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Low cycle fatigue of pseudoelastic NiTi alloy
Kaňová, Monika ; Hutař, Pavel (referee) ; Pantělejev, Libor (advisor)
This work is focused on study of mechanical properties of NiTi alloy which shows pseudoelastic and shape memory behaviour. Functional and structural fatigue of the material is examined. The main aim of this work was to perform and to evaluate a series of fatigue tests. The material was supplied in the form of wire which was gripped in the machine using special grips. In the first part of the experiment, tensile tests are evaluated and the reproducibility of measurements is demonstrated. Then, a series of cyclic tests was performed. Results were analysed together with previous measurements. One part of discussion concerned changes of the hysteresis loops during cycling and their dependence on strain rate. The fatigue life curves were plotted. It was found that these curves have non-standard shapes. The reasons for this are explained in the work.
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Matematické modelování magnetosriktních látek
Vermach, Lukáš ; Kružík, Martin (advisor) ; Zeman, Jan (referee)
4 Title: Mathematical modeling of magnetostrictive materials Author: Lukáš Vermach Department: Mathematical Institute of Charles University Advisor: Priv.-Doz. Dr. habil. RNDr. Martin Kružík Ph.D., Institute of Information Theory and Automation, Academy of Sciences of the Czech Republic Advisor's e-mail address: kruzik@utia.cas.cz Abstract In the present work we introduce an isotermic mathematical model of ferromagnetic shape memory alloys (FSMAs). FSMAs are a special class of magnetostrictive materials, i.e. materials which deform their shape on account of external magnetic field or which change magnetization as a consequence of strain. This property originates from phase transformations that occur within the material when being exposed to external loading. First, the stationary model of FSMA is formulated. The thermodynamical potential is composed (Helmholz free energy) and its non-quasiconvexity is discussed. The quasicon- vexification is performed via the relaxation theory, i.e. quasiconvex envelope construction. For such a model the existence theory is built. Then, taking advantage of the stationary case the evolutionary model is developed. The attention is drawn to hysteresis, which arises from energy dissipation. The time discretization leads to a sequence of hysteresis-modified stationary problems (the...
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Variational Methods in Thermomechanics of Solids
Pelech, Petr ; Kružík, Martin (advisor) ; Dondl, Patrick (referee) ; Zeman, Jan (referee)
The thesis is devoted to study of continuum mechanics and thermodynamics and the related mathematical analysis. It consists of four self-contained chapters dealing with different aspects. The first chapter focuses on peridynamics, a non-local theory of continuum mechanics, and its relation to conventional local theory of Cauchy-Green elasticity. Similar compar- isons has been used for proving consistency and for determining some of the material coefficients in peridynamics, provided the material parameters in the local theory are known. In this chapter the formula for the non-local force-flux is computed in terms of the peridynamic interaction, relating the fundamental concepts of these two theories and establishing hence a new connection, not present in the previous works. The second and third chapters are both devoted to Rate-Independent Systems (RIS) and their applications to continuum mechanics. RIS represents a suitable approximation when the internal, viscous, and thermal effects can be neglected. RIS has been proven to be useful in modeling hysteresis, phase transitions in solids, elastoplasticity, damage, or fracture in both small and large strain regimes. In the second chapter the existence of solutions to an evolutionary rate-independ- ent model of Shape Memory Alloys (SMAs) is proven. The model...
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Relaxace v mechanice kontinua tuhé fáze
Pathó, Gabriel ; Kružík, Martin (advisor) ; Zeman, Jan (referee)
This work deals with the modelling of shape-memory alloys, in particular with the steady-state model of martensitic thin films. After the introductory motivation the crystallographic structure of the materials is described followed by the introduction of the link between the lattice and continuum model. The next parts of the work focus on the possible solutions of the given 3D variational problem (quasiconvexification, Young measures) and on derivation of thin film theories with the aid of different tools (regularization,-convergence). The last part takes over an approximation of an obtained model and sketches numerical experiments on a Ni-Mn-Ga alloy.
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Mathematical modelling of thin films of martensitic materials
Pathó, Gabriel ; Kružík, Martin (advisor) ; Kalamajska, Agnieszka (referee) ; Šilhavý, Miroslav (referee)
The aim of the thesis is the mathematical and computer modelling of thin films of martensitic materials. We derive a thermodynamic thin-film model on the meso-scale that is capable of capturing the evolutionary process of the shape-memory effect through a two-step procedure. First, we apply dimension reduction techniques in a microscopic bulk model, then enlarge gauge by neglecting microscopic interfacial effects. Computer modelling of thin films is conducted for the static case that accounts for a modified Hadamard jump condition which allows for austenite--martensite interfaces that do not exist in the bulk. Further, we characterize $L^p$-Young measures generated by invertible matrices, that have possibly positive determinant as well. The gradient case is covered for mappings the gradients and inverted gradients of which belong to $L^\infty$, a non-trivial problem is the manipulation with boundary conditions on generating sequences, as standard cut-off methods are inapplicable due to the determinant constraint. Lastly, we present new results concerning weak lower semicontinuity of integral functionals along (asymptotically) $\mathcal{A}$-free sequences that are possibly negative and non-coercive. Powered by TCPDF (www.tcpdf.org)
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Variational Methods in Thermomechanics of Solids
Pelech, Petr ; Kružík, Martin (advisor) ; Dondl, Patrick (referee) ; Zeman, Jan (referee)
The thesis is devoted to study of continuum mechanics and thermodynamics and the related mathematical analysis. It consists of four self-contained chapters dealing with different aspects. The first chapter focuses on peridynamics, a non-local theory of continuum mechanics, and its relation to conventional local theory of Cauchy-Green elasticity. Similar compar- isons has been used for proving consistency and for determining some of the material coefficients in peridynamics, provided the material parameters in the local theory are known. In this chapter the formula for the non-local force-flux is computed in terms of the peridynamic interaction, relating the fundamental concepts of these two theories and establishing hence a new connection, not present in the previous works. The second and third chapters are both devoted to Rate-Independent Systems (RIS) and their applications to continuum mechanics. RIS represents a suitable approximation when the internal, viscous, and thermal effects can be neglected. RIS has been proven to be useful in modeling hysteresis, phase transitions in solids, elastoplasticity, damage, or fracture in both small and large strain regimes. In the second chapter the existence of solutions to an evolutionary rate-independ- ent model of Shape Memory Alloys (SMAs) is proven. The model...
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Application of the spectral method to the simulation of the phase-field model for martensitic transformation
Sejková, Klára ; Tůma, Karel (advisor) ; Kružík, Martin (referee)
For some alloys martensitic transformation is responsible for the so-called shape memory effect and pseudoelasticity. These properties are used in a wide range of industry applications. Each of these materials is transformed to the shape it was manufactured in when heated to its critical temperature (austenite phase) no matter how seriously it was deformed at lower temperatures (martensite phase). Looking at the microstructure, one can observe significant change of crystalographic lattice depending on temperature and deformation. This the- sis focuses on modelling the evolution of microstructure during deformation for materials in the martensite phase. In this case, the creation of multiple variants of martensite is observed, divided by interfaces where a part of energy is stored. This behaviour can be described by the phase-field model. The numerical im- plementation of this model using the standard finite element method requires large computational costs. The aim of this thesis is to implement this model in MATLAB using a spectral method based on the fast Fourier transform, which is suitable for solving problems on a periodic domain. It is interesting to com- pare the computation using spectral method on a conventional PC with the computation written in FEniCS computed on a cluster. However, the...
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Mathematical modelling of thin films of martensitic materials
Pathó, Gabriel ; Kružík, Martin (advisor) ; Kalamajska, Agnieszka (referee) ; Šilhavý, Miroslav (referee)
The aim of the thesis is the mathematical and computer modelling of thin films of martensitic materials. We derive a thermodynamic thin-film model on the meso-scale that is capable of capturing the evolutionary process of the shape-memory effect through a two-step procedure. First, we apply dimension reduction techniques in a microscopic bulk model, then enlarge gauge by neglecting microscopic interfacial effects. Computer modelling of thin films is conducted for the static case that accounts for a modified Hadamard jump condition which allows for austenite--martensite interfaces that do not exist in the bulk. Further, we characterize $L^p$-Young measures generated by invertible matrices, that have possibly positive determinant as well. The gradient case is covered for mappings the gradients and inverted gradients of which belong to $L^\infty$, a non-trivial problem is the manipulation with boundary conditions on generating sequences, as standard cut-off methods are inapplicable due to the determinant constraint. Lastly, we present new results concerning weak lower semicontinuity of integral functionals along (asymptotically) $\mathcal{A}$-free sequences that are possibly negative and non-coercive. Powered by TCPDF (www.tcpdf.org)
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Matematické modelování magnetosriktních látek
Vermach, Lukáš ; Kružík, Martin (advisor) ; Zeman, Jan (referee)
4 Title: Mathematical modeling of magnetostrictive materials Author: Lukáš Vermach Department: Mathematical Institute of Charles University Advisor: Priv.-Doz. Dr. habil. RNDr. Martin Kružík Ph.D., Institute of Information Theory and Automation, Academy of Sciences of the Czech Republic Advisor's e-mail address: kruzik@utia.cas.cz Abstract In the present work we introduce an isotermic mathematical model of ferromagnetic shape memory alloys (FSMAs). FSMAs are a special class of magnetostrictive materials, i.e. materials which deform their shape on account of external magnetic field or which change magnetization as a consequence of strain. This property originates from phase transformations that occur within the material when being exposed to external loading. First, the stationary model of FSMA is formulated. The thermodynamical potential is composed (Helmholz free energy) and its non-quasiconvexity is discussed. The quasicon- vexification is performed via the relaxation theory, i.e. quasiconvex envelope construction. For such a model the existence theory is built. Then, taking advantage of the stationary case the evolutionary model is developed. The attention is drawn to hysteresis, which arises from energy dissipation. The time discretization leads to a sequence of hysteresis-modified stationary problems (the...
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Relaxace v mechanice kontinua tuhé fáze
Pathó, Gabriel ; Kružík, Martin (advisor) ; Zeman, Jan (referee)
This work deals with the modelling of shape-memory alloys, in particular with the steady-state model of martensitic thin films. After the introductory motivation the crystallographic structure of the materials is described followed by the introduction of the link between the lattice and continuum model. The next parts of the work focus on the possible solutions of the given 3D variational problem (quasiconvexification, Young measures) and on derivation of thin film theories with the aid of different tools (regularization,-convergence). The last part takes over an approximation of an obtained model and sketches numerical experiments on a Ni-Mn-Ga alloy.
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