The generalized finite element method: an example of its implementation and illustration of its performance

The generalized finite element method (GFEM) was introduced in Reference 1 as a combination of the standard FEM and the partition of unity method. The standard mapped polynomial finite element spaces are augmented by adding special functions which reflect the known information about the boundary value problem and the input data (the geometry of the domain, the loads, and the boundary conditions). The special functions are multiplied with the partition of unity corresponding to the standard linear vertex shape functions and are pasted to the existing finite element basis to construct a conforming approximation. The essential boundary conditions can be imposed exactly as in the standard FEM. Adaptive numerical quadrature is used to ensure that the errors in integration do not affect the accuracy of the approximation. This paper gives an example of how the GFEM can be developed for the Laplacian in domains with multiple elliptical voids and illustrates implementation issues and the superior accuracy of the GFEM versus the standard FEM. Copyright © 2000 John Wiley & Sons, Ltd.     

The plastic flow and finite element simulation of plastic fine blanking

An idea of fine blanking is put forward where negative clearance affects plastic shearing and the plastic state of material in the shearing zone is examined under the condition of negative clearance. By analyzing of blanking force and stress, the paper brings forward a method of setting up the three-directions pressed stress. The method determines if the material of deformation field enters the plasticity regime. Some parameters that control when the material of blanked zone enters into the plastic state are given. The analysis indicates that the material stays in the plastic regime, when the specific energy of elastic deformation for common carbon steel Q235 reaches 8.34 MPa. The status of plastic flowing in the shearing zone is simulated.     

The role of disconnections in phase transformations

The topological model of phase transformations is described in terms of disconnections. Disconnection motion is shown to produce a variety of phase transformations with accompanying plastic strain. These strains, together with elastic strains associated with equilibrium arrays of interface defects, define expected habit planes and orientation relationships. Non-equilbrium defect arrays resulting from kinetic constraints are discussed. Example applications of the topological model are presented for several types of martensitic transformations and several examples of diffusional transformations.     

A simple approach towards fully stressed design in hyperelasticity exploiting the isoparametric finite element concept

A novel approach towards fully stressed designs in hyperelasticity is discussed leading to closed‐form expressions for the sensitivities of the objective and displacements with respect to design variations. The key idea is the modification of the classical approach coupled with a so‐called design element method offering a lot of parallelism to standard finite element methods. We bypass implicit constraints on dependent quantities and derive an explicit linearly constrained optimization problem solved by means of first‐order procedures. The results obtained with the proposed method are adequate from an engineering point of view though being computed with a simple method. Copyright © 2000 John Wiley & Sons, Ltd.     

Finite element of slender beams in finite transformations: a geometrically exact approach

This article is devoted to the modelling of thin beams undergoing finite deformations essentially due to bending and torsion and to their numerical resolution by the finite element method. The solution proposed here differs from the approaches usually implemented to treat thin beams, as it can be qualified as ‘geometrically exact’. Two numerical models are proposed. The first one is a non‐linear Euler–Bernoulli model while the second one is a non‐linear Rayleigh model. The finite element method is tested on several numerical examples in statics and dynamics, and validated through comparison with analytical solutions, experimental observations and the geometrically exact approach of the Reissner beam theory initiated by Simo. The numerical result shows that this approach is a good alternative to the modelling of non‐linear beams, especially in statics. Copyright © 2003 John Wiley & Sons, Ltd.     

Power of a simple electric multipole of finite size

A simple electric multipole of finite size in the form of a spherical current sheet with a surface current density in the theta direction varying as sin 2theta is considered. The electromagnetic fields outside the spherical surface are of the same form as that of the corresponding point electric multipole situated at the origin and oriented in the z direction. The power is separated into the radiative and the reactive parts and compared with the separation made on the basis of propagating and evanescent waves. The evanescent waves contribute only to the reactive power, and the propagating waves contribute to both the radiative and the reactive powers. The power flux density is also separated into the real and the reactive parts, and the characteristics of the two parts of the power flux density are discussed.     

Nonequilibrium entropy and the second law of thermodynamics: A simple illustration

The objective of this paper is twofold: first, to examine how the concepts of extended irreversible thermodynamics are related to the notion of accompanying equilibrium state introduced by Kestin; second, to compare the behavior of both the classical local equilibrium entropy and that used in extended irreversible thermodynamics. Whereas the former does not show a monotonie increase, the latter exhibits a steady increase during the heat transfer process; therefore it is more suitable than the former one to cope with the approach to equilibrium in the presence of thermal waves.Paper dedicated to Professor Joseph Kestin.     

Loss of ellipticity and structural transformations in planar simple crystal lattices

This work focuses on investigation of structural (phase) transformations in crystal lattices from continuum and discrete points of view. Namely, the continuum, which is equivalent to a simple lattice in the sense of the Cauchy–Born energy, is constructed using long-wave approximation, and its strong ellipticity domains in finite strain space are obtained. It is shown that various domains correspond to variants of triangular and square lattices, and the number of the domains depends on the interaction potential parameters. Non-convex energy profiles and stress–strain diagrams, which are typical for materials allowing twinning and phase transformations, are obtained on the straining paths which connect the domains and cross non-ellipticity zones. The procedures of the lattice stability examinations and estimation of energy relaxation by means of molecular dynamical (MD) simulation are developed, and experimental construction of the envelope of the energy profiles, corresponding to the energy minimizer, is done on several straining paths. The MD experiment also allows to observe the energy minimizing microstructures, such as twins and two-phase structures.     

Equivalent geometric transformations for spin and orbital angular momentum of light

We consider the analogous geometric transformations for spin and orbital angular momentum states of light. Spin angular momentum is manifested as polarization and its possible transformations are typified by those introduced by waveplates and the rotation associated with optical activity. Orbital angular momentum is associated with the mode structure of the beam and, while the action of a waveplate is similar to that of a mode converter, the equivalent analogue of optical activity is not obvious. We reason that the equivalent is a rotation of the transmitted image. We consider the extent to which an image orientation of this type might be achieved by a coherent fibre bundle, twisted around its central axis. The possibility of equivalents to the Kerr, Pockels and Faraday electro-optic effects for orbital angular momentum is raised.     

Theory of paramagnetic spin waves in simple metals in a direct-current magnetic field

The transverse dynamic spin susceptibility of a normal, charged Fermi liquid is found. The formula depends on the first three antisymmetric Landau parametersB ₀,B ₁,B ₂ and is exact to orderk ² in the expressions both for the energy of spin waves and their oscillator strengths. It contains spin-wave poles with1=0 and 1 and easily reproduces all the results obtained previously by perturbation theory.On leave of absence from: Institute of Physics, University of Lattakia, Syria.     

Phase transformations induced by dislocation glide in plastic deformation of alloys

It has been shown that in intense plastic deformation of alloys, dislocation glide gives rise to nonequilibrium phases or disperse structures. The phenomenon is due to the joint action of two factors: acceleration of diffusion and change in the chemical potential of the alloy components in the region of the dislocation core.     

Mathematical models of anisothermal phase transformations in steels,and predicted plastic behaviour

Abstract

n this paper, the kinetics of anisothermal structural transformations are first discussed. Classical models are shown to raise difficulties because they do not take into account the existence of a temperature–dependent equilibrium proportion of the phases. A very simple model incorporating this factor is proposed and shown to lead to a good correlation between experimental and theoretical results it is also shown to be compatible with the thermodynamics of irreversible processes. The model can be extended to include the possibility of isothermal kinetics of the Johnson–Mehl type, as well as the influence of austenite grain size. The influence of the transformations on plastic behaviour (transformation plasticity) is next discussed. A simple model is described using first purely heuristic considerations, then a more microscopic and physical approach. Possible improvements to this model are suggested, especially the inclusion of the fact that the microscopic plasticity generated by volume differences between the phases must influence not only transformation plasticity (Greenwood–Johnson mechanism), but also ordinary plasticity, which must be present at all points on the stress–strain curve.

MST/10     

The fourth-dimention concept in the finite element analysis of transient heat transfer problems

This study presents the finite element analysis for the transient heat transfer problems by introducing the Fourth-dimension concept. Time is treated as an additional dimension in the solution domain thereby Increasing the number of dimensions by one. For instance, a three-dimensional transient problem can be considered as a four-dimensional problem in the x, y, z, t domain and a two-dimensional transient problem can be considered as a three-dimensional steady-state problem in the x, y, t domain, respectively. The variational principle of the finite element method and the techniques existing for steady-state problems can be directly utilized. Numerical calculations were performed for heat conduction problems, laminar-turbulent convective heat transfer problems, and radiative heat transfer problems.     

The role of knife sharpness in the slitting of plastic films

An experimental apparatus has been built that provides information on forces associated with slitting plastic films. The apparatus uses commercially available scissors as an analogue to the counter-rotating knife blades used in industry. Cutting forces were measured using sharp and worn blades at a range of slitting speeds from 0.05–2.5 m s^–1. Two important film-base materials were studied; the first was polyethylene terephthalate (PET) and the second, acetal butylate. The influences of speed and knife-edge radius were measured for each base material. For the PET-based film, the forces increased as the blade became dull and decreased with cutting speed. At low speeds, the force required to cut the acetal butylate film was independent of speed, but a sharp decrease in force was observed at a speed that depended upon the blade sharpness. An empirical model for the slitting process has been developed that can estimate the forces measured.     

虚拟包装的概念及其应用

论述了虚拟可视包装、虚拟物理包装及虚拟包装件,3种虚拟包装技术在包装工程中的应用,指出虚拟包装的研究和应用,对促进包装工业的发展,有极重要的理论和实际意义.     

Mechanisms of particulate filled polypropylene finite plastic deformation and fracture

The plastic deformation and fracture of aluminium hydroxide filled polypropylene has been investigated. A transition between two mechanisms with an increase of the filler volume fraction has been observed. Below a critical filler volume content φcr ≈ 20 vol% (designated region 1) adhesive failure processes and polymer deformation in the neighbourhoods of different particles occur in an uncorrelated manner. Above this critical value (designated region 2) exfoliation along the surface of the initial portion of inclusions causes the formation of craze-like deformation zones transverse to the direction of the loading. The concentration of craze-like zones is essentially determined by the filler content and the level of interphase interaction which in turn depends on the particle size. In region 1 deformation occurs in a macro heterogeneous way with the formation and growth of a neck. The elongation to break decreases with an increase in the mean diameter of the filler phase. At φ>φcr composites, filled with small particles, fail in quasi brittle manner with the formation of a short and narrow neck. In contrast to the case for a small filler concentration, an increase of the inclusion size leads to an increase in the ultimate elongation and a tendency to macro homogeneous yielding. An explanation of the observed behaviour is proposed based on a change in adhesive failure conditions with filler content and size. This revised version was published online in November 2006 with corrections to the Cover Date.     

The role of plastic strain in the mechanism of fracture of metals

Strength of Materials -     

Effect of loading prehistory on phase transformations in chromium-nickel steel with plastic deformation

Results are given for a study of the kinetics of phase transformations in chromium-nickel austenitic steel with repeated plastic deformation including under conditions when prior and repeated loading differ in temperature and form of stressed state. It is established that prior low-temperature deformation intensifies the process of martensite formation at room temperature whereas deformation under room temperature conditions has almost no effect on martensitic transformation kinetics at low temperature.Translated from Problemy Prochnosti, No. 10, pp. 46–50, October, 1991.     

The role of polymer engineering in designing for reliability of plastic products

Designing of reliable plastic products is hardly possible without having a profound understanding of the structure-related properties of plastics. Fundamental research into several failure mechanisms [J. J. Horst, “Changes in glassfibre reinforced injection moulded polyamide due to fatigue loading,” in: A. J. Kinloch (editor),Deformation, Yield, and Fracture of Polymers, Institute of Materials, London (1994), p. 694] and [J. L. Spoormaker, “Reliable plastic products through applying failure analysis and basic principles,” in: V. V. Panasyuk and D. M. R. Taplin (editors),Selected Papers of the 8th Internat. Conf. on Fracture (ICF8, Kiev, Ukraine, June 1994), Elsevier (Pergamon), Oxford, UK (1994), pp. 555–560] is essential in obtaining a profound understanding of the failure behavior of plastic products. Failures related to the construction of the mold and processing of plastics are often very important and must never be neglected in designing for reliability of plastic products. The analysis and documentation of failed plastic products are essential for preventing designers from repeating the same errors all the time. Testing of speciments and products should be carried out extremely carefully because of the complex material behavior of plastics. Delft University, Delft, The Netherlands. Published is Fizyko-Khimichna Mekhanika Materialiv, Vol. 32, No. 4, pp. 17–22, July–August, 1996.