Journal of Theoretical and Applied Mechanics
Volume 35, Number 3, 2005
of Mathematics and Informatics,
G. Bonchev Str., Bl. 8, 1113
G. Bonchev Str., Bl. 4, 1113
Steady-State Plane Wave Propagation in Inhomogeneous 3D Media
Abstract. Wave propagation in infinite inhomogeneous 3D media with spatial co-ordinate–dependent elastic characteristics is studied analytically.
A restricted case of inhomogeneity is considered, where the Poisson’s ratio is fixed at one-quarter, while both shear modulus and density profiles vary proportionally to each other. For this specific case, the body wave speeds remain macroscopically constant and this allows to be recovered the wave equation of 3D elastodynamics for homogeneous case by using the appropriate algebraic transformation method. Two type of inhomogeneous materials are considered: (a1); (a2), where is the shear modulus in homogeneous case.
Two boundary-value problems are solved: (A) wave propagation in infinite 3D space with both types (a1) and (a2) of inhomogeneous material; (B) wave propagation in elastic half-space with quadratic (a1) and exponential (a2) type of inhomogeneity for normal incident longitudinal P-wave. Analytical plane-wave decomposition method is used for solution of the posed problems.
The parametric study done demonstrates that wave fields are sensitive on the type of the inhomogeneous material, on the characteristics of the incident wave and on the geometrical position of the observer.
Key words: wave propagation, inhomogeneous half-space, exponential and square type of inhomogeneity, free-surface and subsurface response analysis.
Laboratore PMMH, CNRS UMR 7636, Groupe de Physique Thermique,
ESPCI, 10 rue Vauquelin, 75231
Acad. G. Bonchev
Str., Bl. 4, 1113
Technical University of
Modelling the impact and spreading of a drop on a dry surface
Abstract. The literature about the problems involving only isothermal processes at drop impact on dry surfaces is reviewed. Some classifications of the observed processes are presented. The threshold between spreading and splashing is discussed. It is shown that a new model of double wave structure overcomes some of prior existing discrepancies between theory and observations. The numerical models, according to the used methods, are divided into two main groups: shock-capturing methods (and other similar methods) and front-tracking methods. Some numerical results show that if viscous forces are not included in the model, the jet velocity is much higher than the experimentally registered and the jetting time is much shorter. However, the viscosity inclusion in the model leads to prominent results in good agreement with experimental ones.
Key words: drop impact, spreading on a dry surface, splashing, numerical modelling.
Department of Astrophysics, Geophysics and Oceanography,
du 6 Aout, B 4000 Liège,
Acad. G. Bonchev Str., Bl. 4, 1113
Ecole Polytechnique, Université de Montreal, Génie Chimique,
Montreal H3C3A7, Canada,
A THERMODYNAMIC DERIVATION OF DRUCKER'S WORK HARDENING RELATION IN PLASTICITY
Abstract. A thermodynamic derivation of the celebrated Drucker relation, one of the key results in the theory of plasticity, is proposed. This is accomplished by using the so-called "Extended Irreversible Thermodynamics" whose basic idea is to elevate the thermodynamic dissipative fluxes to the status of independent variables. In the present analysis, these extra variables will be identified as the components of the plastic stress tensor.
Key words: plasticity, Drucker's relation, irreversible thermodynamics.
Acad. G. Bonchev
Str., Bl. 4, 1113
DIE ROUNDNESS RADIUS ANALYSIS FOR DIFFERENT METALS DURING DEEP DRAWING PROCESS
Abstract. This paper is devoted to the analysis of the material behaviour of five different metal structures (Steel 08 and 10, Aluminum, Copper and Brass 63) by their ability for the relaxing of the complex stress-strain states arisen in the blank volume depending on the lowest critical die roundness radius during deep drawing process.
The deep drawing process is simulated by using ADM and FEM numerical codes. The results are presented by “Drawing Force – Punch Travel”–diagrams. On the base of difference in the diagrams the conclusions are drawn that the ordered cubic body centered structures of Steel 10 and Brass 63 show a different kind of breaking in comparison with the cubic face centered lattice of Aluminum and Copper.
Key words: deep drawing process, approximate discrete method, finite element method, die roundness radii.
Bonchev Str., Bl. 4, 1113
MATHEMATICAL ANALYSIS OF STRESS INDUCED PRESSURE RELAXATION IN OSTEONS
Abstract. The objective of the present study is to present a new approach to explaining the experimentally observed relaxation times at stress induced fluid flow in bone. The principle idea is based on the assumptions for fluid exchange between the lacunar-canalicular system and the matrix micro-porosity. The basic difference between the present concept and the concept exploited by Cowin and co-workers (1994, 1995, 1997, 1998, 1999) is in the acceptance of interstitial fluid flow at the micro-structural level. Cowin and co-workers entirely reject the idea of fluid exchange between the lacunar-canalicular porosity and micro-porosity, which is in contradiction with the physiological point that each bone compartment including the micro-porosity should be fluidly acceptable for metabolic exchange processes. On the base of mathematical analysis of anatomical model of Petrov and Pollack (2000) the experimental observation of two relaxation times, at step type bone samples loading, is explained quantitatively for first time in the literature.
Key words: stress induced, fluid flow, bone osteon.