Journal of Theoretical and Applied Mechanics

Volume 35, Number 4, 2005



Stanimir Iliev, Nina Pesheva


Institute of Mechanics, Bulgarian Academy of Sciences,

Acad. G. Bonchev Str., Bl. 4, 1113 Sofia, Bulgaria,



Asymptotic solutions of the quasi-static relaxation of liquid drops taking into account the dissipation during the contact line motion


Abstract. The spontaneous quasi-static relaxation dynamics of liquid drops on solid surfaces in the partial wetting regime is studied. We base our study on the phenomenological approach suggested in de Ruijter et al. (Langmuir 15 (1999) 2209-2216) which uses the standard mechanical description of dissipative system dynamics and which introduces a phenomenological dissipation term proportional to the contact line length. We derive here asymptotic solutions of the differential equations describing the base radius and the contact angle relaxation, for small initial deviations of the base radius from the final equilibrium value in the case of spherical cap approximation of the drop shape. We find that the time relaxation of the base radius and the contact angle are given by a sum of exponential functions up to a second order in the expansion of the small parameter. We compare the asymptotic solutions with the numerically obtained solutions and we find a very good agreement.


Key words: liquid drops, relaxation, dissipative system dynamics, dynamic contact angles.


Nina Philipova


Institute of Mechanics, Bulgarian Academy of Science,

Acad. G. Bonchev Str., Bl. 4, 1113 Sofia, Bulgaria,





Abstract: A model for hydraulic design of drip irrigation lateral is developed by applying the theory of spatially varied flow. The influence of the temperature on the kinematics viscosity of water is read by a coefficient in the formula of Darcy-Weisbach for head loss due to friction. A block-scheme is made by using SIMULINK-MATLAB for solving the determined two differential equations. As a result diagrams for distribution of flow rate, pressure head along the pipe length and some other characteristics are obtained.


Key words: spatially varied flow, drip irrigation, hydraulic design.


H. Smilkov, Ch. Betchev


University of Chemical Technology and Metallurgy,

8, St. Kl. Ohridski Blvd., 1756 Sofia, Bulgaria,



G. Georgiev


Faculty of Chemistry, Sofia University St. Kl. Ohridski”,

1, J. Bourchier Blvd., 1164 Sofia, Bulgaria




Abstract. The method of Dynamic Mechanical Analysis (DMA) has been used for the mechanical properties determination of polyzwitterionic hydrogels based on the sulphobetaine monomer 3-Dimethyl-(Methacryloyloxyethyl) Ammonium Propane Sulfonate (DMAPS) and cross-linked by Ethylene glycol DiMetAcrilate (EDMA). The investigations performed show that the dynamic mechanical modulus of these hydrogels increases with temperature and degree of cross-linking. This experimental result confirms a theoretical model for self-alignment of the polyzwitterions in solution, hydrogel and solid state. In accordance with this model, domains from contrary oriented dipoles incorporated in polyzwitterions side chains were created as a result of the self-alignment. Evidences for destruction and formation of these domains were identified by a differential scanning calorimetry.


Key words: dynamic mechanical analysis, polyzwitterionic hydrogel, self-organization.


N. Nikolov, A. Baltov


Institute of Mechanics, Bulgarian Academy of Sciences,

Acad. G. Bontchev Str. Bl. 4, Sofia 1113, Bulgaria,



Influence of the size and structure of grains on the mechanical behaviour of nanocrystalline materials


Abstract. A numeric parametrical analysis of the mechanical behaviour of nano-crystalline materials is performed depending on both the structure and mechanical characteristics of grains. The grains are composed from a central elastic part having a plastic cover. The models of linear elastic body are used as mechanical characteristics of central elastic part on meso-level. The models of perfect plastic and elastic–plastic bodies describe the plastic properties of grain plastic covers. The profiles of strain and stress distributions in the loaded end of samples containing 1, 4, 5 and 20 grains are given. For two cross sections it is established that the material is deformed according to different hardening curves depending on the mechanical properties, sizes and structures of the nano-crystalline grains. The maximum strain and stresses in the sample are given depending on the thicknesses of plastic covers and the grain sizes. The respective conclusions are drawn.


Key words: nano-materials, structures, mechanical behaviour.


R. Krieg


Forschungszentrum Karlsruhe GmbH, Institut für Reaktorsicherheit,

Postfach 3640, 76021 Karlsruhe, Germany


M. F. Robbe


Commissariat à l’Energie Atomique de Saclay,

Bât 120, 91191 Gif sur Yvette cedex, France,



overview of German and French works relative to slug impact. PART 1: EXPERIMENTAL RESULTS


Abstract. One of the possible consequences of an in-vessel steam explosion in a PWR is the upward acceleration of a slug of molten fuel and its impact against the upper head of the reactor pressure vessel. The impact may cause a failure of the head and lead to missiles endangering the reactor containment.

Slug impact is studied by the German and French research centres FZK and CEA-Saclay. The experimental aspects are studied by means of the German experiments BERDA. The tests consist in accelerating a projectile against a reduced-scale model of a reactor head and analysing the influence of several parameters of the projectile and the head on the head response.


Key words: impact, projectile, failure, nuclear reactor, safety.


Gergana Nikolova


Institute of Mechanics, Bulgarian Academy of Sciences,

Acad. G. Bonchev Str., Bl. 4, Sofia 1113, Bulgaria,





Abstract. We present a simple geometrical biomechanical model of the Bulgarian woman based on a representative anthropological investigation (2854 females) partially published in Yordanov et al. [1]. The model consists of 14 segments that are relatively simple geometrical figures (frustum of cone, ellipsoid, etc.) and is oriented to application in medicine and engineering. On the basis of the average values obtained in the above investigation we construct the “average” Bulgarian woman with height 1,58 m and mass 65,3 kg. Using the model we calculate analytically and estimate numerically the mass of the segments, as well as their center of mass position and inertial characteristics. Wherever possible we present a comparison with the data available in literature and observe a good agreement with the results of our model.


Key words: body segment parameters, anthropometry, segment mass, center of mass.