
Modeling of phase transformations in shape memory materials
Frost, Miroslav ; Maršík, František (advisor) ; Rohan, Eduard (referee) ; Seiner, Hanuš (referee)
Title: Modeling of phase transformations in shape memory materials Author: Miroslav Frost Department: Mathematical Institute of Charles University Supervisor: Prof. Ing. František Maršík, DrSc., Mathematical Institute of Charles University Abstract: This thesis presents a new thermomechanical threedimensional con stitutive model of NiTibased shape memory alloys. The model was formulated within the framework of generalised standard models and it features a novel form of the dissipation function, which combines contributions stemming from the phase transformation between austenite and martensite and from the reorienta tion of martensite. The change in the material response associated with the phase transformation between austenite and Rphase as well as material anisotropy and tensioncompression asymmetry are also covered. The timeevolutionary problem of a quasistatic mechanical loading of a NiTi body with prescribed temperature evolution was formulated and analyzed within the framework of energetic so lutions. The corresponding timeincremental minimization problem provided a conceptual algorithm utilized in the numerical treatment. The constitutive mod el was implemented into the finite element package Abaqus. Several numerical simulations were performed and compared with experiments. Keywords:...


Identification of changes in mechanical characteristics of human axial system as a result of loading and relaxation regime
Van der Kamp Kloučková, Kateřina ; Jelen, Karel (advisor) ; Maršík, František (referee) ; Rosina, Jozef (referee)
Problem: A lot of attention is given to the safety of the driving and the possibility to register fatigue of the drivers. Driving cars is monotony and static. Vibration loading, which causes changes in the axial system. This causes discomfort and fatigue to drivers after some time of exposure to the loading. Hypothesis: It is possible to prove the changes of mechanical characteristics (indicators) of the axial system using the TVS (transfer vibration through spine) method. By using TVS method before and after different types of loading or before and after relaxation it is possible to detect changes of the viscoelastic properties. This can be done by checking changes in the way of waves transfer through the axial system of the observed participants. Objective: Verify the possibility of use of TVS method to register changes of the viscoelastic characteristics of the axial system. Method: The TVS was chosen as a detection method. The method is based on the use of fivemsec semibandwidth γ pulse stimuli and consequent application of continuously changing harmonic stimuli which periodically differ between 5Hz and 160Hz to the vertebrae C7 and L5. This wave is carried through the axial system and its acceleration on the spinous processes between C7 and S1 is scanned with the help of accelerometric...


Biochemical and mechanical processes in synovial fluid  modeling, analysis and computational simulations
Pustějovská, Petra ; Málek, Josef (advisor) ; Süli, Endré (referee) ; Jäger, Willi (referee) ; Maršík, František (referee)
vi Title: Biochemical and mechanical processes in synovial fluid  modeling, mathematical analysis and computational simulations Author: Petra Pustějovská (petra.pustejovska@karlin.mff.cuni.cz) Department: Matematický ústav UK, Univerzita Karlova v Praze Institut für Angewandte Mathematik, Universität Heidelberg Supervisors: prof. RNDr. Josef Málek CSc., DSc. (malek@karlin.mff.cuni.cz) Matematický ústav UK, Univerzita Karlova v Praze, Prof. Dr. Dr. h.c. mult. Willi Jäger (jaeger@iwr.uniheidelberg.de) Institut für Angewandte Mathematik, Universität Heidelberg Abstract: Synovial fluid is a polymeric liquid which generally behaves as a viscoelastic fluid due to the presence of polysaccharide molecules called hyaluronan. In this thesis, we study the biological and biochemical properties of synovial fluid, its complex rheology and interaction with synovial membrane during filtration process. From the mathematical point of view, we model the synovial fluid as a viscous incompressible fluid for which we develop a novel generalized powerlaw fluid model wherein the powerlaw exponent depends on the concentration of the hyaluronan. Such a model is adequate to describe the flows of synovial fluid as long as it is not subjected to instantaneous stimuli. Moreover, we try to find a suitable linear viscoelastic model...


Generace vířivosti rychlostního pole gradientem entropie
Novák, Martin ; Maršík, František (advisor) ; Grmela, Miroslav (referee)
The master thesis studies the impact of the entropy gradient on the vorticity of ve locity field, particularly by applying the linear momentum balances. These balances are formulated for Thermoviscous fluids (later fluids) and Thermoviscouselastic ma terial (later solids) with the other balances (energy, mass, etc.). In order to derive these balances, the Classical continuum mechanics approach is used along with the respec tive Variational principles. The thesis emphasizes the Variational principles applica tion representing the modification of the Bateman principle [Bat29] and its comparison with the Classical approach, linked to the L. Crocco work [Cro37], particularly in the case of vorticity generation. It is pointed that by the definition of the dissipative en tropy sdis a harmony of both approaches can be achieved and that, in the case of an appropriate limit, the direct effect of the entropy gradient on the vorticity of velocity field can be demonstrated. By applying this conclusion the relationship between the change of circulation among a closed curve and released heat on the given geometry is indicated.


Numerical simulation of cerebrospinal fluid transport
Žáček, Petr ; Maršík, František (advisor) ; Otáhal, Jakub (referee)
Modelling of cerebrospinal fluid flow is important for understanding its influence on central nervous system, especially spinal cord. One of the reasons for its study is a disease called syringomyelia that probably develops as a result of severance of neural pathways by bubbles emerging during the propagation of pressure (expan sion) disturbances through spinal cord and its surroundings. It is characterized by fluidfilled cavities in spinal cord. In this thesis, a model of fluidfilled coaxial elastic tubes is proposed that can help us simulate pressure disturbances propa gation through spinal cord including its interactions and possible increase as the result of interferences or reflection. We derive quasionedimensional governing equations in the form of nonlinear hyperbolic system of conservational laws and with its numerical solution by twostep LaxWendroff method with added artifi cial viscosity we can quantitatively estimate almost twofold increase of pressure difference. 1


Analysis of spontaneous collapse in elastic tubes
Netušil, Marek ; Maršík, František (advisor) ; Horný, Lukáš (referee)
Interaction of fluid with elastic tube is complicated issue studied by many scientific departments around the world. Object of this thesis is to analyze simplified onedimensional model. At the beginning, used balance equations and basics of hyperelasticity are presented. Then we review three most common materials used for the description of blood vessels and other soft tissues. For these materials we introduce a method which we use to derive a relation between tube deformation and transmural pressure (i.e. difference between inner and outer pressure). In mathematical section we give brief review of theory of nonlinear hyperbolic equations and some relatively new results in the field of existence and uniqueness of a solution of onedimensional hyperbolic system. The "building stone" of these results is a solution of the socalled Riemann problem. We use a method for finding exact solutions to the Riemann problem to analyze studied model of fluidtube interaction and study dependence of the qualitative behavior of the solution on the material properties of the tube wall.


Termodynamická analýza procesů v palivových článcích s pevnými oxidy
Vágner, Petr ; Maršík, František (advisor) ; Némec, Tomáš (referee)
The fuel cells are the technology of the future. Although their discovery dates back to the 19th century the nature of how they work hasnt been adequately explained so far. This thesis focuses on description of solid oxides fuel cells (SOFC) for which ion conductive electrolyte and high operating temperature are distinctive. The mathematical model of SOFC developed in this thesis is formulated in terms of the mixture theory. The model development was constrained and simplified by isothermality, timestationery and 1D approximation. The model equations characterize gas and ion transport and electric current flow in the fuel cell. Eventually comparison of the thesis model equations with the SOEC (solid oxides electrolysis cell) model developed at the Institute of Chemical Technology in Prague showed that both approaches lead to a similar conclusion. This thesis can be used as a basis for an experimental verification of the mixture theory. 1


Termodynamická analýza procesů v polymerní elektrolytické membráně palivového článku
Pavelka, Michal ; Maršík, František (advisor) ; Málek, Josef (referee)
Thermodynamic analysis of processes in electrolytic fuel cell membrane Michal Pavelka April 12, 2012 Abstract Hydrogen fuel cells1 may become a key technology of 21st century, and it is important to be able to describe their behavior, therefore. In this work we focus on hydrogen fuel cells with a polymerelectrolyte membrane. For the membrane we adopt an existing model2 . We for mulate the model in the framework of the mixture theory which we develop similarly as has been done in the classical textbook of Mazur and de Groot3 . However, refining the concept of potential energy of a material point, we introduce new terms called internal potential ener gies which enable us to describe macroscopic consequences of internal forces between water and polymer in the membrane and to describe the influence of gradient of surface tension of water in the membrane. We solve the model in 1D approximation. Consequently, we calculate the influence processes in the membrane have on efficiency of the fuel cell. 1 see for example Larminie, J. and A. Dicks. Fuel Cell Systems Explained. 2nd edition. John Wiley & Sons Ltd., 2003. ISBN 047084857X. 2 Weber, A. Z. and J. Newman. Transport in PolymerElectrolyte Membranes I, II, III. J. Electrochem. Soc., 150 (7), A1008A1015, 2003; 151 (2), A1311A1325, 2004.; 151 (2), A1326A1339,...


Mathematical Simulation of Osteodegenerative Process in Cervical Spine segment
Barsa, Pavel ; Maršík, František (advisor) ; Otáhal, Stanislav (referee) ; Hemza, Jan (referee)
Aim: The aim of following study is to simulate different types of loading on cervical vertebra and to identify if mechanical stress concentration in utmost positions corresponds with osteophytes localization find in clinical practice. The objective of our investigation is to develop a theoretical model that may elucidate clinical observation regarding the predilection site of bone remodeling. We will focus our attention on the physiological changes inside the cervical vertebral body. Methods: Real 3Dgeometry of the fourth cervical vertebra had been made by commercially available system ATOS II. It is highresolution measuring system using principles of optical triangulation. Such flexible optical measuring machine projects fringe patterns on the surface of selected object and the pattern is observed with two cameras. 3D coordinates for each camera pixel were calculated with high precision and a polygon mesh of the object's surface was further generated. ANSYS program has been used in the next step to calculate strains and stresses in each finite element of the virtual vertebra. Applied forces used in the experiment were of physiological magnitude and direction and mechanical stress distribution inside the vertebra has been calculated. Mechanical loading in neutral position has been characterized by...


Matematická analýza a výpočtový algoritmus RayleighovyPlessetovy rovnice v okolí prudkého kolapsu bublinky.
Petrík, Peter ; Maršík, František (advisor) ; Rudolf, Pavel (referee)
The RayleighPlesset equation is commonly used to describe the dynamics of spherical bubbles in water. However, as highspeed observations show, the bubble looses its spherical shape during the violent collapse and often ssions into a number of smaller bubbles before it rebounds again or dissolves completely. The objective of the work is to bridge the gap between the \spherical\ RayleighPlesset approach and the \nonspherical\ behavior of the collapsing bubble in conditions when the RayleighPlesset equation is no longer valid. The objective is achieved in 3 steps. First, the new criterion for the assessment of the reliability of the RayleighPlesset equation is proposed. Second, the analysis of the shape stability of the spherical surface of the bubble during the collapse lead to the development of a physical model, which incorporates the loss of shape stability, surface energy dissipation and the ssion process. Moreover it estimates the number of bubble fragments as well as conditions when the ssion occurs. Finally, theoretical results are incorporated into the complex numerical code, with the focus on error estimation, specially propagation of rounding error. The sample numerical results for typical hydrodynamic cavitation situations were calculated. The results of this work have to be further con rmed...
