Studies and Teachings at the National University ”Lvivska Politecnika”, Ukraine
(Department of High Mathematics, Institute of Applied Mathematics and Fundamental Sciences)

Winter Term 2010/2009
Mathematical Analysis, Statistics and Probability Theory, Differential Equations, PDEs

Summer Term 2009
Mathematical Analysis, Differential equations, PDE’s, Operations Research

Winter Term 2007/2008
Mathematical Analysis, Statistics and Probability Theory, Theory of Complex Variable Functions

Summer Term 2008
Mathematical Analysis, Differential equations, PDE’s, Operations Research

Winter Term 2006/2007
Mathematical Analysis, Statistics and Probability Theory, Theory of Complex Variable Functions

Summer Term 2006
Mathematical Analysis, Statistics and Probability Theory, Differential Equations

Winter Term 2005/2006
Mathematical Analysis, Statistics and Probability Theory, Theory of Complex Variable Functions

Summer Term 2005
Mathematical Analysis, Differential Equations

Winter Term 2004/2005
Mathematical Analysis, Statistics and Probability Theory of Complex Variable Functions

Summer Term 2004
Mathematical Analysis, Differential Equations

Microstructural modeling and optimization of metal matrix composites

Project: Numerical microstructure optimization of melt-infiltrated metal-ceramic composites

Summary: A numerical two-scale method for the microstructure optimization of microsamples and components made of melt-infiltrated metal-ceramic composite materials with maximum macroscopic stiffness under quasi-static mechanical loading is to be developed. The macroscopic modeling is carried out using the FE method. Each integration point in the element, which consists of several domains (of areas of the same orientation and geometry of the inclusions), represents the microstructure at the microlevel. The effective stiffness of the microstructure at the microlevel under the effect of the macroscopic distortions is determined using micromechanical two-step homogenization methods certainly. The inelastic material behavior of the individual material phases is taken into account incrementally by corresponding material laws when determining the tangent stiffness of the individual domain in the first homogenization step. The effective stiffness at the integration point is determined in the second homogenization step. The limitations on design variables of the optimization should be defined from the statistical studies of the microstructure and from knowledge of the manufacturing process. The optimization problem should be solved iteratively, first for a simple problem and then for a cap-shaped prosthesis. To determine the material laws for individual phases and to verify the microstructure modeling and optimization, numerous existing experimental data from studies of micro and macro samples as well as from FE models of the real microstructure are introduced.

Typical microstructure of melt-infiltrated metal-ceramic composites (photographs by S. Roy IWK1)

In Books

Piat R., Dietrich S., Gebert J.-M., Stasiuk G., Weidenmann K., Wanner A., Böhlke T., Drach B., Tsukrov I., Bussiba A.:
Micromechanical Modeling of CFCs Using Different Pore Approximations.
In Ed: Krenkel W., Lamon J.: High Temperature Ceramic Materials and Composites, AVISO Verlagsgesellschaft mbH, Berlin, Germany,
590-597 (2010).

In Journals  (Bold Font: Refereed Journal Article)

2009

Hachkevych A., Musij R., Stasyuk H. :
Coupled Thermomechanical Problem for an Electroconductive Plate under the Uniform Electromagnetic Action.
Materials Sci.  45(4), 532-541 (2009)
DOI:10.1007/s11003-010-9211-6

2005

Musii R., Stasyuk H.:
Equations of Dynamic Problem of Thermoelasticity in Stresses in a Three-Orthogonal Coordinate System.
Materials Sci., 41(1), 74–81 (2005)
DOI 10.1007/s11003-005-0134-6

2004

Stasyuk H.:
System of Equations of the Dynamic Problem of Thermoelasticity in Stresses for an Elliptic Cylinder.
Materials Sci., 40(5), 635–642 (2004)
DOI 10.1007/s11003-005-0093-y

2003

Hachkevych A., Musij R., Stasyuk H.:
Thermoelastic State of a Conducting Plate under the Action of an Electromagnetic Field in the Form of Damped Sinusoid.
Materials Sci., 39(6), 780–787 (2003)
DOI 10.1023/B:MASC.0000023507.81534.27

Hachkevych A., Musij R., Stasyuk H.:
Thermal Stressed State of a Hollow Metallic Cylinder under the Action of Electromagnetic Field in the Mode of Damped Sinusoid.
Materials Sci., 39(5), 682-690 (2003)
DOI 10.1023/B:MASC.0000031642.38997.a6

2002

Musij R., Stasyuk H.:
Thermoelastic State of a Hollow Conducting Cylinder under the Action of a Quasistationary Radio-Wave Pulses.
Materials Sci., 38(3), 351–360 (2002)
DOI 10.1023/A:1021717531970

Publications in Russian and Ukrainian

Hachkevych A., Musij R., Stasyuk H.:
Plate Coupled Dynamical Thermomechanical Problem for the Electroconductive Plate under Nonstationary Nonuniform Electromagnetic Action
National University Lviv Polytechnic Bulletin - Physics and Mathematics Series. - 2009. - V. 45, No 4. - P. 87-93. (in Ukrainian)

Hachkevych A., Musij R., Stasiuk H., Shymchak J.:
Mathematical Modeling of Heat and Mechanical properties of Materials of Electroconductive Solids under the Pulse Amplitude Modulated Electromagnetic Fields
Studia i Monografie (Politechnika Opolska, Opole, Poland), 2008, No. 237, P. 45-55 (in Russian).

Hachkevych A., Musij R., Stasyuk H., Shymchak J.:
Determination of the Thermostressed State of the Electroconductive Solids under Pulse Electromagnetic Fields
Theoretical and Applied Mechanics, 2006, No. 41, P. 9-17 (in Russian).

Hachkevych A., Musij R., Stasyuk H.:
Thermomechanical State of the Hollow Electroconductive Sphere under Electromagnetic Action
Theoretical and Applied mechanics, 2005, No. 40, P. 9–17 (in Russian).

Musij R., Melnyk N., Stasyuk H.:
Investigation of the Thermomechanical Behavior of the Electroconductive Plate under Electromagnetic Pulse
Applied Problems in Mechanics and Mathematics, 2004, No. 2, P. 153–160 (in Ukrainian).

Hachkevych A., Musij R., Stasyuk H.:
Temperature Fields and Stresses of the Long Hollow Cylinder under Electromagnetic Action of the Pulse Amplitude Modulated Signal
Theoretical and Applied Mechanics, 2004, No. 39, P. 168–181 (in Russian).

Stasyuk H.:
Temperature Fields and Stresses in the Electroconductive Plate Under Quasi-Steady Radiopulses
Visnyk National University "Lvivska Politekhnika" "Computer Projecting Systems. Theory and Practice", 2003, No. 444, P. 39–46 (in Ukrainian).

Musij R., Shvec L., Dudnyk O., Hissovska N., Stasyuk H.:
Calculation of the Temperature Field in the Cylindrical Panel under Induction Heating with Quasi-Steady Electromagnetic Field
Math. Problems of Mechanics of Heterogeneous Structures, 2000, Vol. 1, P. 367–370 (in Ukrainian).