‐torsional loadings

Abstract

In the material modeling of experimental axial‐torsional strain control tests, the hoop and radial strains are always unknown, a priori, and hence can not be viewed as inputs. This greatly complicates constitutive model analyses because the resulting differential equations become highly nonlinear. To tackle this problem, we demonstrate two new formulations. By using the two‐integrating factors idea we derive two Lie type systems in the product space M ¹⁺¹?M ¹⁺¹. The Lie algebra is the direct sum so(1, 1)?so(1, 1), and correspondingly the symmetry group is the direct product SO_o (1, 1) ?SO_o (1, 1). Then, by using the one‐integrating factor idea we convert the nonlinear constitutive equations to a Lie type system X=A(X, t)X with A?sl(2, 1, R), a Lie algebra of the special orthochronous pseudo‐linear group SL(2, 1, R). The underlying space is a cone in the pseudo‐Riemann manifold. Consistent numerical methods are also developed according to these Lie symmetries.     

Comparing the Compressibility of Ludipress with the Other Direct Tableting Agents by Using Acetaminophen as an Active Ingredient

Abstract

Ludipress is a direct tableting agent which acts as an unique component, is really a multi component. In this study Ludipress compressibility and powder technological properties are compared with the other kind of DC agents (Avicel PH 102, Elcema G 250 and Elcema P 050) which are structurally based on cellulose. Acetaminophen has been chosen as an active ingredient.

The compression properties of powders and three direct tableting agent were investigated using the Heckel and Kawakita equations. Each formulations and compressed tablets which are compacted by hydraulic press with different pressure value were photographed by scanning electron microscope.

As a result Ludipress shows stable flow properties and the dilution potential of Ludipress is lower than the other DC agents.     

On the concept of relative and plastic spins and its implications to large deformation theories. Part I: Hypoelasticity and vertex-type plasticity

Summary The concept of relative spinW _D/S is introduced to facilitate the formulation of large deformation stress-rate models of inelasticity. Roughly speaking, it is a measure of non-coaxiality between stress and deformation rate of the formW _D/S =W–W _S withW _S andW signifying the angular velocities or spins of the two material frames corresponding to the stress and strain rate respectively. It is suggested that an objective stress rate be defined with respect toW _S for use in the constitutive equations and this requires explicit representations forW _D/S reflecting the aforementioned non-coaxiality. It is shown that this practice leads conveniently to an elegant generalization of previous proposals resorting to either use of a variety of different spins or considerably complex constitutive equations, in order to dispense with undesirable oscillatory solutions of simple shear problems.With 5 Figures     

Structure and mechanism of the deformation of Grade 2 titanium in plastometric studies

ABSTRACT

In this paper, the results of plastometric and material studies on grade 2 titanium are presented. Cylindrical titanium samples were compressed at elevated temperatures on a Gleeble thermo-mechanical simulator. The process was captured in the form of stress-strain diagrams. Then, for the chosen-deformed samples, structural studies were performed on a digital light microscope. On the basis of the results, it was possible to determine the plastometric processing conditions that are most suitable for the fragmentation of the grains of the tested titanium. In order to find optimal processing parameters, it was also important to describe the plastometric process through the appropriate constitutive equations. Material constants in this equation were determined on the basis of a hyperbolic sinusoidal equation.

This paper is part of a thematic issue on Titanium.     

Model for consolidation of Ti-6AI-4V/SiC fibre composite from plasma sprayed monotape

Abstract

A model has been developed for the consolidation of low pressure plasma sprayed (LPPS) titanium alloy matrix/silicon carbide fibre composites. Empirical constitutive equations were combined with an analytical model to describe the deformation of the rough surface region. The same constitutive equations were combined with alternately analytical and empirical yield criteria to describe the deformation of the regions of closed porosity surrounding the fibres. The two submodels were then combined with finite element analysis to make predictions of relative density and grain size as functions of pressure, temperature, and time, as well as predictions of the variations in porosity with position and fibre spacing. Experiments to validate the model were carried out using Archimedes' principle and both optical and scanning electron metallography. Data were found to agree reasonably well with predicted values.     

Analysis of vapor condensation in porous media

Abstract

The present work analyzes the problem of vapor condensation in porous media. Specific consideration is given to a transient‐state one‐dimensional formulation, representing a porous slab exposed to the saturated vapor from one side and the cold plate on the other side. When condensation occurs, three zones will exist inside the porous medium. Near the cold plate, a liquid zone is expected. Adjacent to this zone and extending into the medium will be a two‐phase zone which is dominated by capillary and vapor phase transport. Ahead of this zone the medium will remain saturated with vapor phase. Predictions from the three‐zone model used in this study have been compared with the two‐zone model which neglects the effect of surface tension forces. The results show that the two‐zone model can only predict the condensation phenomena in low permeability media. Capillary pressure or surface tension effects become significant and cannot be neglected during the condensation of vapor in high permeability media.     

Elasto‐plastic deformation of upsetting by boundary element method

Abstract

This paper presents the utilization of boundary element method (BEM) to analyze the elasto‐plastic deformation of upsetting problems. Method of successive elastic solutions is used in the nonlinear analysis; both the linear strain hardening and the power law relation are used as constitutive equations of the material. For the later model the slope of strain hardening at each step is modified to a more correct prediction to make the deformation step larger and to obtain better convergence. The result may verify the stress‐strain curve as it does, and verify the similar pattern of the plastic zone propagation as Roll's result by finite element method. It is shown that various frictional conditions and width‐height ratios of the workpiece also influence the propagation behavior of plastic zones.     

Efficient thermo‐mechanical model for solidification processes

A new, computationally efficient algorithm has been implemented to solve for thermal stresses, strains, and displacements in realistic solidification processes which involve highly nonlinear constitutive relations. A general form of the transient heat equation including latent‐heat from phase transformations such as solidification and other temperature‐dependent properties is solved numerically for the temperature field history. The resulting thermal stresses are solved by integrating the highly nonlinear thermo‐elastic‐viscoplastic constitutive equations using a two‐level method. First, an estimate of the stress and inelastic strain is obtained at each local integration point by implicit integration followed by a bounded Newton–Raphson (NR) iteration of the constitutive law. Then, the global finite element equations describing the boundary value problem are solved using full NR iteration. The procedure has been implemented into the commercial package Abaqus (Abaqus Standard Users Manuals, v6.4, Abaqus Inc., 2004) using a user‐defined subroutine (UMAT) to integrate the constitutive equations at the local level. Two special treatments for treating the liquid/mushy zone with a fixed grid approach are presented and compared. The model is validated both with a semi‐analytical solution from Weiner and Boley (J. Mech. Phys. Solids 1963; 11 :145–154) as well as with an in‐house finite element code CON2D (Metal. Mater. Trans. B 2004; 35B (6):1151–1172; Continuous Casting Consortium Website. http://ccc.me.uiuc.edu [30 October 2005]; Ph.D. Thesis, University of Illinois, 1993; Proceedings of the 76th Steelmaking Conference, ISS, vol. 76, 1993) specialized in thermo‐mechanical modelling of continuous casting. Both finite element codes are then applied to simulate temperature and stress development of a slice through the solidifying steel shell in a continuous casting mold under realistic operating conditions including a stress state of generalized plane strain and with actual temperature‐dependent properties. Other local integration methods as well as the explicit initial strain method used in CON2D for solving this problem are also briefly reviewed and compared. Copyright © 2006 John Wiley & Sons, Ltd.     

Strain energy density – a molecular appraisal

Abstract

The interaction potential between two clusters simulating the crack tip on the lattice level is derived in this work. Employing molecules as the building blocks and the Lennard‐Jones potential as the Green's function, the close‐form solution shows that the 1/r‐type of singularity is an intrinsic behavior of the energy field when mutual attraction dominates the lattice interactions. This behavior is now proven, explicitly, to be independent of the constitutive equation of the material.     

Analysis of first‐order partial differential equations via shifted Chebyshev polynomials

Abstract

The method of Chebyshev polynomials is introduced to represent approximate solutions of first‐order partial differential equations consisting of two independent variables. A set of linear algebraic equations is obtained by using the properties of Chebyshev polynomials and Kronecker product to analyse first‐order partial differential equations. The coefficient vector of Chebyshev polynomials of the first‐order partial differential equations can be obtained directly from Kronecker product formulas, which are suitable for computer computation. A numerical example for a set of first‐order partial differential equations is solved by a Chebyshev polynomials approximation and the results are satisfactory.     

A new boundary integral equation method for analysis of cracked linear elastic bodies

Abstract

A novel integral equation method is developed in this paper for the analysis of two‐dimensional general anisotropic elastic bodies with cracks. In contrast to the conventional boundary integral methods based on reciprocal work theorem, the present method is derived from Stroh's formalism for anisotropic elasticity in conjunction with Cauchy's integral formula. The proposed boundary integral equations contain boundary displacement gradients and tractions on the non‐crack boundary and the dislocations on the crack lines. In cases where only the crack faces are subjected to tractions, the integrals on the non‐crack boundary are non‐singular. The boundary integral equations can be solved using Gaussian‐type integration formulas directly without dividing the boundary into discrete elements. Numerical examples of stress intensity factors are given to illustrate the effectiveness and accuracy of the present method.     

Effect of carbon content on plastic flow behaviour of plain carbon steels at elevated temperature

Abstract

In the present study the effect of carbon composition on the hot flow behaviour of two different plain carbon steels is analysed. For this purpose the constitutive equations describing the stress–strain (σ–?) relationships at a given strain rate ? and temperature T were determined for each steel. Uniaxial hot compression tests were performed to characterise the mechanical behaviour of the alloys. It was observed that irrespective of the test conditions, the low carbon steel displayed similar flow stresses to the high carbon steel. Comparison of the characteristic parameters of the constitutive equations describing the high temperature flow behaviour of these steels, together with values reported in the literature enabled determination of the effect of carbon content on flow behaviour. It has been found that flow stresses can be rationalised as a balance between work hardening and softening processes (basically dynamic recovery). At high temperatures and small strain rates, the high carbon steel showed lower hardening rates and slower dynamic recovery kinetics than the low carbon steel. In contrast, at low temperatures and large strain rates, the high carbon steel displayed higher hardening rates and recovery rates than the low carbon steel.     

Simulation of penetration into porous geologic media

We present a computational study on the penetration of steel projectiles into porous geologic materials. The purpose of the study is to extend the range of applicability of a recently developed constitutive model to simulations involving projectile penetration into geologic media. The constitutive model is nonlinear, thermodynamically consistent, and properly invariant under superposed rigid body motions. The equations are valid for large deformations and they are hyperelastic in the sense that the stress tensor is related to a derivative of the Helmholtz free energy. The model uses the mathematical structure of plasticity theory to capture the basic features of the mechanical response of geological materials including the effects of bulking, yielding, damage, porous compaction and loading rate on the material response. The new constitutive model has been successfully used to simulate static laboratory tests under a wide range of triaxial loading conditions, and dynamic spherical wave propagation tests in both dry and saturated geologic media.     

Sequentially linearizable initial‐boundary value problems for a neo‐hookean cylinder

Abstract

The sequential linearizabilities of some initial‐boundary value problems for the plane‐strain equations of motion of the neo‐Hookean solid are studied. The initial‐boundary value problems are formulated for a cylinder in plane‐strain condition and subjected to shear and radial deformations or tractions on its inner and outer surfaces. The results obtained extend the previous concept about the sequential linearizability of the governing equations for the neo‐Hookean solid to the sequential linearizability of initial‐boundary value problems for the governing equations.     

Experimental Determination of the Mechanical Behaviour of Compacted Exfoliated Vermiculite

A series of compacted exfoliated vermiculite samples were prepared, and their mechanical behaviour was experimentally studied. The vermiculite was first exfoliated and after compacted in order to obtain a material with good thermal and mechanical properties. The as‐prepared samples have been tested under compressive loading. Some parameters effect was studied, as the porosity and the type of the compacted exfoliated vermiculite. The samples of this porous media display two steps for the stress–strain behaviour under uniaxial compressive loading, that is initial nonlinear deformation, strain‐hardening ‘pseudo‐platform’ stage.     

Studies on constitutive equations of first and second order viscoelasticity

Summary The first and second order constitutive equations of continuous media with fading memory are formulated in this paper based on the mechanical theory and the appropriate invariant theoretics. Both isotropic and transversely isotropic media are studied. Restrictions imposed by the theory of irreversible (non-equilibrium) thermodynamics lead to further simplifications.

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Zusammenfassung Ausgehend von den Grundlagen der Mechanik und der entsprechenden Invariantentheorie werden Grundgleichungen erster und zweiter Ordnung für Kontinua mit Erinnerungsschwund formuliert. Es werden sowohl isotrope als auch orthotrope Medien studiert. Beschränkungen, die durch die irreversible Thermodynamik auferlegt werden, führen zu Vereinfachungen.

     

Mixed finite element method for coupled thermo‐hydro‐mechanical process in poro‐elasto‐plastic media at large strains

A mixed finite element for coupled thermo‐hydro‐mechanical (THM) analysis in unsaturated porous media is proposed. Displacements, strains, the net stresses for the solid phase; pressures, pressure gradients, Darcy velocities for pore water and pore air phases; temperature, temperature gradients, the total heat flux are interpolated as independent variables. The weak form of the governing equations of coupled THM problems in porous media within the element is given on the basis of the Hu–Washizu three‐filed variational principle. The proposed mixed finite element formulation is derived. The non‐linear version of the element formulation is further derived with particular consideration of the THM constitutive model for unsaturated porous media based on the CAP model. The return mapping algorithm for the integration of the rate constitutive equation, the consistent elasto‐plastic tangent modulus matrix and the element tangent stiffness matrix are developed. For geometrical non‐linearity, the co‐rotational formulation approach is utilized. Numerical results demonstrate the capability and the performance of the proposed element in modelling progressive failure characterized by strain localization and the softening behaviours caused by thermal and chemical effects. Copyright © 2005 John Wiley & Sons, Ltd.