Journal of Theoretical and Applied Mechanics

Volume 39, Number 2, 2009




Ivanka Stamova


Department of Mathematics, Bourgas Free University,

8000 Bourgas, Bulgaria,



Lyapunov method for boundedness of the solutions of impulsive functional differential equations with respect to sets


Abstract. In the present paper problems related to the boundedness of the solutions of impulsive functional differential equations with respect to sets of sufficiently general type are considered. The investigations are carried out by means of piecewise continuous functions, which are analogues to the classical Lyapunov functions coupled with the Razumikhin technique.


Key words: impulsive functional differential equations, boundedness of the solutions, Lyapunov method, Razumikhim technique.


Stanimir Iliev, Nina Pesheva


Institute of Mechanics, Bulgarian Academy of Sciences,

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



Dimitar Iliev


Department of Mathematics and Informatics, Sofia University,

5, J. Bourchier St., 1164 Sofia, Bulgaria,

e-mail: diliev@fmi.uni–


On the quasi-static relaxation of the contact line in the Wilhelmy-plate geometry: asymptotic solutions of а contact line dissipation model


Abstract. The quasi-static motion of straight contact lines is considered in the context of the “Wilhelmy plate” geometry: a vertical homogeneous solid plate is withdrawn at constant velocity from a bath of liquid. We apply a model, which takes into account explicitly the dissipation due to the moving contact line. Asymptotic solutions are derived of the differential equations describing the capillary rise height of the contact line and the contact angle relaxation. We find that the time relaxation of the height and the cosine of the contact angle are given by sums of exponential functions. The asymptotic solutions are compared with experimental results and with numerically obtained solutions which are based on lubrication theory with a correction factor for finite contact angles.


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


L. Hadj-Taïeb, E. Hadj-Taïeb


Unité de Recherche: Mécanique des Fluides Appliquée et Modélisation,

ENIS, B.P. W 3038 Sfax, Tunisia,





Abstract. A mathematical model has been developed to calculate transient flows in viscoelastic pipes with vapour cavitation. This model takes into account both the viscoelastic behaviour of the pipe wall and the vapour cavitation phenomenon. When the liquid pressure falls below the vapour pressure, a bubbly cavitating flow of homogeneous liquid-vapour mixture occurs in some part of the pipeline. The mixture density is expressed by means of a non linear expression of the liquid volume fraction. The pipe wall behaviour is simulated based on the mechanical principle by introducing additional viscoelastic term into the mass balance fluid equation. The application of mass and momentum conservation laws yields to a system of hyperbolic partial differential equations. The later is resolved by the finite differences scheme of Lax-Wendroff. The proposed model is tested for transient flows with and without vapour cavitation. The obtained numerical results are discussed and compared with experimental data.


Key words: transient flow, vapour cavitation, viscoelastic pipe, finite differences, fluid-structure interaction.


M. Derras, D. Tréheux


LTDS, UMR CNRS 5513, Ecole Centrale de Lyon,

36 av. Guy de Collongue, 69134 Écully Cedex, France,



B. Serier


LECM, Département de Génie Mécanique, Université Djillali Liabes,

BP 89 Cité Larbi Ben M’hidi, Sidi Bel Abbés 22000, Algérie,



Finite element analysis of thermal residual stresses and fracture of metal/ceramic bonds


Abstract. In this study, a finite element analysis was used to investigate the residual stress in a nickel-alumina bimaterial. The rate-dependent inelastic behaviour of metal at high temperature has been taken into consideration. The high value of these residual stresses occurs on the ceramic side near to the interface, which may result in failure by cracking away from the bond during the cooling stage of the joining process. In order to understand the fracture behaviour of near interface crack during the cycle of cooling, stress intensity factor and energy release rate under thermal loading condition were evaluated.


Key words: bimaterial, alumina-nickel, bonding, creep, residual stress, crack.


M. Elmeguenni, B. Bachir Bouiadjra, M. Benguediab, A. Mankour, A. Benhamena


Department of Mechanical Engineering, University of Sidi Bel Abbes,

BP 89, Cité Ben M’hidi, Sidi Bel Abbes, 22000, Algeria,



Finite element analysis of elastic–plastic interaction effect of the microdefects near the crack tip in confined plasticity


Abstract. In this study the finite element method is used to analyse the effect of microdefect presence near a main crack on the shape and the size variation of the plastic zone ahead the main crack for small scale plasticity in Aluminium alloy 2024 T3. The effects of the horizontal and the vertical distance between the crack tip-microdefect on the plastic zone are analysed. The obtained results show that the plastic zone shape and size ahead the crack tip are very influenced by the microdefect presence. Furthermore, the shape and size of the plastic zone ahead the crack tip are very influenced by the presence of the inclusion. The reduction rate of the plastic zone size can exceed 75% in the close vicinity of the crack tip.

The presence of the microcavity affects in very significant way the shape and the size of the crack plastic zone. Moreover, the relative distance between the crack tip and the microcavity has a very important effect on the size of the confined plastic zone.

The microcrack presence can provoke the division of the plastic zone ahead of the main crack in two parts. It is also shown that the effect of the microcrack disappears when the relative distance between the two cracks exceeds 10%.


Key words: main crack, inclusion, micro-cavity, micro-crack, plastic zone, Finite Element Method (FEM).


Junhua Zhao


Institute of Nano Science, Nanjing University of Aeronautics and Astronautics, 210016 Nanjing, China,

Department of Structural Engineering, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway,

e-mails: junhua.zhao@ntnu,no;


Role of elasticity and an analogy solution for three-dimensional elastic–plastic crack-tip fields


Abstract. A three-parameter analogy solution for mode-I Three-Dimensional (3D) crack tip fields (stress, strain and energy fields) at whole plastic zone in power hardening materials is presented under small scale yielding condition by introducing the elastic-plastic Poisson's ratio ve and out-of-plane stress constraint factor Tz. The influence of elastic deformation and energy on the near tip constraint for each layer is investigated along the thickness. It is interesting to find that the effect of elastic deformation in this sensitive region of the forward sector ahead of a crack tip is considerable and should be mainly taken into account. The elastic strain energy is always higher than the plastic strain energy and is the dominant term in this sensitive sector. The T-stress has great effect on the elastic and plastic strain energy. It can be found that all the values of ve decrease with the increase of Tz for a given T-stress and increase with increasing absolute value of T/σ0 at a same Tz for different n on the ligament. Finally, the 3D elastic-plastic finite element analysis is carried out to validate the analogy solution.


Key words: elastic-plastic crack-tip fields, out-of-plane stress constraint factor Tz, elastic-plastic Poisson's ratio ve, T-stress, three-dimensional crack.