Journal of Theoretical and Applied Mechanics

Volume 36, Number 2, 2006




A. Nedev


Institute of Mechanics, Bulgarian Academy of Sciences,

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





Abstract. This paper is devoted to the numerical investigation of the influence of the stamp specific Blank-Holder Pressure (BHP) on the Drawing Force (DF) upon four different metal structures Steel 08, Copper, Aluminum and Brass 63 during deep drawing process. The analysis is done for three blank thicknesses depending on different values of BHP. The numerical results for the DF at several values of the strain hardening material exponent are also given. The deep drawing process producing a cylindrical cup with inside diameter 50 mm from blank of diameter 105 mm and thicknesses 0.5, 1.5 and 3 mm is considered. In the case of thickness 1.5 mm, which is taken as a basic one, the obtained results for materials Steel 08, Aluminum and Brass 63 are compared with the experimental ones.

The deep drawing process is simulated by using FEM-ANSYS code. The results are presented by “Drawing Force-P – Punch Travel-S” diagrams. On the basis of the differences in the “P-S” diagrams a conclusion is drawn about the reasonable range of BHP in every considered case.


Key words: deep drawing process, finite element method, blank-holding pressure.


V. A. Kovtun, T. V. Semenova, Yu. M. Pleskachevsky


V. A. Belyi Metal-Polymer Research Institute of NASB,

32a, Kirov Street, 246050 Gomel, Belarus,



M. Mihovski


Institute of Mechanics, Bulgarian Academy of Sciences,

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





Abstract. Strain-strength properties of structurally inhomogeneous metal-polymer powder materials formed by electrocontact sintering were studied by using computer simulation. Displacements of the nodal contact points and distribution fields of equivalent stresses were calculated in various cross-sections of the copper-PolyTetraFluoroEthylene (PTFE) composite under the action of distributed compressive loads. The mesoscopic structural level effect on the defect formation processes and regularities of plastic deformation in a group of metal-polymer powder particles have been studied.


Key words: strain-strength properties, Stress-Strain State (SSS), composite powder metal-polymer materials.


N. Nikolov


Institute of Mechanics, Bulgarian Academy of Sciences,

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





Abstract. This paper considers the loss of stability of the plastic forming process during deep drawing process of circular blank having diameter 105 mm and thickness 1.5 mm. The Steel 08kp, Steel 10, Aluminum, Copper, and Brass 63 represent different blank material structures. The coefficient of deep drawing is 0.476 close to the limiting one.

Comparisons between numerically obtained effective and critical strains are given at the end of second geometrical stage and under maximal drawing force for the blank area covering the punch roundness and supporting two-dimensional tension. Localization of plastic strains could be expected in these areas. On this basis, the forming limits are predicted.


Key words: deep drawing, numerical experiments, limiting strains, localization of plastic strain.


Nikolay K. Vitanov


Institute of Mechanics, Bulgarian Academy of Sciences,

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



Khristo Tarnev


Technical University of Sofia,

8, St. Kl. Ohridski Blvd, 1000 Sofia, Bulgaria,


Holger Kantz


Max Planck Institute for the Physics of Complex Systems,

38, Str., 01187 Dresden, Germany



Abstract. We discuss the problem for detecting long-range correlations in sequences of values obtained by generators of pseudorandom numbers. The  exponent for a sufficiently long sequence of uncorrelated random numbers has the fixed value . The presence of long-range correlations leads to deviation from this value. We calculate  by the method of MultiFractal Detrended Fluctuation Analysis (MFDFA). We discuss frequently used tests for randomness, finite sample properties of the MFDFA, and the conditions for the correct application of the method. The fluctuation function  used in the MFDFA reacts to trends caused by low periodicity presented in the pseudo-random number generator. In order to select appropriate generators from the numerous possibilities we propose a test for the ensemble properties of the generated pseudo-random sequences with respect to their robustness against presence of long-range correlations, and a selection rule which orders the generators that pass the test. In addition for each selected generator we choose pseudo-random sequences with appropriate length on the basis of the closeness of the  exponent of the generated sequence to its value 1/2 characteristic for the case of absence of correlations.


Key words: multifractal detrended fluctuation analysis, -exponent, random number generators, long-range correlations.


Petia Dineva


Institute of Mechanics, Bulgarian Academy of Sciences,

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



Dietmar Gross


Institute of Mechanics, Darmstadt University of Technology,

64289 Darmstadt, Germany,



Tsviatko Rangelov


Institute of Mathematics and Informatics, Bulgarian Academy of Sciences,

Acad. G. bonchev Str., Bl. 8, 1113 Sofia, Bulgaria,



Wave scattering in cracked piezoelectric materials - a BIEM approach


Abstract. A non-hypersingular traction Boundary Integral Equation Method (BIEM) is developed for the solution of Boundary Value Problems (BVP) describing wave scattering by cracks in an infinite plane region. The numerical solution is based on a frequency dependent fundamental solution obtained by Radon transform. The proposed method is an efficient and flexible approach without limitations concerning the type of the material, the crack geometry, the type of the incident wave and the wave parameters.

            The accuracy and convergence of the method is validated by comparing the calculated Stress Intensity Factors (SIF) with existing results obtained with other methods. In this context the dependence of the SIFs on the frequency, the incidence angle and the wave type is discussed. For the considered cases of a cracked piezoelectric, elastic-anisotropic and elastic-isotropic continuum the method ensures a good accuracy and high efficiency.


Key words: piezoelectric material, wave scattering by cracks, non-hypersingular traction BIEM, stress intensity factors.