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Deformations of light activated shape memory polymers
Cehula, Jakub ; Průša, Vít (advisor) ; Tůma, Karel (referee)
Light activated shape memory polymers (LASMPs) are smart materials with the ability of remembering a deformed state (temporary shape) due to exposure to ultraviolet (UV) light and returning to the permanent (original) shape by the exposure to UV light with a different wavelength. In this work, we solve specific boundary values problems, namely inflation of a hollow cylinder and inflation of a hollow ball made of LASMPs. Both problems are solved for large deformations. Next, we modify MERLIN 2, software for modeling large deformations of nonrigid origami-like structures. The original software package MERLIN 2 works with a reduced representation of origami-like structures and can be used to model nonlinear dynamics of such systems. We modify the software in such way that it is applicable to LASMPs origami-like structures in which the folding hinges react to UV light. To demonstrate the robustness of modified MERLIN 2 code we will simulate shape memory behavior of complicated origami-like structures such as Kresling pattern.
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Thermomechanical interaction between outer ice shells and deep oceans on icy moons of Jupiter and Saturn
Malík, Jiří ; Souček, Ondřej (advisor) ; Tůma, Karel (referee)
The thesis contains a survey of numerical tools for studying thermomechanical interactions of a two-phase system contained in a domain with an upper bound- ary that forms a free surface. The enthalpy diffused-interface formulation is used for an approximation of the phase change interface and the computing algorithm is benchmarked against an analytical solution of the Stefan problem. Arbitrary Lagrangian-Eulerian kinematical description of the continuum is applied to over- come the difficulty in the form of the free surface. The validity of the approach is examined on a thermal convection benchmark problem. 1
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Computation of viscous flows due to an oscillating cylinder of rectangular cross section.
Outrata, Ondřej ; Hron, Jaroslav (advisor) ; Tůma, Karel (referee)
Incompressible flows due to an oscillating cylinder of rectangular cross section in viscous fluid are governed by Navier-Stokes equations. In this thesis, these equations will be reformulated in a weak sense and their solution approximated by Finite Element Method. Fictitious Boundary Method is used as a tool to handle time dependent boundary. Behavior of a fluid was computed using these methods and is illustrated for various parameters, especially a behavior of the vortices originated in liquid He II is compared to an experiment.
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On the response of nonlinear dynamical systems to step input
Jiříček, David ; Průša, Vít (advisor) ; Tůma, Karel (referee)
We analyse response of a system, whose dynamic is governed by non- linear differential equations. In particular, we are interested in response to step input. Equation we are working with is constitutive relation of Maxwell type viscoelastic fluid. We motivate the constitutive relation, using one-dimensional Maxwell spring-dashpot model as a analogy to viscoelastic behaviour. The non- linear operator in the constitutive relation is an objective time derivative. We show why the constitutive relation contain such a operator. The essential char- acterization of viscoelastic fluid is their response in creep and stress relaxation tests. In these tests one is interested in the response to step input. This from the mathematical point of view means, that we need to solve a nonlinear differential equation in a generalized setting that allows one to work with jump discontinu- ities. We briefly introduce appropriate tool for solving the generalized equation. The mathematical tool is Colombeau algebra, which is a generalization of the- ory of distributions to nonlinear setting. We compare 4 different objective time derivatives of stress tensor in two different settings - simple shear and biaxial extension. We give explicit formula for the height of jump in stress as a response to jump in motion. 1
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Inflow and outflow boundary conditions on artificial boundaries
Kubáč, Vojtěch ; Lanzendörfer, Martin (advisor) ; Tůma, Karel (referee)
In the beginning of this thesis we introduce the basic properties of the fluid mechanics, mainly for stationary incompressible flow. In the next section we show the weak formulation of derived (Navier-Stokes) equations and some of the boun- dary conditions. Finally, the biggest part of this thesis is occupied by numerical experiments with simple planar flows. We seek for suitable inflow and outflow boundary conditions on an artificial boundary for the problem of outflow from a long channel or inflow to that channel. 1
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Modelling of viscoelastic materials with temperature dependence
Miloš, Vojtěch ; Hron, Jaroslav (advisor) ; Tůma, Karel (referee)
Materials such as asphalt, polymers or the Earth's crust tend to behave in a way that can be described neither with a model of viscous fluid, nor a model from solid mechanics. There are indeed models capable of capturing these so called viscoelastic phenomena far better, but they are based on the presumption of constant temperature. In many cases, e.g. in the glass industry or in geophysics, the properties of a viscoelastic material strongly depend on temperature. That is why it is precisely these changes that need to be described. There are viscoelastic models used in practice that take into account the material parameters' dependence on temperature, however, they do not consider the viscoelastic nature of the material when describing the temperature evolution. The objective of this thesis is to derive thermodynamically consistent viscoelastic models with temperature dependent parameters and the appropriate evolution equation for temperature, implementation of the models and computing simple test simulations. Powered by TCPDF (www.tcpdf.org)
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Identification of rate type fluids suitable for modeling geomaterials
Tůma, Karel
In the present thesis we study and compare different viscoelastic rate-type fluid models capable of describing response of geomaterials such as asphalt. Using new thermodynamic approach proposed by Rajagopal and Srinivasa (2000) we derive several classes of non-linear viscoelastic models that generalize standard Oldroyd-B and Burgers models. We show that the new models achieve better results in fitting experimental data with asphalt than the previously considered models (Oldroyd-B, Burgers, Rajagopal and Srinivasa (2000)). In particular they are able to capture the behavior of asphalt observed recently in experiments (torque overshoot and two relaxation mechanisms), which is not possible to describe by the other models. Using both the standard and the newly derived models we compute full simulations of viscoelastic flow with the finite element method in fixed domains and incorporating the Arbitrary Lagrangian-Eulerian description also in deforming domains. For example, we study rolling of asphalt or creation of ruts in the road with the real material parameters obtained by fitting the experiments. Powered by TCPDF (www.tcpdf.org)
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Identification of rate type fluids suitable for modeling geomaterials
Tůma, Karel ; Málek, Josef (advisor) ; Čadek, Ondřej (referee) ; Vohralík, Martin (referee)
In the present thesis we study and compare different viscoelastic rate-type fluid models capable of describing response of geomaterials such as asphalt. Using new thermodynamic approach proposed by Rajagopal and Srinivasa (2000) we derive several classes of non-linear viscoelastic models that generalize standard Oldroyd-B and Burgers models. We show that the new models achieve better results in fitting experimental data with asphalt than the previously considered models (Oldroyd-B, Burgers, Rajagopal and Srinivasa (2000)). In particular they are able to capture the behavior of asphalt observed recently in experiments (torque overshoot and two relaxation mechanisms), which is not possible to describe by the other models. Using both the standard and the newly derived models we compute full simulations of viscoelastic flow with the finite element method in fixed domains and incorporating the Arbitrary Lagrangian-Eulerian description also in deforming domains. For example, we study rolling of asphalt or creation of ruts in the road with the real material parameters obtained by fitting the experiments. Powered by TCPDF (www.tcpdf.org)
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Deformations of viscoelastic materials - modeling and computational analysis of selected models
Tůma, Karel ; Málek, Josef (advisor) ; Matyska, Ctirad (referee)
In the present work we derive two nonlinear models for incompressible rate type fluids that describe the behaviour of the viscoelaastic fluids. Making the linearization of the elastic response, we obtain two models similar to the popular models for viscoelastic fluid - Oldroyd-B and Burgers model. Furthermore, we modify the nonlinear model by assuming that one of the coefficient depends on the first invariant of the deformation gradient. We present an experiment that documents the stress relaxation of asphalt in the cylindrical geometry. We study the flow at two different eometries - the paralel plate flow and the axially symmetric cylinder flow. If it is possible, the problems are solved analytically, otherwise they are solved numerically. We investigate what model is capable of fitting the experimental data.
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Fourier method for solving partial differential equations
Tůma, Karel ; Knobloch, Petr (referee) ; Pokorný, Milan (advisor)
Na./cv prace: Fouricrova metoda pro feseni parc.ialnich dirornncialnich rovnic Autor: Karri Tuma Katedra (ust.av): Matematicky ust.av UK Vedouci bakalafske praoo: Mgr. Milan Pokorny, Ph.D. e-mail vodouciho: pokorny@karlin.mff.cuni.cz Abstra.kt: V pfedlo/ene praci odvodime rovnici vedeni tepla a.rovnici slruny. Ty pak nasledno. fesime v jodno prost.orove dimenxi ponioci Fonricrovy me- tody apocivajfci v separaci promennych a nale/eni feseni vc l.varn ncko- nccnc' fady. Zaljyvainc so t.fonii ru/nymi okrajovynii podininkanii. Dah^ vy- sotrujomo vlastnosii foscni tcchlo dvou problcmu. Provadinio analyzu kon- vorgtuicc fx'soni vu tvaru fad v -/avislosti na pocat.ocnich podminkach uloh. Uka/c-me. /o pornoci Fouriorovy inolody l/.c fosil lako stucionarni ulohy, konkrctno so zabyvanio Laplaccoviju rovnici s okrajovynii podminkami na ruznych oblasloch (kruh. vyscc. vyscc mc/ikru/f, mraikru/i). Klicova slova: Parcialni diforoncialni rovnico, Fouricrova tnot.oda, rovnico vodoni lopla, rovnico sLruny. Title: Fourier method for solving partial differential equations Author: Karel Tuma, Department: Matematicky ustav UK Supervisor: Mgr. Milan Pokorny. Ph.D. Supervisor's e-mail address: pokorny@karlin.raff.cuni.cz Abstract: In the present work we derive the heat equation and the wave equation. They arc- solved in one space...
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