Issue 3
JTAM, Sofia, vol. 34 Issue 3 (2004)

Extended Thermodynamics of Thermo-Elasticity, Visco-Elasticity and Visco-Plasticity

G. Lebon1, A. Baltov2, M. Grmela3
1Liège University, Department of Astrophysics, Geophysics and Oceanography, 17 Allée du 6 Aout, Sart Tilman B5, B 4000 Liège, Belgique
2Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 4, 1113 Sofia, Bulgaria
3University of Montreal, Ecole Polytechnique, Génie Chimique, Montreal H3C 3A7, Canada


The objective of this paper is to propose an original description of thermo-elasticity, visco-elasticity and visco-plasticity based on Extended Irreversible Thermodynamics. Although the latter has been widely used as a support of fluid mechanics, this work is a first attempt to apply this thermodynamic formalism to deformable solids. After a short recall of the bases and tenets of Extended Irreversible Thermodynamics, we consider as a first application the problem of thermo-elasticity, i.e. the simplest coupling between heat transport and deformation. The most original result is that the classical Fourier law is substituted by a Cattaneo equation allowing for the effects of inertia. In a second part, one examines the more complex behaviour of visco-elastic bodies before dealing, in a further section, with the problem of visco-plasticity. The originality of the present description compared to more classical treatments is emphasised. It is shown that Extended Irreversible Thermodynamics opens the way to a simple and attractive approach of these important aspects of continuum mechanics and that, contrarily to some criticisms, it accommodates the case of deformable solids.

JTAM, Sofia, vol. 34 Issue 3 pp. 01 (2004)

Nonconvex Numerical Approach to the Seismic Soil-Pipeline Interaction under Instabilizing Environmental Effects

A. A. Liolios1, K. A. Liolios1, S. Radev2, T. Angelov2
1Democritus University of Thrace, Dept. Civil Engineering & Dept. of Environment Engineering, GR-67100 Xanthi, Greec
2Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 4, 1113 Sofia, Bulgaria

A numerical approach is presented for an hemivariational inequality problem arising in structural engineering. This problem concerns the dynamic soil-pipeline interaction under soil degradation caused by environmental effects. Unilateral contact conditions due to tensionless and elastoplastic softening-fracturing behaviour of the soil as well as due to gapping are taken into account. The numerical approach is based on a double discretization, in space by FEM and /or BEM and in time, and on nonconvex optimization. So the number of the problem unknowns is significantly reduced and a nonconvex linear complementarity problem is solved in each time-step.

JTAM, Sofia, vol. 34 Issue 3 pp. 02 (2004)
FEM Modelling of Thermo-Mechanical Behaviour of Two-Phase Laminated Plates

L. Parashkevova, J. Ivanova, N. Bontcheva
Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 4, 1113 Sofia, Bulgaria

The FEM is used to study the thermoelastic behaviour of a two-phase functionally graded plate at high temperature loading. The layers are distributed exponentially through the plate thickness. The ceramic phase is brittle elastic with different tensile and compression strength limits. The metallic phase is elastic-plastic. The thermal and mechanical properties of both materials strongly depend on temperature. Several failure criteria at different boundary conditions are applied to predict the stable state of the structures of interest. The optimal design is based on two cost functions, comparing stress-strain fields and temperature variations corresponding to different layer distributions or volume concentrations.

JTAM, Sofia, vol. 34 Issue 3 pp. 03 (2004)
Numerical Modelling of Consolidation with Uncertainty in Soil Properties

R. Iankov1, M. Datcheva1,3, E. Popova2, T. Schanz3
1Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 4, 1113 Sofia, Bulgaria
2Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 8, 1113 Sofia, Bulgaria
3Professur Bodenmechanik, Bauhaus Univ. Weimar, Coudraystrasse 11C, D-99423 Weimar, Duetschland

A coupled hydro-mechanical problem with an uncertain parameter is presented. Application of interval methods of obtaining of sharp safety regions for the response variables under a worst case scenario and for a sensitivity analysis of the mechanical system is demonstrated. A boundary value problem for one-dimensional consolidation under a constant load where the elastic modulus of the solid skeleton is assumed to be uncertain and varying within prescribed bounds is solved. Deterministic and interval solutions are obtained and analysed.

JTAM, Sofia, vol. 34 Issue 3 pp. 04 (2004)
Dynamical Analysis of Cell Function Models. A Review

V. Petrov1, E. Nikolova1, J. Timmer2
1Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl.4, 1113 Sofia, Bulgaria
2Centre for Data Analysis and Modelling, University of Freiburg, Eckerstr. 1, 79104 Freiburg, Germany

The system analysis of cell functions and especially mitosis (growth and division) in eukaryotes is so complex that it defies understanding by verbal arguments only. The insight into details of biochemical kinetics of cell functions requires mathematical modeling of the type practiced in the classical dynamics, i. e. by differential equations. In this paper we review dynamical modeling of cell signal pathways and more in detail - division in eukaryotes. The recent development of dynamical synthesis and analysis of cell function models is described in general terms, and molecular mechanisms of mitosis control are presented verbally. The transition from verbal to mathematical description of Novak-Tyson model of mitosis control is considered, in order to illustrate “in action” the application of dynamical modelling to the cell cycle process. Moreover, a subtle dilemma of bistable or self-oscillatory character of cell cycle is discussed in terms of the theory of dynamical systems.

JTAM, Sofia, vol. 34 Issue 3 pp. 05 (2004)
A Scanning Laser Photometric Technique for Investigation of Erythrocyte Sedimentation

V. Kavardzhikov, N. Kounov, K. Prodanov
Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl.4, 1113 Sofia, Bulgaria

A scanning laser densitometer is elaborated, which is designed for an effective investigation of blood samples with hematocrit values layng in the interval 30%-65%. The densitometer is used for obtaining of blood samples sedimentation pictures after a precise adjustment and callibration. One of these pictures is demonstrated as an example. Density fluctuations of sedimenting erythrocyte substantion, having relatively high spatial frequences, are clearly visualized and monitored for a first time.They reveal a structure formation in the sediment during the first two hours of sedimentation process. A numerical processing and parametrisation of the sedimentation pictures utilizing unitary Karhunen-Loeve transformation is carried out.

JTAM, Sofia, vol. 34 Issue 3 pp. 06 (2004)