A coupled three-phase soil model, consisting of a deformable soil skeleton and the fluid phases water and compressed air, applicable for tunnelling below the ground-water table by means of compressed air, is presented. In this model interactions of the flow of the fluids in the soil with the deformations of the soil skeleton are taken into account in a physically consistent manner. The theoretical background and the implementation of the model into a finite element code are briefly addressed. Several applications dealing with the numerical simulation of laboratory tests and a full-scale in-situ experiment are discussed. These experiments focus on the flow of (compressed) air in dry as well as semi-saturated soil.

O.D. Makinde, T.M. Acho, P. Sibanda and E.M. Lungu. The biomechanics of atherosclerosis development. CAMES 2003 (10)

In this paper, we investigate the bio-mechanics of atherosclerosis development in human physiology. Blood is modelled as an incompressible fluid of variable viscosity flowing in a slightly diverging channel (i.e. large artery) of small aspect ratio [1]. The hypothetical viewpoint in this work is the existence of relationship between the atherosclerosis development, blood viscosity, flow separation and turning points in the flow field. The problem is tackled by asymptotic approximation and the graphical results are discussed quantitatively.
[1] O.D. Makinde. Effect of variable viscosity on arterial blood flow. Far East J. Appl. Math., 4(1): 43-58, 2000
*Keywords:* aorta, blood viscosity, bifurcation study, atherosclerosis development.

A.V. Kuznetsov. Limitation of the single-domain numerical approach: Comparisons of analytical and numerical solutions for a forced convection heat transfer problem in a composite duct. CAMES 2003 (10)

The aim of this paper is to establish the bounds of applicability of the single-domain numerical approach for computations of convection in composite porous/fluid domains. The large number of papers that have utilized this numerical approach motivates this research. The popularity of this approach is due to the simplicity of its numerical formulation. Since the utilization of the single-domain numerical approach does not require the explicit imposing of any boundary conditions at the porous/fluid interface, the aim of the this research is to investigate whether this method always produces accurate numerical solutions.

S.-J. Wu, M.-H. Chang and Y.-M. Hwang. Three-dimensional finite element simulations of various roll's shape during three-roll planetary rolling processes. CAMES 2003 (10)

The purpose of this paper is to analyze the bar rolling process by means of various roll's shapes under the reduction zone of a three-roll planetary mill. The problems were solved with the aid of the finite element program MARC adopting the large deformation-large strain theory and the updated Lagrangian formulation (ULF) and a mesh rezoning procedure was adopted to improve the unexpected error of element turning inside out. The mesh system of the whole bar billet was established by using three-dimensional brick elements, and the three-dimensional elastic-plastic finite element model in MARC was chosen to perform the simulation of the three-roll planetary rolling processes. Totally five different roll's shapes were used to simulate the rolling process. The numerical results; such as the equivalent von Mises stress and plastic strain distributions, rolling force, rolling moment, billet speeds at the entrance and exit planes of the roll gap, etc., are useful in the design of three-roll planetary rolling processes.
*Keywords:* three-roll planetary rolling process, mesh rezoning, roll's shape design.

R. Younsi, A. Harkati and D. Kalache. Numerical simulation of heat and mass transfer in composite fluid-porous layer with transverse magnetic field. CAMES 2003 (10)

The aim of this paper is to simulate numerically the two-dimensional steady state double diffusive flow in a composite fluid-porous layer, submitted to a transverse magnetic field. Both the temperature and solute gradients are imposed horizontally, and the two-buoyancy effects can either augment or counteract each other. The Darcy equation, including Brinkman and Forchheimer terms to account for viscous and inertia effects, respectively is used for the momentum equation, and the SIMPLER algorithm, based on finite volume approach is used to solve the pressure-velocity coupling. An extensive series of numerical simulations is conducted in the range: tic field. Both the temperature and solute gradients are imposed horizontally, and the two-buoyancy effects can either augment or counteract each other. The Darcy equation, including Brinkman and Forchheimer terms to account for viscous and inertia effects, respectively is used for the momentum equation, and the SIMPLER algorithm, based on finite volume approach is used to solve the pressure-velocity coupling. An extensive series of numerical simulations is conducted in the range: *Ra*=1e5, 1e-8<=*Da*<=1, *N*=1, *Le*=10 and *Ha*<=100. This study is limited to *Pr*=7 for the binary solution of (Na2Co3). This choice is motivated by the experimental work on phase change realized in laboratory. It is shown that the main effect of the porous layer is to reduce the heat and mass transfer when the permeability is reduced. Isotherms and streamlines are plotted for several values of Hartman (*Ha*), Darcy number (*Da*) and porous layer thickness (*Xp*). The effect of the magnetic field is found to be rather significant on the flow pattern, heat and mass transfer.
*Keywords:* double diffusion, porous media, magneto-hydrodynamics, finite volume method.

P. Dluzewski, G. Jurczak and H. Antunez. Logarithmic strain measure in finite element modelling of anisotropic hyperelastic materials. CAMES 2003 (10)

A new finite element to analyze problems of *anisotropic* hyperelasticity is presented. The constitutive equations are derived by means of the energy method, which leads to the stress measure conjugate to the logarithmic strain. Equilibrium equation are integrated in the current configuration. Multiplicative - instead of additive - decomposition of the time derivative of a strain tensor function is applied as a crucial step that makes possible the formulation for anisotropic hyperelastic materials. Unlike previous known anisotropic large deformation models, the one here presented assures the energy conservation while using the anisotropic elastic constants and the logarithmic strain measure. It is underlined that for the first time a model including all these features is presented. Some numerical examples are shown to illustrate the results obtained with this model and to compare them with other known anisotropic models.
*Keywords:* finite element method, logarithmic strain measure, elastic material, anisotropic material, constitutive behaviour.

A. Glema, T. Lodygowski and P. Perzyna. Localization of plastic deformations as a result of wave interaction. CAMES 2003 (10)

The main objective of the paper is the investigation of the interaction and reflection of elastic-viscoplastic waves which can lead to localization phenomena in solids. The rate type constitutive structure for an elastic-viscoplastic material with thermomechanical coupling is used. An adiabatic inelastic flow process is considered. Discussion of some features of rate dependent plastic medium is presented. This medium has dissipative and dispersive properties. In the evolution problem considered in such dissipative and dispersive medium the stress and deformation due to wave reflections and interactions are not uniformly distributed, and this kind of heterogeneity can lead to strain localization in the absence of geometrical or material imperfections. Numerical examples are presented for a 2D specimens subjected to tension, with the controlled displacements imposed at one side with different velocities. The initial-boundary conditions which are considered reflect the asymmetric (single side) tension of the specimen with the opposite side fixed, which leads to non-symmetric deformation. The influence of the constitutive parameter (relaxation time of mechanical perturbances) is also studied in the examples. The attention is focused on the investigation of the interactions and reflections of waves and on the location of localization of plastic deformations.

J. Szuba and A. Borkowski. Graph transformations in architectural design CAMES 2003 (10)

This paper deals with computer-aided design of layouts of buildings. The methodology based upon graph grammars and graph transformations allows the designer to distract itself from details and to consider the functionality of the designed object, the constraints and the requirements to be met and the possible ways of selecting optimum alternatives. The specification of building is made in the UML with the aid of the FUJABA system. After this has been accomplished, a proper graph grammar is generated automatically. Such a grammar defines a class of objects that fulfill prescribed requirements and deliver required functionality. The user of the proposed system can browse members of that class, i.e. compare alternative plausible designs, using any commercially available visualization tool.